text: Compressed Sensing Phase Retrieval Matthew L. Moravecr , Justin K. Rombergg , and Richard G. Baraniukr r Department of Electrical and Computer Engineering, Rice University g School of Electrical and Computer Engineering, Georgia Tech ABSTRACT The theory of Compressed sensing (CS) allows for signal reconstruction from a number of mea- surements dictated by the signal's structure, rather than its bandwidth. The information in signals which have only a few nonzero values can be captured in only a few measurements, such as random Fourier coefficients. However, there exist scenarios where we can only observe the magnitude of these coefficients. It is natural to ask if such measurements could still capture the signal's information, and if so, how many are needed. We have found an upper bound of O(k 2 log(N ) random Fourier modulus measurements needed to uniquely specify k-sparse sig- nals. In addition to using a signal's structure to observe it with fewer measurements, we also propose a method to use this structure to aid in recovery from the Fourier transform modulus. Existing methods to solve this phase retrieval (PR) problem with complex signals require a priori signal assumptions on the signal's support. We have shown that a constraint based upon signal structure, the 1 norm, is also effective for PR. Not only does it help recover structured signals from their Fourier transform modulus, but it can do so with fewer measurements than PR traditionally requires. Keywords: Compressed sensing, phase retrieval, projection algorithms 1. INTRODUCTION In many physical scenarios for signal processing, the measurement process can be time consuming or expensive. High frequency radar is beginning to test the limits of analog to digital conversion. Sensors for terahertz electromagnetic frequencies cost many times times more than those for the visible spectrum. MRI scans can take over an hour. The irony of these situations is that in each case the wide-band signal in question is undeniably structured, yet aside from general bandwidth considerations, no assumptions about this structure are made to ease the sensing process. The field of compressed sensing (CS) [1–3] takes the logical step of making measurements that take a signal's structure into account, and taking only as many measurements as the structure requires. CS has already seen practical success such as imaging with a single pixel [4] and reduction in MRI scan time [5]. Since random samples of a signal's Fourier transform are one way to make CS measurements, it would seem the benefits of CS can apply to when we have access to the an object's diffraction pattern, since it closely approximates the object's Fourier Email: {moravec, email@example.com, firstname.lastname@example.com Transform. Taking the object's structure into account, we could randomly sub-sample the diffraction pattern, rather than needlessly observe the entire thing. Signal reconstruction from less measurements could affect such fields as crystallography, astronomy, and wavefront sensing. Making the jump to applying CS in these cases introduces a new challenge–the measurements of the complex-valued diffraction pattern are in practice made with sensors that can only observe its intensity. In this paper we present both theoretical and practical results to demonstrate that we can indeed take random Fourier measurements and reap their benefits though we cannot observe their phase. We show that the number of magnitude-only measurements sufficient for perfect recovery is of the order of k 2 log N for sparse signals, where N is the length of the signal and k is the number of nonzero elements. In the process of finding a way to recover signals from sub-sampled Fourier transform mod- ulus, we developed a new method of phase retrieval that is based on a signal's structure. Phase retrieval (PR) is the process of recovering the phase, given just the magnitude, of a signal's Fourier Transform, thereby recovering the signal itself. It amounts to finding a reconstruction candidate signal that has the same bandwidth and Fourier modulus as the original. Since the Fourier modulus constraint set is non-convex, there is not a straightforward method of perform- ing PR. Alternating projection strategies work if the signal constraints are stringent enough. Positivity is an effective constraint for real signals, and exact support constraints perform well for complex-valued data. Such a support constraint is somewhat unrealistic, and unfortunately, PR of complex-valued data is notoriously difficult apart from a strict support constraint. We introduce a new constraint of structure on the signal and use this to recover the signals. To enforce this structure we require that the 1 norm of the reconstruction candidate match that of the true signal, in addition to matching the Fourier modulus. With this constraint we have been able to recover signals that normally would only be recoverable if their support were known. In addition to aiding in reconstruction enforcing signal structure matches with random Fourier measurements to result in needing fewer measurements to reconstruct. To illustrate the effectiveness of a structure constraint for PR we consider a terahertz imaging example (Figure 1). Terahertz (THz) imaging offers the benefits of x-ray imaging without ionizing exposure. In [6] the diffraction pattern of an object illuminated by a collimated THz beam is scanned, and its magnitude recorded. Since it is not a perfect plane wave hitting the object, its diffreaction pattern is the Fourier transform of a complex-valued signal. As such, loose support constraints (25% of the diffraction pattern size, to ensure there is no aliasing( are not effective in recovering the signal. To enforce structure of the reconstructed object, we estimate and use the 1 norm as a constraint. As a side benefit, we are able to perform reconstruction with fewer measurements than traditionally needed for PR. This can be useful because existing methods for terahertz imaging perform a raster scan of an object, recording the intensity of a focused beam at each location where it passes through the object. This can be a time-consuming task. An array of THz detectors could be made to speed up acquisition time, but would be very expensive. By using CSPR, we can save time and expense by randomly sampling the diffraction pattern. This paper is organized as follows. Section 2 provides background on CS and PR. In Section 3 we introduce the compressibility constraint for PR and show how it both helps recovery Object THz transmitter THz receiver 6cm 12cm Fourier Transform Modulus compressibility constraint loose support constraint randomly sub-sample compressibility constraint Figure 1. A THz trasmitter illuminates an object, in this case a T-shaped aperture. The far-field diffraction pattern is focuesed in to a reasonable distance with a lens, and is recureded with a raster- scanning receiver. The 64 × 64 pxel diffraction pattern is approximately the modulus of the signal's Fourier transform. We perform PR with a compressibility constraint and retrieve the object. A loose support constraint is not effective, as the algorithm cannot find an intersection between the support and Fourier modulus constraint sets. We also use the compressibility constraint with only 2.5% of the measurements and still nearly recover the object. The method of recovery is explained in Section 3.3 of this paper. and allows for less measurements, and describe the algorithm we use to implement CSPR. We conclude the paper with numerical results, both simulated and from physical application. 2. BACKGROUND 2.1. Compressed Sensing Traditionally, digital signal processing has meant first observing a signal, then processing it in some way that enhances it and/or prepares it for storage or transmission. The sampling part of this process is governed by the Nyquist rate for band-limited signals. Shannon sampling is the best that can be done to recover a sampled signal if all that is known about a signal is that it is band-limited. However in many cases the signal class can be more specified. We expect a natural band- limited signal to be structured and hence "sparse" in some basis. This means that a large signal can be represented well with only a few of its elements or a few of the coefficients of its transform. Smooth signals are sparse in the Fourier basis and piecewise smooth signals are sparse in a wavelet basis. Knowing that a signal is sparse gives much more information than just knowing it is band-limited. Transform coding uses this knowledge to efficiently store or represent this signal, however it was not until the last two years that this type of structure was exploited in sampling the signal. Fully sampling a compressible signal is wasteful. Just as we only save the "important parts" when storing or transmitting signals we ought to strive to sense only the significant content of a sparse signal. CS aims to efficiently observe such signals. 2.1.1. Efficiency of Compressed Sensing Consider a signal x ∈ RN . Let x be compressible, meaning that if the magnitude of its elements were ordered from greatest to smallest they would decay like n−1/p . Many natural signals satisfy this condition when represented as a linear combination of vectors from a basis Ψ that sparsifies the signal. The best k term approximation of x is defined as xk , and is equal to x at the k largest entries and is 0 otherwise. The k term approximation error σk (x) is defined as x − xk 2 and is bounded by Ck 1/2−1/p . Let y be linear measurements of x where y = Φx. The "miracle" of CS is that x can be reconstructed with error O(σk (x)) with only n measurements, where n is O(k log(N ) and is much smaller than N [1–3]. This is to say that the CS recovery of a given signal has optimal error and is accomplished not by sampling the whole signal but rather only as much as the structure of the signal requires. 2.1.2. Measuring and Reconstruction Accurate signal recovery from limited measurements requires more than the sparsity of a signal. The measurement matrix Φ must satisfy certain properties so that no matter what the sparsifying matrix Ψ may be, Φ will capture all the significant information. In [2] it is shown that if Φ is a random Fourier ensemble, it can capture information in a structured signal with high probability, and furthermore this recovery is attained via 1 minimization: x = arg min x 1 s.t. y = Φx. (1) x CS properties holding for a random Fourier ensemble and 1 minimization being the key to recover are the inspiration for our PR method which uses random Fourier modulus values and an 1 constraint. 2.2. Phase Retrieval In many areas of science and engineering, such as crystallography, astronomy, and wavefront sensing, measurements of a complex-valued signal must be made with sensors that can only observe its intensity. These magnitude-only measurements are acceptable in instances like pho- tography, since our eyes also only observe intensity of a light field. However in certain appli- cations, the phase of a signal is very important information to have. An object's diffraction pattern, like from a crystal illuminated by an x-ray, or a landscape illuminated by a laser [7], closely approximates the object's Fourier transform. It would be useful in these circumstances to recover the object from its transform, but the phase of the diffraction pattern would have to be known in addition to the magnitude. The task of PR is to recover the Fourier phase information in order to perform this seemingly hopeless inverse problem. Methods for PR are introduced by Fienup in [8, 9]. His concern, as ours, is PR from the intensity of an unknown object's Fourier transform.∗ In these papers he shows a way to accurately recover a discrete signal from its transform modulus, and finds surprising his algorithms' ability to recover the phase from a variety of random starting points. 2.2.1. Unique Recovery The theory behind this uniqueness of recovered results is explained by Hayes in [10]. Observing the magnitude (squared) of a signal's Fourier transform is equivalent to observing the autocor- relation, as these are Fourier transform pairs. Having a signal's autocorrelation is equivalent to knowing the z-transform of its autocorrelation. This polynomial is the product of the signal's z-transform, and the transform of it's flipped version. Therefore if a signal's z-transform is irreducible, then it is the only signal which will yield it's autocorrelation (excepting a shifted or flipped version, since the absolute position and orientation of the signal are irretrievably lost with the phase). Since virtually all polynomials in two or more dimensions are irreducible, one can be sure that if a recovered signal has finite support, and has the same autocorrelation as the original signal, it is indeed equal to the original signal. Hayes also explains the conditions needed to guarantee that a recovered signal has the same autocorrelation as the original signal. To do this he considers how one would know if the z- transform of a signal's autocorrelation were equivalent to that of the original signal's. For a signal of support N , the z-transform of the autocorrelation is a polynomial of degree 2N − 1. In order for two polynomial functions of degree 2N − 1 to be equal, they must have the same evaluations at 2N locations. These 2N locations may be chosen as distinct locations anywhere on the complex plane, but it is convenient to consider equally spaced positions about the complex unit circle. The z-transform of the autocorrelation evaluated at these points is the discrete Fourier transform (DFT) of the autocorrelation at these points, which is simply the magnitude-squared ∗ The phase problem, in general, refers to the task of recovering the phase of an object's Fourier transform, given its magnitude, and the magnitude of the object itself. of the original signal's Fourier transform. Through these relations he shows a signal in two or more dimensions is uniquely specified by its DFT modulus. 2.2.2. Recovery Methods While this work addresses the uniqueness of a recovered solution, it provides no guaranteed method of finding a candidate solution with the necessary support size and DFT modulus. This problem is an optimization in which a reconstruction candidate's distance from these constraint sets must be minimized. Since the Fourier modulus constraint set is non-convex, it is a non- convex optimization. Though problems of this nature are difficult because only exhaustive algorithms can guarantee convergence, there are a variety heuristics that do well in solving this particular optimization [11]. To help find a solution these heuristics should preferably have significant a priori signal information in addition to the Fourier modulus and maximum support size constraints. This information could be positivity, explicit support, or a histogram of signal values. 3. COMPRESSED SENSING PHASE RETRIEVAL 3.1. 1 Constraint for Phase Retrieval Though the Fourier modulus and bandwidth constraints are sufficient to guarantee a unique solution, finding the intersection of these two sets is a difficult problem, since the Fourier modulus constraint set is non-convex. Were both sets convex, alternating projections would find the intersection. Despite the non-convexity, projection algorithms can be used to solve the problem. One in particular, Fienup's hybrid input-output algorithm† , can find the intersection even in the presence of local minima. However, if a signal is complex-valued, the loose sufficiency constraints of maximal bandwidth (which may be derived from the autocorrelation) which can guarantee the existence of a unique solution are not sufficient in practice to find the solution. A typical algorithm may search indefinitely for a global minimum, getting trapped by local minima in a condition known as stagnation [12]. Exact support constraints are needed to aid in finding a solution. The reason they work is they reduce the size of the constraint set, ostensibly making it an easier process for iterative projection procedures to find the solution. Other strict constraints can also reduce the set size. A histogram constraint defines a dis- tribution of pixel values that the image must satisfy. A sparsity constraint (referred to as a number of non-zero constraint in [13]) forces the image to have a certain number of non-zero elements. A drawback of these constraints is that they may be unknown quantities which are difficult to estimate. We propose an 1 constraint. The 1 norm of a signal is the sum of the absolute values of its components or its coefficients in a transform basis. It is similar to both sparsity and histogram constraints but is more forgiving: an exact distribution is not needed, nor an exactly sparse signal. Rather the value of the signal's 1 norm is needed, and this could be estimated and then † Fienupand others refer to these as algorithms, but strictly speaking they are not, since the running length to find a solution is indefinite. optimized over a single degree of freedom. We have found that this constraint is just as effective as a strict support constraint. Section 4.1 provides empirical support for our assertion. This constraint can be useful with all measurements, but is especially helpful in that it can be used with a structured signal to recover it with less measurements than bandwidth would require, bringing us to the second contribution of this paper. 3.2. Theoretical Recovery It has been shown by others, and discussed in the introduction, that the number of measurements needed to guarantee uniqueness in PR is a function of the bandwidth: the Fourier modulus must be sampled twice as much in each dimension as the bandwidth of the original. However we know more about the signal than this. We know that natural signals will probably have a relatively small number of coefficients in a sparsifying basis, compared to the total size of the signal. Intuition says that if only a few pieces of information of the signal suffice to represent it well, then only a few measurements should be needed to capture this information. We have access to linear measurements of the signals autocorrelation, as the intensity of a signal's Fourier transform is equivalent to the Fourier transform of its autocorrelation. Each Fourier magnitude measurement is a linear projection of the signal's autocorrelation onto a complex sinusoid. The good news for us is that a random collection of these projections is sufficient to specify a sparse autocorrelation, and which is sufficient to uniquely specify the signal. Lemma 1. Suppose x[n] is a two-dimensional sequence of complex-numbers of support N1 × N2 , and x has a z-transform which, except for trivial factors, is irreducible and nonsymmetric. Then x[n] is uniquely specified by its Fourier transform modulus, and an M (≥ 2N1 × 2N2 ) point DFT is sufficient for this unique specification. Proof sketch: Hayes proves in theorem 9 of [10] that sequences of real numbers are uniquely specified by their DFT modulus, as a consequence of their z transforms being irreducible. These arguments also follow for complex sequences as long as their z-transforms are also irreducible. This means that if x ∈ CN1 ×N2 has an irreducible z-transform, and there exists an x ∈ CN1 ×N2 such that |F x| = |Fx| on a 2N1 × 2N2 lattice, then x ∼ x (the two signals are equal within a flip, shift, and/or a constant phase factor). Since the autocorrelation is a Fourier transform pair with a signal's Fourier Transform intensity (its modulus-squared), then the Lemma implies that a signal's autocorrelation is sufficient to uniquely specify it. Hayes notes that the irreducible requirement is not strict in two or more dimensions for complex signals, since they correspond to a set of measure zero [14]. Since an arbitrary complex signal is specified by its autocorrelation, we must now consider how many measurements of a signal's autocorrelation are needed to specify it. We consider the case in which the signal has only a few non-zero complex entries, whose values and locations are unknown. Theorem 1. Suppose x[n1 , n2 ] ∈ CN1 ×N2 has an irreducible z-transform, and is k sparse. Let N = N1 N2 . Then with probability of at least 1 − O(N −ρ/α ) for some fixed ρ > 0, O(k 2 log(N )) random Fourier modulus measurements of x are sufficient to uniquely specify it. Proof: Since x is k-sparse in Ψ, its autocorrelation is at most k 2 sparse in some Ψ. For a k 2 - sparse signal in some basis Ψ, it was shown in [3] that due to the Uniform Uncertainty Principle of a random Fourier ensemble, only n = O(k 2 log(N )) are needed to specify a signal, with the probability stated above in the theorem. This means that, with overwhelming probability, if autocorrelation Rx matches Rx at n random Fourier locations, and both Rx and Rx are k 2 sparse, then Rx = Rx . From the lemma, this implies that x ∼ x. This gives a new paradigm for defining the number of Fourier modulus measurements needed to capture the information in a signal, and is significant because it scales with the signal's structure, rather than its bandwidth. Though the theorem applies to signals sparse in space, we have seen in practice the same results for a signal sparse in a different basis, such as wavelets. We have also observed that the order of measurements needed scales more like k log N than k 2 log N . 3.3. Practical Recovery As with the case of regular PR, our goal is to find a signal x that lies in the intersection of two constraint sets. For us the constraint sets are slightly different. One set is all signals which have the same Fourier modulus values as x at specified random locations. The other set is all the signals which have the same 1 norm as x, or whose coefficients in some transform basis have the same 1 norm as the coefficients for x. Like with regular PR, we would like to find an x that minimizes the distance between the two sets (since the two sets intersect this distance will be zero). In our case, as with regular PR, the Fourier constraint set is non-convex. For us the 1 constraint set is also not convex, where a support constraint is convex. The presence of many local minima in the distance between the two constraint sets precludes a direct optimization procedure. Rather we use the same kind of iterative projection scheme that is used for regular PR. There are many variants of Fienup's original error reduction and Hybrid Input-Output algorithms, and one that we found effective and implemented is Relaxed Averaged Alternating Reflections (RAAR) [15]. Starting with x(0) , an initial guess of random values, each successive step is calculated as a combination of projections and reflections: 1 x(n+1) = [ β(R1 Rm + I) + (1 − β)Pm ]x(n) . (2) 2 Pm x refers to taking the current iterate x and projecting it onto Fourier modulus space, by taking its Fourier transform, fixing the magnitudes of a defined subset to match the known values while keeping the phases the same, and then performing an inverse transform. Rm x is a reflection defined as Rm x = 2Pm x − x. The reflection R1 = 2P1 x − x where P1 x is the projection of x onto a known 1 norm. This is accomplished by uniformly adding or subtraction a constant value to the magnitudes of the entries of x until x 1 reaches the desired value. We stop the applications of RAAR once the difference between a modulus projection, and a subsequent 1 projection, P1 Pm x(n) − Pm x(n) 2 E= , (3) Pm x(n) 2 reaches a negligible value, implying that we have a candidate solution which lies in both con- straint sets. 4. PERFORMANCE There are two issues to consider as we evaluate the performance of these PR methods for different signal sizes (N ), number of nonzero values (k), and number of measurements (n). One is the rate of convergence, how often a particular kind of signal will converge in a defined amount of time. The other is the error of reconstructed signals. For the signal sizes we have considered, simulation suggests that CSPR performs just as well as PR in terms of convergence, and as well as CS in terms of accuracy. For converged signals, the simulation affirms that k 2 log N is indeed an upper bound on the number of measurements needed for perfect reconstruction. 4.1. Convergence To evaluate the effectiveness of the 1 constraint for regular PR, we compare it in different kinds of simulations, against exact and loose support constraints (see Table 4.1). In each test the second constraint is the modulus of the input signal's Fourier transform. For each combination of test and constraint we perform the RAAR algorithm on 500 randomly generated signals, recording the number of times a convergent solution is found within 1000 iterations. As expected, we find the exact support constraint almost always converges for signals which are sparse in space. We also find that loose support constraints, which ensure that the solution does not alias the Fourier transform modulus, are not effective. As discussed in the introduction, this has been known for some time. The 1 constraint performs fairly well for sparse signals, but appears to be effected more than the exact support constraint is for growing signal sizes. This may suggest that the 1 constraint is more sensitive to local minima when searching for a solution. The 1 is better than the strict support constraint when a signal is structured, but takes a full amount of bandwidth. This is illustrated in the test in which the 64 pixel image has every pixel as non-zero, but is composed of only 5 wavelets. The exact support constraint does not really the search space very much, since there are many non-zero pixels compared to the number of Fourier measurements. However the 1 constraint, does restrict the search space more and converges at a higher rate. The findings support the idea that a smaller search space results in more convergent solutions. The dimensionality of exact support constraint set is much smaller for sparse signals, which is why this constraint performs better when the ratio of non-zero pixels to image size is small. The 1 constraint has a similar property, except its behavior is related not to the number of non-zero pixels, but to the number of non-zero coefficients in an arbitrary basis. For sensing scenarios in which the signal has a large bandwidth but is very structured, the 1 offers more hope for finding a solution than an exact support constraint alone. Table 1. The convergence properties of PR with different constraint sets are compared under different tests. In two cases, "exact support" and "loose support" (anti-aliasing) are equivalent, because the number of non-zero pixels is at the anti-aliasing bandwidth limit of N/4. Percent Convergence Test strict support constraint 1 constraint loose support constraint N = 64, k = 5 99.8% 59.6% 5.4% N = 64, k = 5 (wavelets) .6% 38.4% – N = 64, k = 64 2.2% 2% – N = 256, k = 20 100% 16.8% .2% 4.2. Accuracy To determine how accurate the algorithm is for various measurement rates, we consider k-sparse signals and empirically determine how many Fourier modulus measurements are needed for different signal sizes and sparsity rates for consistent (95 %) exact recovery of 100 converged solutions. We hold N constant and vary k, and also hold k constant and vary N , in order to empirically understand the dependence of the number of measurements on these values. We compare these results with those found via regular CS if the phases were known, using the SPGL1 solver ‡ . For convergent solutions we find that the number of measurements needed does not appear to follow a k 2 log N trend but appears to be closer to the k log N , as Figure 2 shows. When the signal size is held constant, the number of measurements needed increases linearly. The slope is the same as for CS with the known phases, though more measurements are needed for CSPR. When k is held constant, the number of measurements follows a sub-linear trend, just as CS does, though as in the other case loosing the phase results in needed more measurements. These results support the theorem and give confidence that the number of Fourier mea- surements truly is a function of the structure of the signal, rather than its bandwidth. This knowledge, along with the effectiveness of the 1 constraint, lead us to believe that the princi- ples of CS apply even when only the modulus of measurements is observed, and that the same structure which allows for less measurements aids in PR reconstruction. 5. ACKNOWLEDGEMENTS We would like to thank Wai Lam Chan and Dan Mittleman for the terahertz data. ‡ TheSPGL1 solver can perform 1 minimization for complex signals and measurements, and is free for download at http://www.cs.ubc.ca/labs/scl/index.php/Main/Spgl1. 100 100 CSPR CSPR CS CS 80 80 60 60 n n 40 40 20 20 0 0 0 2 4 6 8 10 12 0 20 40 60 80 100 k N (a) (b) Figure 2. For a given value of N and k, enough trials of CSPR are performed on randomly generated signals until 100 convergent solutions have been found. The number of measurements n recorded is the smallest value needed so that at least 95 are perfectly reconstructed. In (a) we hold N constant at 64 and vary k. The number of measurements needed increases linearly. In (b) we hold k constant at 5 and vary the signal size. The increase in the number of measurements needed is sub-linear. In each case the number of measurements needed has a trend similar to that of CS with the phases known, though clearly more measurements are required. REFERENCES 1. D. Donoho, "Compressed sensing," IEEE Transactions on Information Theory 52(4), pp. 1289– 1306, 2006. e 2. E. Cand`s, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory 52(2), pp. 489–509, 2006. e 3. E. Cand`s and T. Tao, "Near optimal signal recovery from random projections and universal encoding strategies," IEEE Transactions on Information Theory 52(12), pp. 5406–5425, 2006. 4. D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, "A new compressive imaging camera architecture using optical-domain compression," Proc. of Computational Imaging IV at SPIE Electronic Imaging, San Jose, CA , January 2006. 5. M. Lustig, J. Santos, J. Lee, D. Donoho, and J. Pauly, "Compressed sensing for rapid mr imaging," Proc. of SPARS , 2005. 6. W. Chan, M. Moravec, R. Baraniuk, and D. Mittleman, "Terahertz imaging with compressed sensing and phase retrieval," to appear in CLEO-2007 , May 2007. 7. J. Fienup, "Lensless coherent imaging by phase retrieval with an illumination pattern constraint," Optics Express 14(2), pp. 498–508, 2006. 8. J. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Optics Letters 3(1), pp. 27–29, July 1978. 9. J. Fienup, "Phase retrieval algorithms: a comparison," Applied Optics 21(15), pp. 2758–2769, August 1982. 10. M. H. Hayes, "The reconstructionn of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP- 30(2), pp. 140–154, 1982. 11. S. Marchesini, "A unified evaluation of iterative projection algorithms for phase retrieval," Rev. Sci. Instrum 78, 2007. 12. J. R. Fienup and C. C. Wackerman, "Phase-retrieval stagnation problems and solutions," J. Opt. Soc. Am. A 3, pp. 1897–1907, 1986. 13. H. He, "Simple constraint for phase retrieval with high efficiency," J. Opt. Soc. Am. A 23, pp. 550– 556, 2006. 14. M. H. Hayes and J. H. McClellan, "Reducible polynomials in more than one variable," Proceedings of the IEEE 70(2), pp. 197–198, 1982. 15. D. R. Luke, "Relaxed averaged alternating reflections for diffraction imaging," Inverse Problems 21, pp. 37–50, 2005.


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The learning hardway6th November, 2003 by db_staff - This article is over multiple pages: 1 2 3 4 5 6 7 8 9
The brandy market has suffered decades of decline worldwide but it is finally looking buoyant again, says Nick Faith
COGNAC REMAINS the king of brandies, as it has been since the early 18th century. It is, and has always been, by far and away the most important brandy on the international scene.
Of course, any country which grows grapes also makes brandy from them and, usually, what are called "pomace brandies" or marcs and grappas to the non-specialist.
Nevertheless, most major brandyproducing countries, like South Africa, Australia, Mexico and the United States, sell very little if any brandy outside their borders.
Indeed, Cognac's dominance was confirmed recently when Gallo, producer of by far the best-selling American brandy, started to market an excellent cognac of its own. And in truth only two brandies, Armagnac from Gascony and Brandy de Jerez, are of any consequence on the world market, though a look at page 28 will confirm that they trail far behind Cognac.
And while fine grappas, the only well-established pomace brandy, are becoming increasingly fashionable, the quantities involved are minimal.
Over the past 30 years, however, Cognac's position has looked increasingly wobbly. For a start it has lost a whole generation of drinkers.
This was partly because of its old-fashioned image, but the problem was greatly exacerbated by a classic case of hubris which affected almost everyone involved in the production and sale of the precious stuff.
By 1976, as sales soared worldwide and stocks dropped, the amount of land planted to grapes in the Cognac region rose to reach 110,000 hectares (272,000 acres) making it by far the biggest region devoted purely to white grapes in France.


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Narrow your search
Eight months after seeing it at CES, the Android-based ZTE Grand X finally has a due date.
Typical price: $189.00
Although it's one of the cheapest smartphones around, you're better off saving your money for a slightly pricier handset.
Available today on T-Mobile and on May 19 for MetroPCS, the entry-level Concord II sports a 4-inch screen, a 5-megapixel camera, and Android 4.3.
Pricing not available
ZTE makes a smartwatch debut at CES 2014 with BlueWatch, but it feels a little too familiar.
Pricing not available
Skip the ZTE Prelude altogether and nab another inexpensive prepaid handset, like the Nokia Lumia 521 or LG Optimus F6.
Skip the ZTE Prelude altogether and nab another inexpensive prepaid handset, like the Nokia Lumia 521 or LG Optimus F6.
The contract-free ZTE Majesty is a 3G handset sporting a 5-megapixel camera, Android Jelly Bean, and a low $170 price tag.
With its fast processor and LTE, the ZTE Overture is a great deal from Aio Wireless and one of the carrier's best starter smartphones.
The Open II features a 2-megapixel camera and Firefox OS, and has its sights on emerging markets.
Pricing not available
The Grand S Pro is a good deal with a carrier agreement, but U.S. Cellular has other phones that are faster and more reliable.


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Today's Word of the Day means...
(also damned) Cursed; accursed; wretched: What do I do with this damned thing? adv: You seem damn stupid all of a suddeninterjection
(also damn it) An exclamation of disappointment, irritation, frustration, etc: Damn, it's gone!verb
To execrate; condemn; curse: Damn this dictionary! (1770s+)Related Terms


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Tobacco Control Index Page
New Report Reveals Most Quit-Friendly and Least Quit-Friendly States for Smokers
December 7, 2011
New Report: States Slash Funding for Tobacco Prevention Programs by 36 Percent
November 30, 2011 - A new report released today by a coalition of public health organizations—including the American Lung Association—finds that states have slashed funding for tobacco prevention programs to the lowest level since 1999, threatening the nation's progress against tobacco use.
Tobacco Limits in Major League Baseball Contract a Victory for Players and Kids' Health
November 22, 2011 - MLB and players' union take historic first steps to get tobacco out of the ballgame
American Lung Association Opposes Ruling to Block Implementation of Cigarette Graphic Warning Labels
November 7, 2011 - Ruling to block the implementation of new cigarette graphic warning labels is a direct threat to public health.
American Lung Association Awarded $800,000 to Help Create Healthier U.S. Communities
September 15, 2011 - On Tuesday, the American Lung Association was awarded a Federal grant of $800,000 to implement Expanding Smokefree Communities, a project that will promote tobacco-free living and healthy and safe physical environments by reducing tobacco use and promoting smokefree air policies in underserved communities and regions across the country.
American Lung Association Celebrates U.S. Food and Drug Administration's Final Rule Requiring Graphic Warning Labels on Cigarette Packs
June 21, 2011 - The American Lung Association heralds the announcement today by the U.S. Food and Drug Administration (FDA) on its final rule requiring graphic health warning labels on all cigarette packages and advertisements.
U.S. House Rejects Rep. Stearns' Amendment to Give $392 Million Gift to Big Tobacco
June 17, 2011
House Appropriations Amendment Would Weaken FDA's Authority over Tobacco, Unleash Big Tobacco on America's Kids
June 1, 2011
American Lung Association Reflects on Progress of Smokefree Air Laws at the State Level
April 21, 2011
FDA Advisory Committee Concludes Removal of Menthol Cigarettes Would Benefit Public Health
March 18, 2011


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Littlefield High School dismissed early on Monday after a bomb threat was found scribbled in a bathroom stall.
The high school was evacuated and the Lubbock County Bomb Squad was called in.
Littlefield ISD Superintendent Jerry Blakely said, "We will do everything possible to find out who wrote this threat."
They were given the all clear at 2 p.m. and classes will resume normally on Tuesday, Sept. 10.
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Book an event at Oddyssea Outside.
We would be delighted to host your birthday party, corporate event, or any other special event in our event space, Oddyssea Outside. Packages include access to our attractions, activities, and dedicated space for your event. Contact us to schedule your event.
This is the latest, up-to-date listing of shop and outside related events. Subscribe to our newsletter as well (bottom of this page) to get push notification of upcoming events and workshops.
The Oddyssea Outside Garden will be open to the public August 29th-Sept 1st 10am-6pm.
Activities for the weekend of August 29th-Sept 1st: The featured activity this week is DIY Coastal Fairy Cottages. In addition, these other activities will be available. Uncover Treasure with Metal Detectors, Sand Art, Abalone Sea Terrarium, Mason Jar Lanterns, Terrarium Buffet, Driftwood Boats, Earth's Treasure Necklace, and Message in a Bottle at Oddyssea Outside. In addition, we have always available experiences of exploring Half Moon Bay on electric bicycles, mining for treasure in the flume, and break your own geodes.
Terrarium Tuesdays – Build your terrarium project at Oddyssea Inside and get a 10% discount.
Past Events:
June 19th, 5-7pm, Oddyssea Outside Ribbon Cutting with the Half Moon Bay Chamber of Commerce and City of Half Moon Bay movers and shakers.
June 13th, Oddyssea Outside Soft Opening. Your first chance to see what we've been up to outside.
May 17th, 6-9pm, Rock the Block, the annual spring street fair on Main St in downtown Half Moon Bay.
December 6th, 6-9pm, Night of Lights, fantastic fun in downtown Half Moon Bay after dark.
October 19th & 20th, Half Moon Bay Art & Pumpkin Festival. Note: We will be open 9am-5pm Saturday & Sunday to match Festival Hours instead of our usual 10am-6pm.
September 19, 2013, Annual International Talk Like a Pirate Day. Avast Ye Maties. Talk like a pirate, get some booty!
May 18th 4pm-8:30pm – Rock the Block!
March 14th 10am-6pm – Raspberry Pi Party on Pi Day!
February 9th 2-5pm, SOMA Valentine's HeART Walk.
December 12th, 12/12/12 day – 12% off anything in the shop when you visit in person.
December 9th 2-5pm – SOMA Holiday Art Walk. Visit the great galleries and shops in the 600-800 blocks of Main Street in beautiful downtown Half Moon Bay, California.
December 7th, 6-9pm – 13th Annual Night of Lights on Main Street in downtown Half Moon Bay.
December 6th – Jungle Terrarium Workshop led by "The Dirty Girl Gardener" (Jennifer Segale.) Logistics and Sign-up Here.
October 13th & 14th, Half Moon Bay Art & Pumpkin Festival.
Serrarium Workshop, September 27, 6:30pm at the shop.
September 19, 2012, 10th Annual International Talk Like a Pirate Day. Avast Ye Maties. Talk like a pirate, get some booty!
September 15th, 11am, Grand Opening Ceremony at the shop. We'll cut the ribbon and celebrate with $1 off solar butterflies and dragonflies all day. Join us!
August 5th, SOMA Summer Art Stroll
Book an event at Oddyssea Outside.


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GoPro® HERO3+™ Black Edition Adventure Camera
- SuperView video mode captures world's most immersive wide-angle perspective
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Manufacturer model #: CHDHX-302.
Need Help? 7 days a week: 7am to 10pm CT or call 1.800.227.7776 anytime


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And Then There's This: How Stories Live and Die in Viral Cultureby Bill Wasik
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"An odd but happy marriage of sociological observation and Gonzo- style adventure."
Journalist and new media provocateur Bill Wasik journeys to the edge of our churning and rambunctious viral culture to illuminate how anyone with a computer can initiate a small ripple of a story that can turn into a tsunami. While exploring this fascinating landscape, Wasik (who organized the very first flash mob in 2003) conducts six experiments himself. This book is a must-read for anyone interested in journalism, business, technology, and how cultural information spreads. Wasik's tour is great, stimulating and fun.
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Rated 3.6 out of 5 by 462 reviewers.
Rated 2 out of 5 by Moby King suite Was not up to par. Staff was rude, unwanting to help. October 26, 2012
Rated 3 out of 5 by Blacklight Lack of response I always travel with a black light and inspect the room prior to use. However, the room was not ready at the time of arrival. When I arrived later in the evening I checked the room with my black light. There was urine on the floor, on the toilet, and splashed on the back of the bathroom door. There was blood on the bed skirt. There was also dust buildup on the carpet along the baseboard. There were water soap/spots on the shower/bath walls. When I notified the staff in the morning of the state of the room apologies were offered and promises made. When I returned that evening, the bed skirt had been replaced but the other issues remained. September 18, 2013
Rated 3 out of 5 by brutus1 Great location;Disappointing service I received a letter in my room from the General Manager informing me that I will receive a survey from Sheraton requesting that I rate my guest experience at the hotel a 10. If a hotel actually provides a level 10 experience, then it wouldn't be necessary to solicit a 10 rating. Based on my experience, I would suggest that they spend more time training their employees to provide the service at the level they are requesting the guest to rate. I would hope that an honest assessment of a guest's experience would be more helpful to the hotel to improve its service. May 25, 2014
Rated 4 out of 5 by Templin48 Great downtown location wonderful property nice amenities great location attentive staff June 24, 2014
Rated 4 out of 5 by KarensHoliday This hotel extrememly comfortable & clean. The room was very clean and we were upgraded to get a great view of the square. Loved that we were able to go to the Club Lounge for complimentary breakfast. Go early though because the food gets sparse the closer you get to 10am. Had a scary experience in one of the elevators. It couldn't decide if it was going up or down. I reported it to the Club Lounge staff and again the next morning to the front desk. The front desk said they would take care of it. Asked for more towels and someone brought them promptly with a smile! Asked the bellman for restaurant suggestions and he was so nice and helpful. We had a great experience, thank you! February 28, 2012
Rated 1 out of 5 by Business22 Tired Hotel, needs attention This hotel at one time probably was pretty nice. It is a far cry from that now. There was mold in the bathroom (that needed to be gutted), tub drained slow, door was damaged, just poor all around. The hotel was noisy due to maintenance, Restaurant overcooked my medium rare tuna to well done. I would not stay here again. I would not recommend this hotel. Parking was also bad. Was afraid that could not park SUV due to low ceiling. Got a nasty note for parking in garage after I had cleared parking in valet area with front desk due to fear of damaging vehicle. Twenty five bucks a day to park was steep as well. Lousy entrance from garage too. Just gross. December 2, 2012
Rated 2 out of 5 by ATrain76 Absolutely Hit and Miss I've been at this hotel 3 times in the last few months and my experience has been consistent....in that it has been consistently INconsistent. During my most recent stay we had a variety of issues in our room (complete lack of shower pressure, dirty floors, malfunctioning toilets, etc). The buggy system is a joke. Every time I've been there I've requested one to have my luggage brought to/from my car and I've never had one brought to me quicker than half an hour...and on more than one occasion, they simply couldn't find one and I had to haul luggage for 5 people quite a long way. That's is simply unacceptable. In addition, the front desk staff were completely UNaccomodating when I attempted to get details about where they were. They were also generally unhelpful in many other ways...i.e. telling me an extra rollaway bed was available and it would be brought up soon...when I didn't have it within an hour and called back to check they said they were mistaken and one wasnt available...not knowing whether something is available or not is generally incompetent, but not calling back and having the decency to say so is inexcusable. The fitness center is also barely adequate in that most of the equipment is barely functioning and ridiculously noisy...nevermind that the lobby WIFI cant even reach down there. My experience would have been wholly unpleasant if it werent fot the gal running the club lounge who was an absolute gem...helpful in every possible way...friendly and polite. All the staff should take a cue from her when it comes to truly treating your guests like clients and not like inconveniences July 4, 2012
Rated 1 out of 5 by BLRD Discounted rate should not mean discounted service. Of all the service staff I had interacted with during my stay, only 2% were polite and helpful. The attitudes and mannerisms of the front desk employees were far below expectations. I have never been treated so rudely. When I would ask a question, I would receive a rude response or a question with an extremely inappropriate attitude. The air conditioning in the room did not work. The television only had approximately 40-50% of the channels offered. The hot water lasted only a few minutes. Internet was offered as part of the rate offered for the room during the convention stay. I was not provided with this information during my check-in, when I called down to the service desk I was met with attitude and received the answer in a negative tone then hung up on. When I notified the front desk that the air conditioning was not working properly, the response I received was "They're working on it! If it's blowing its working"! I was personally too frustrated with my experience to even bring up the hot water; but instead included on my comment card. I was sent to the wrong meeting room when I asked where I was to go for my meeting (I was sent downstairs rather than the 21 floor). I had a package waiting for me at the front desk and when I came to pick it up I was first told that it wasn't there, and then rudely asked to describe it. I understand that this was a busy time- the conference I was attending had over 200 attendees, but being in customer service it is important to greet with a smile and treat your guest with respect. The least they could have done was apologize for their inappropriate behavior. I usually enjoy my stays at the Sheraton, but after all this I do not think I will be staying at one again. May 2, 2012
Rated 3 out of 5 by EagleRock Mostly unremarkable We were passing through on a long road trip and chose this hotel as we love the Sheraton brand for our young family, especially the suites. Unfortunately, this hotel was not adequately staffed when we arrived (11pm), had no luggage carts available, no valet available, and they then said it "looks like we upgraded you to a suite" when in fact our original reservation (what we paid for) was a suite. This hotel wasn't "bad" but was merely adequate when compared to the entirety of our SPG experience. We would try the Westin in town the next time we are passing through even though we prefer the Sheraton branch of SPG to Westin usually. July 20, 2013
Rated 3 out of 5 by JohnQBusinessTraveler Great Location I have stayed at this hotel several times and the location is perfect. This time I got a suite and found it comfortable and spacious. THey have tried to upgrade the older style with some nice new features. Overall the hotel needs some updating but the improvements do help. The rooms are clean (with the exception of the TV screens). The furniture is less than stellar (couch looked like a cat had a field day on it) but generally comfortable. The bed was exceptionally comfortable and the room was quiet. I was disappointed in the front desk staff at check in as they were unimpressed with my SPG status and did not recognize me at all. November 25, 2013
Rated 1 out of 5 by SJK72 Worst hotel stay ever I feel compelled to write this review because it was such a bad experience and others need to be forewarned. To preface what I am about to say, it is relevant to mention I am very vested in staying at Starwood hotels, am a platinum level member, own multiple timeshares through the Starwood Vacation Ownership program, and have never had a bad experience in any of their properties ... until now. I have stayed at this property a few other times and while the service has always been a bit hit or miss and the hotel is in desperate need of updating, the location is good and overall value has been sufficient. However, what happened this time means that I will never return. There was work being done in the hotel on some of the upper floors - which I understand is needed from time to time. However, this work didn't just happen during the day but into all hours of the night AND so close to rooms where guests were staying that the noise was keeping people up. The first night was irritating but not bad enough to keep me awake. The second night though was an entirely different story. The noise was literally so loud I could barely hear someone when I was on the phone. This continued on so long that finally at MIDNIGHT, I couldn't take it anymore. I called the front desk and the person acted like she had no idea what I was talking about. She said she'd send someone to check into it and ask them to stop. Noise continued. I called again at 12:30AM, she said she knew some work was being done and would ask them to stop. Again, noise continued. I called again and after 3-4 calls, I finally reached her around 1AM and was told she'd send someone again and tell them to stop. Noise continued. Finally, at around 2AM, I left the hotel and went elsewhere. No idea if and when it stopped but do know that the 2nd person in my party in another room heard noise on and off throughout the night. There are multiple problems with all of this. 1) Who schedules work like this during the middle of the night and then why so close to guest rooms that it keeps people up all night?! 2) The service around the issue was horrible. I called multiple times and nothing was resolved. I was never offered to switch rooms to another part of the hotel. Never offered any compensation on the room (I would have never charged a customer for such an experience). No one ever followed up to make sure it got resolved or that I was happy. Nothing. Nada. Zero. 3) Where is the management in all of this? If a customer had such an experience, I'd sure as heck make sure a manager was involved and that person would ensure the issue got resolved and the customer was happy. Instead, all I received was a 3,000 point bonus. That for horrible service, a night of absolutely no sleep, and having to leave and pay for another hotel room elsewhere! Completely unacceptable and really an insult. Also, this was in addition to all the other things about the hotel that weren't good ... but I won't go into that here. In the end, I think this experience says a lot about the hotel management and culture and is the reason I won't ever return. Period. January 24, 2014
Rated 2 out of 5 by traveler2809 average I asked for a King bed when I checked in and was told the only room was a handicap accessible room but that the only difference was the shower. I was very mislead. Not only was the shower barely accessible for someone handicap, the bathroom ceiling had a leak and water sprays all over the floor. The "towel racks" are the required assistance bars that are around the toilet. THe hand towels hung on the bar behind the toilet and were touching the back of the toilet and toilet handle/flush. It was very gross. The bath towels all hung on the other bar next to the toilet. If you would actually need to use the bar for assistance off or on the toilet, you'd have to move all the towels somewhere -- but there isn't anywhere else to put them except the floor. There is no shelf or bench or other rack for items to be placed on. The counter space is non existent...I had to put all my toiletries on the floor under the sink. The shower is not wide enough for anyone - handicap or not - to sit or stand in. The shower head is on the long wall (not the typical short wall/top of the shower), which made it even more difficult to shower and not have water spray all over the bathroom floor. The shower curtain was cloth, so when the water did spray on it, it just pushed the curtain back and water went everywhere. During my stay, the TV randomly went out - right as I was showered, in bed and ready to watch my favorite show. I called down to have someone come take a look and try to fix it. I got a call from the manager 3 mins later telling me sorry they can't fix it and that she'll give me HALF a nights stay for free. HALF? I got HALF the amount of SPG points added to my account since they couldn't fix it. She couldn't change my room bc they were completely sold out that night. She did offer for me to go downstairs and watch TV in the bar -- they don't play the sound on the TV's there. No thanks. I told her no one had even come up to look at it and try. She immediately sent the "engineer" on duty and he just looked to see if it was plugged in and the said the digital signal was messed up and he'd go see how to fix it and come back or call. I never heard from anyone again. This hotel also charges $11.95 per day per device for internet. It's slow and pricey. You'd think it'd be free or less than $11.95 per day considering it is 2012 and the internet is no longer the newest invention of our time. The hotel is very loud - you could hear everything going on in the hallways, hear the elevators (which are RIDICULOUSLY slow) and even hear the people in the room next to me. The guests in the room next door were enjoying themselves to the point where not only could I hear everything, but the wall was shaking and causing my bed to shake. It was very disturbing. Also, there is construction - at the hotel and outside the hotel, which is VERY VERY loud. A few good things about this hotel is that is close to the canal - a beautiful part of downtown - tons of runners, bikers, walkers, etc. enjoying the sites and weather. It has a Starbucks attached that serves their full menu of breakfast sandwiches, which is cheaper than the breakfast buffet at the hotel. Overall, I was very unhappy at this hotel. I do not recommend it unless you are ready for something noisy and a wet bathroom. May 21, 2012
Rated 3 out of 5 by Coach43 WONDERFUL LOCATION & GREAT STAFF With a super location & wonderful staff, I just couldn't believe that our hotel room was not air conditioned. Also, as a SPG member we were not informed when we checked in that there was a "Club Room." We didn't find out until we saw on the elevator that there was such a room on the 10th floor. When we inquired at the front desk about the availablity of the "Club Room," we were told that it was only for Platinum Members, however, since your here let me have your room key, I this will get you in. Also, we found that the five elevators were very inconsistent. I must admit, that I have never seen a more effiencent hotel staff, and I have traveled around the world. April 1, 2013
Rated 3 out of 5 by KSue88 Stay has some challenges The gym and view were excellent, and the front desk was always helpful when approached in person. My main challenges were with the internet- unreliable and extra cost (not typical in the hotels I have been traveling for business). The room also had no towels the first night. When I called down for towels at 12am, they took awhile to come up (20 minutes+). I called back and was told that the staff/security had "other things to do" and they were coming. I would have appreciated a bit more courtesy. I will be traveling to Indy at least twice a month for the next six months. This experience made me want to book another hotel. August 22, 2013
Rated 5 out of 5 by terran An Amazing Overnight Experience. I cashed in some of my SPG points for a free night here, after we came across a last-minute opportunity to head to Indy. This was one of the nicest and most surprising stays I've had. 1. Despite booking a basic King room, I scored a free upgrade to a suite...in addition to the check-in gifts. 2. The staff was very friendly. Kudos to Damien for all of his help! 3. The room was great. Clean, spacious, and comfortable. 4. The pool area was nice and large...and being rooftop, the city view was great! 5. The bar area had a really nice atmosphere and fast, friendly service. Kudos to you guys, this was a really great trip! August 26, 2013
Rated 5 out of 5 by Varyaag GenCon Experience My group stayed at this hotel for GenCon and I thought it was fantastic, my only problems with the room were the small space, and the lack of a fridge or microwave, other than that it was great. A few of my other friends rented a private meeting room in the basement for a game we were going to play, renting the room came with service, a phone to call up and ask for whatever we wanted from the restaurant/bar. This was Excellent, the other places we were trying to rent the meeting rooms for were asking upwards of $1200 for a twelve hour time slot where as the Sheraton was free. We tipped heavily for the fantastic service. August 30, 2013
Rated 5 out of 5 by SDidaho Excellent smaller downtown Indianapolis hotel Attended a small conference, and everything was superb. Staff were friendly and attentive, service was excellent, and accomodations very comfortable. The meeting rooms and food and beverage was above average. Location was central and within convenient walking distance to many restaurants and cultural landmarks. June 9, 2014
Rated 1 out of 5 by Goldie Please Clean My Room I stayed at this hotel for5 nights over New Years Weekend. I had to asked for more towels every day because when they cleaned the room they would only leave 2 towels for 2 guess. Also on 2 different days they didnt clean our room, even asking 3 different times for them to clean it. I shouldnt have to beg for my room to be cleaned, but apprentely here you have to, but it doesnt mean they will clean it. When we said something to the front desk, they acted like it was no big deal. There also was a fight outside our room with broken glass and things being thrown, no apology was even made to us. I have been a memeber of starwoods for years, but yet nothing was done for it. January 12, 2012
Rated 5 out of 5 by Jackson19 Nice hotel The only complaint I would have is the first room we were given was full of smoking smell. We were given another room and we were very satisfied. My only comment would be there needs to be a strong follow up to customers that do not follow the rules. They were letting that previous customer off the hook. He should have been fined and banned from SPG hotels in the future. Your good customers deserve this response!!. That is up to the Cleaning staff to immediately report each violation(which they don't) and then to have the Management follow up with the customer and SPG to kick they violators out of the system!!! October 10, 2013
Rated 4 out of 5 by JPal607 Wonderful service - few complaints The friendliness and helpfulness of every staff member I encountered was the most enjoyable part of my stay. The room was comfortable and clean, and the Club access was well worth the cost of the upgrade. I only have two complaints: nowhere on the website did the description mention a microwave, and a refrigerator was described as costing extra. Thus, I didn't bring along my own food, which I often do to save money. Turned out my room had both, but that didn't help me to find out after arrival. Secondly, the walls are too thin. I could hear the flushing and coughing of people in nearby rooms. March 24, 2014
Rated 4 out of 5 by mpmsu2003 Good Value and Decent Location Downtown We usually stay at the Sheraton when we travel to Indianapolis. Primarily because we travel to Indy for major sporting events with friends and family. During the Indy 500, NCAA Playoffs and Tournaments the prices at every hotel within 20 miles of Downtown go through the roof. The Sheraton seems to be the affordable option for most of the people we travel with and I can not say we have ever been disappointed. The Sheraton is in a good location and within walking distance to just about everything Indy has to offer. The rooms are pretty standard and the staff is usually very helpful. Always an enjoyable visit... April 12, 2012
Rated 4 out of 5 by RunnerIMM Great location to downtown Indy This was a last minute booking and I got the last king reservation. Upon arrival was upgraded to Club Level, as only remaining room was accessible. Needed a bathtub and staff was quick to make a room change. New room was clean. Bathroom problems: tile grout coming up on the floor, and the toilet seat (clearly an afterthought after construction was completed) hit the counter, forcing you to hold the seat up in order to use the toilet. Beds were fluffy and very comfortable. Cable had problems of losing the signal every few minutes. Everything downtown is within easy walking distance, and parking was a breeze. November 7, 2012
Rated 3 out of 5 by ColFlag Close to Circle Center Mall We only stayed here for the night. The room we stayed in was a double and was much smaller than we expected. Especially, for the price, which was a deal, however, compared to other area hotels. The bathroom was very small with the toilet practically in front of the sink! The seat would not stay up either because of being positioned so close to the sink vanity/countertop. Craziest setup I have ever seen in any hotel. The price to park caught us by surprise. I must have missed that somewhere in the hotel description. Other than that, the hotel is within walking distance of many attractions and restaurants. November 17, 2013
Rated 5 out of 5 by Kimmie2119 We will definitely be back to this hotel! This hotel was super clean. The beds are excellent and very comfortable. The poolside and monument circle view is terrific. The rooftop pool is a great relaxation area that we loved as well. June 6, 2014
Rated 5 out of 5 by Melvin6985 Great updates Impressive updates in rooms and common areas! Friendly staff at check in and check out. June 8, 2014
Rated 5 out of 5 by Coop14 Friendly and Fun The front desk gave me a map with walking tour suggestions. I enjoyed the fresh lemon water in the lobby when waiting to meet my party. I was running late and asked for breakfast 'to go' and was on my way in no time. Pool and exercise room were terrific. a great experience during the NCAA crew races, June 2, 2014
Rated 5 out of 5 by Bri7 june Room was very nice. Closing doors in the hallway were very loud. June 8, 2014
Rated 4 out of 5 by Legionaire66 Problems Hotel has great features and is located near almost everything. However on a two night stay the only thing the maid did was make bed and replenish soap and shampoo. They never emptied my trash or gave me new glasses to drink out of. I expected better especially I was on the Club level. The hotel should be able to tell you of all ways to get there from airport. I usually took Carey Limo, which was recommended by hotel but they doubled their rates in a year. found out by searching internet that the city ran a bus shuttle that ran every half hour for half the old price and dropped you in front of hotel. September 30, 2013
Rated 5 out of 5 by EJ4U89 Great Service! Upon arriving at the hotel, we had some trouble checking in due to a 3rd party travel website through which we had booked our stay. However, it was handled more than appropriately by one of the employees, MJ. She was awesome! The other employees we encountered during our stay were very nice and personable. All of our party agreed that the beds were very comfortable, and the view of the city centre from our window was great! We'd definitely stay here again and recommend it to anyone considering it! May 11, 2014
Rated 5 out of 5 by bobbilee Lovely Hotel We were there for a 2 night stay and came to celebrate our 41st wedding anniversary. Our main event was the Indiana Roof Ballroom Big Band Series. We stayed previously at another hotel, which I will not name, that was attached to the ballroom. This hotel is far superior. We were treated better by the front desk, by the attendant in the club lounge. The continental breakfast and evening snacks in the Club lounge were delicious. It is definitely worth upgrading to the Club level. Rooms are spacious there also. There are multiple restaurants within walking distance and it is just about 2 1/2 blocks from the ballroom. We will definitely stay here when we return. Thanks for a lovely weekend. June 11, 2013


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Results 1 to 2 of 2
Thread: Thoughts on Bella?
May 24th, 2014 10:16 AM #1
Thoughts on Bella?
I'm warming to the name Bella, although I dislike it as a nickname for Arabella, as I feel like Arabella is almost too pretty to be shortened. However, I'm a bit concerned with it, as I know it's very popular as a dog's name - to the point where, I actually only know 1 human Bella, and it's just a nickname for her (her actual name is Carmela).
My family does have a tendency to use very acceptable human names for their pets, such as:
Maggie May
Maggie (yes, two different dogs)
Daisy Mae
Molly/Mollie (again, two)
Because of who a few of these pets belong to, I actually likely can't use some of them (Keira, Oliver and Lilly mostly).
I feel like because of the names my family does use for animals, Bella is very much a possibility for the next pup or kitten my aunties or cousins get, which would, depending on the aunt or cousin, would render the name unusable (I have one aunt and cousin in particular who would most definitely say that a name, such as Keira is a dog's name only now).
So, is Bella ok to use, or should I avoid it like the plague and add it to the never ending list of 'pets only' names?"While some of the brightest of our celestial bodies are actually extinct now, their energy long since cooled; miraculously, because they float in the heavens so far away from us now, their beautiful light will continue to shine on us forever, and the glow will be so bright, it'll warm your heart, it'll make your eyes glisten, and it'll make you think to yourselves; what a concept"
May 24th, 2014 10:36 AM #3☆ isabella rose & mason jude ☆


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Basecamp Jobs
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Automated Software Test Engineer
London -
Arsenal Football Club
Development of the Clubs software testing strategy... Specific Experience: HTML/CSS, Javascript, JSON, XML. TDD and/or BDD frameworks such as BeHat, Cucumber, Gherkin, JBehave... Performance testing tools such as LoadRunner or JMeter... Project management and tracking tools such as JIRA, Confluence, Maven or Basecamp. Source code repositories such as...
Salary: Competitive + Excellent Benefits PackagePosted: 19 days ago


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|Oprah reportedly to star in 'The Shack' film adaptation
|Written by Gina Meeks
|Wednesday, 07 May 2014 08:52 AM EDT
Hoping to capitalize on the recent success of faith-based films, Hollywood has plans for the best-selling novel The Shack (Windblown Media/Hachette Book Group) to hit the big screen.
Oscar-winner Forest Whitaker will direct The Shack adaptation, and it will reportedly star Oprah Winfrey and British actor Idris Elba. Whitaker may also play a supporting role in the film.
The 2007 novel, written by William P. Young, remained on the New York Times best-seller list for more than three years. Summit Entertainment gained the rights to produce a film adaptation last year and plans to begin shooting this summer in Vancouver or Atlanta.
The novel details the tragedy the main character Mackenzie (Mack) Philips goes through when his youngest daughter is abducted and murdered. Elba—known for portraying Russell "Stringer" Bell in HBO's The Wire—will play Mack, who journeys to a mysterious shack in the Pacific Northwest after suffering from severe depression.
Though it's not known who Winfrey will play, Mack encounters three versions of God while in the shack—one of them Papa, an African-American woman.
The other two manifestations of God Mack meets are Jesus, a Jewish carpenter, and Sarayu, an Asian woman he later realizes is the Holy Spirit.
The Shack sold more than 18 million copies, but not every Christian was pleased with its message.
Southern Baptist Theological Seminary President R. Albert Mohler Jr. has called the book "deeply subversive," "scripturally incorrect" and "downright dangerous."
Author and Mars Hill Church Senior Pastor Mark Driscoll also had harsh words for the novel, saying, "It misrepresents God."
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Social Media Campaign Sensation Raises $41.8 million in 3 WeeksCasting...READ MORE
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Twitter Profile: Barack Obama (obamaposts)
Location: 4 more years / President Elect. This page is in no way affiliated with Barack Obama or the White House. Inspiring, Funny, and Honest Tweets. BELIEVE
Twitter Profile: Barack Obama (yes_we_can_12)
August 4, 1961- ??? President of the United States. Married with 2 children live in the white house. I am the 44th President.
barack obama in books | chapters.indigo.ca
The Stranger: Barack Obama In The White House. by Chuck Todd. November ... The People Vs. Barack Obama: The Criminal Case… by Ben Shapiro.
Barack Obama - Uncyclopedia, the content-free encyclopedia
Barack Obama, seen here with the White House in the background. Notice the contrast between his black suit and the white building. "
Obama, Romney, prepare for high-stakes second debate; Obama to be ...
14.10.2012 [Vancouver Sun] - WASHINGTON - The next eight days could prove critical for both Barack Obama and Mitt Romney — the two bitter rivals for the White House square off for their second and third prime-time debates, both well aware that their first faceoff dramatically
Barack Obama met sa campagne en veilleuse avant le second débat
12.10.2012 [LaPresse.ca] - Barack Obama a regardé avec attention le débat vice-présidentiel opposant son colistier Joe Biden au républicain Paul Ryan alors qu'il faisait route vers Washington, de retour de la Floride à bord de Air Force One, le 11 octobre. PHOTO AFP/WHITE HOUSE
Barack Obama and Bill O'Reilly's testy interview | Chatham ...
WASHINGTON - President Barack Obama accused Fox News on Sunday of keeping alive controversies the White House believes have been ...
Barack Obama | Financial Post
As the crisis in Ukraine has escalated, U.S. executives have been dropping off the list of attendees for the May 22-24 forum; meanwhile the White House is doing ...
Twitter Posts: Marvin Smilth (PrezFan)
2012.01.18 Angelina Jolie and Brad Pitt visit Barack Obama at White House ... http://t.co/QbaLZeWR
Twitter Posts: Kristen Hartley (kristenhartley)
2012.01.18 Angelina Jolie and Brad Pitt visit Barack Obama at White House ...: The Hollywood star game President Barack Oba... http://t.co/O1465HOx
Google Groups: Obama for president anyone
18.01.2007: Obama steps into White House race Barack Obama at an event honouring Martin
Iran Praises Deal As Recognition Of Nuclear Rights
25.11.2013 - enrichment. The White House says President Barack Obama telephoned Netanyahu Sunday, telling the Israeli prime minister he wants
TransCanada's inspection procedures under scrutiny
15.10.2012 [Toronto Sun] - In January, President Barack Obama denied TransCanada's original application for the pipeline, citing concerns about the project's environmental impact. The White House argued more time was needed to review the proposal. TransCanada has since
Barack Obama & family: news and photos – HELLO! Online
Bradley Cooper and Suki Waterhouse looked inseparable as they arrived hand in hand to the White House for a state dinner hosted by Barack Obama and his ...
Barack Obama | Windsor Star
LaSalle's Luke Willson got to shake hands with United States President Barack Obama at a reception at the White House in Washington, D.C. ...
Barack Obama | ecoSanity.org - See. Act. Inspire!
Sunday, Nov. 6, 2011 -- 12,000 people gathered in Washington D.C. and surrounded the White House to demand that President Obama reject the proposed ...
Barack Obama and Joe Biden Run Around the White House - Lets Move
Let's Move! - Lets Move #barack obama, #joe biden, #politics
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McDonald's Joins War on Childhood Obesity, Plans to Make Meals Healthier
07/26/2011 // WPB, FL, USA // Personal Injury Lawyers News // Nicole Howley
It's nice to see one fast food chain taking the step in the right direction. While McDonald's has a lot of work ahead of them to get their meals in an acceptable calorie range, it will hopefully prompt other fast food restaurants who offer kids meals, like Burger King, to revamp their menu. But, let's remember, it is still the parent's responsibility to ensure that their child is eating right, and not feeding them fast food everyday.
Tags: fast food restaurants, fight childhood obesity, kids meals, kids menu, McDonalds
Media Information:
Phone: 561-247-1646
Url: West Palm Beach Personal Injury Lawyer News
Read the full story on:How McDonald's Plans to Make Happy Meals Healthier
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Great Battle Cyber is a video game series published exclusively in Japan by Banpresto and Namco Bandai Games (formerly Bandai) that began in 1990, that serves as crossover between Ultraman, Kamen Rider (also known as Masked Rider) and Gundam.
The Daedaleus Overmind System (D.O.S.), central control program for earth's space armada has gone berzerk! Pow! Bam! Boom! Explosions, death, destruction, ahhhh! Only one choice now, stupid humans: Call in the Peace Police! Take command of Justice Ship Dnomn8r-3, and bring molten beams of truth and hot blaster justice to the Overmind's Cyber Circuit defense grid! Blast your way through waves of digital enemies and unbelievable bosses to reach the Overmind's inner sanctum.
Agent Nimb fights agains time to save the world. He has been assigned his first task- to get into an abandoned warehouse and test the new life support system. He needs activate supercomputer Hexadecimal number16 to reach his aim and he needs to use nitrogen catalyst to activate Hexadecimal number16. However this wont be easy task, there will be lots of enemies waiting to stop him.
In 2029, all the agents of the "Man in Black"(service in charge of monitoring relationships of humans with other life-forms) perished when the "MIBL" headquarters became wiped out as a result of attack conspired by hostile-minded aliens and certain powerful tellurians aspiring to slacken control over the "saucermen"'s dealings on the earth...
The year is 3018 and it's another golden age in history of humanity. Transgalactical construction corporations revel an ambitious plan to create the largest spaceport ever. To do so they creat a unique multitask cyber units - "Astros" and there mission is to build whatever the cost. The space operator controles red, green and blue Astros in attempt to use there abilities in special colormarked activity points.
This version is not 100% compatible with iPhone OS4 (you may experience some background images display issues). Next release is to come in a few days. ToiletBuster is the latest release from Cyber-Duck Ltd. Are you fast enough to tap and kill all the germs in 5 levels of different toilets environments. Try to reach the top of the leader board to become the ultimate Toilet Buster!
As a sequel of earlier worldwide mega hit, LightBike2 has finally come back with juiced up updates. Drive through the cyber space as fast as the light, and have dead heat battles with opponents all over the world! With simple operations, anyone can have control over LightBike. Newly "Jump" added to its action makes the game much more strategic! In addition of normal stages,a 3D stage has been added. A new game mode "Death match mode" has been added. Possible to play realtime match games.


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|Sorry wrong comment
#9305006, By SBfistfun PlayStation 4
SBfistfun 124 posts
Seen 2 hours ago
Registered 8 years ago
Dark Souls 2 - Crown of the Old Iron King guide Every bonfire, boss and loot item in DLC episode two.
Hearthstone: Naxxramas strategy guide Beat every Heroic boss and class challenge in the game.
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GAINESVILLE, Fla. – The first time Kelvin Taylor carried the ball at Glades Day School in Belle Glade, he found a hole and darted for a 10-yard gain.
Taylor was in eighth grade.
Click here for the original story.
Welcome to SECTalk.com
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The 2014 Interbike book delivery is coming up. But surely, you might […]
Janette Ryan
Hello, I'm an eBook!
ATTENTION: This item is an eBook. It can be read on iOS, Android, MAC and PC's with a supported eReader. It is not a physical book. eBooks are available via download immediately after you've checked out.
This item will be downloaded electronically after checkout.
Over the past decade there has been radical reform at all levels of China's education system as it attempts to meet changing economic and social needs and aspirations. Changes have been made to pedagogy and teacher professional learning and also to the curriculum - both at the basic education level, from kindergarten to year 12, and at the higher education level. This book focuses on reform at the early childhood, primary and secondary levels, and is the companion book to China's Higher Education Reform and Internationalisation, which covers reform at the higher education level.
Education Reform in China outlines the systematic transformation that has occurred of school curriculum goals, structure and content, teaching and learning approaches, and assessment and administrative structures, including the increasing devolvement of control from the centre to provincial, district and school levels. As well as illustrating the changes that are occurring within classrooms, it demonstrates the continuity of cultural and educational ideas and values in the midst of these changes, showing that reform does not just involve the adoption of foreign ideas, but builds on and even resurrects traditional Chinese educational values. Importantly, it considers how exchanges of people and ideas can contribute to new ways of working between Western and Chinese educational systems.
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"Made in Italy" exhibition at the Arlington Museum of Art, Arlington, TexasPosted on September 15, 2009
The Arlington Museum of Art will feature an exhibit of photography by students and faculty from UT Arlington who studied in Florence, Italy this June. The exhibit will open Saturday, September 19th with an opening reception on Friday, September 25th from 6 to 9 pm. This summer undergraduate and graduate students studied under the direction of Kenda North, professor in photography at UTA, at the Santa Reparata International School of Art. The exhibit will include photographs, large scale prints and self-published books in the main gallery of the AMA. The photographs represent personal responses to living in Florence for a month, as well as trips to Venice, Lucca, Rome and Cinque Terre. These are images which challenge typical travel photography, both in concept and in presentation. Participating artists are Ashley E. Allen, Jesse Barnett, Kimberly Bell, Justin Bolle, Annie Donovan, Casey Kopecky, Erica Martinez, Katie Nixon, Amber Lea Taylor, Jenny Todd, Daniel Guiterrez, Laurie L. Ward and Kenda North (faculty). Exhibition sponsors include the Arlington Camera, Imaging Spectrum, Kar Lynn Arts, Red River Paper and the Department of Art and Art History at UT Arlington. This is the fifth exhibit of student/faculty work studying in Florence at the Santa Reparata International School of Art at the AMA. The exhibit closes October 18, 2009. The Arlington Museum of Art is located at 201 West Main Street. The Museum is open Wednesday through Friday from 1:00 to 5:00, Saturday from 10 to 5 and Sunday from noon to 5. For more information, contact the Arlington Museum of Art at 817-275-4600 or Kenda North at email@example.com.


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Cat 5 Cable
Shielded Cat 5 Cable
Shielded Cat 5 Cable To Protect From EMI
CAT 5 is a type of twisted pair cable facilitating high quality signal transmission. The cable consists of four pairs of twisted copper wires covered by an outer sheath or jacket and that is why they are called shielded, otherwise called unshielded. The shield may consist of some twisted wires, untwisted spiral copper tape or a conducting polymer tape. The basic function of the shield is to: * To prevent signal loss due to interference. * To prevent electromagnetic radiations to interfere with devices.
Shielded cables were designed mainly to withstand sources powerful enough to generate a field of Electromagnetic Interference, or EMI. EMI affects an ordinary CAT 5 cable's data transmitting ability. In modern day building structures, some very basic EMI sources are found very close to those shafts which carry power and communication lines. As a result of this omnipresence of EMI, the ability of conventional CAT 5 cable to carry data gets hampered.
Different type of lighting, generators and elevator motors within the building have the ability to produce some powerful EMI fields. The EMI can go through the cable very easily and hamper the transmission of data, thereby shutting down the communication system. If there is no shield on your CAT 5 patch cables, the EMI from may pass through the cable. When it is near a source of EMI, chances are that data transmission will suffer and network communication may collapse. Since it is not always possible to avoid data transmission cables from running close to such areas, it is better that we use shielded CAT5 cables. They would negate the possibility of when they are running near high voltage power cables. Due to the presence of such a blockage in the shielded CAT 5 cables, they facilitate secured and unaffected data transmission.
GeFen CAT5e is one such shielded CAT5e cable which is available in the market in various lengths. Gefen CAT5e cables are said to guarantee good video quality. But this is when they are used with Gefen CAT5 extension products only. In order to ground the shielded CAT5 cable, it is terminated into the RJ45 connectors.
HyperLink 10/100 Base-T Shielded CAT5 Lightning Surge Protector It provides protection against lightening to Ethernet networks. They are compatible with 10/100 Base-T devices and protects Ethernet data pairs. It also protects against EMI interference. The material cast aluminum and the Ethernet connector used is Shielded RJ45 Jack.It operates between a temperature -40C to +80C.
Cat 5 Cable Menu
- Cat 5 Cable
- Cat 5 Network Cable
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- Shielded Cat 5 Cable
- Network Cable
- Ethernet Cable
- Ethernet Cable Testers
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We came there with our car. The main reason we picked this hotel is that it has an underground and protected parking. So we didnt have to worry about our car. Also, the price was very affordable : 230€ for 2 nights for 4 people, breakfast included. In a 4* ? Good deal. The place is what i'd call 'working... More
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