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Aspiring tattoo artists don't necessary have to meet any educational requirements, and many artists learn the trade via apprenticeships. However, to receive a license, some states require individuals to undergo mandatory training in skin infections and disease prevention. Check with local regulatory agencies to see if they require classroom experience.
There are several educational programs that teach the art of tattoo. These include the Denver Body Art School, the World's Only Tattoo School in Louisiana, and the Tat Institute, which offers online training programs.
These programs may not be necessary, however, and aspiring tattoo artists might want to look for an apprenticeship instead. Most tattoo artists learn the craft on the job, under the guidance of licensed professionals. The Alliance of Professional Tattooists recommends that apprenticeships last three years. After this training period, apprentice artists apply for a license. They may have to take courses in infections, diseases, and blood-borne pathogen prevention before being allowed to apply.
To become a licensed tattoo artist, applicants may have to take a written exam and demonstrate their artistry in a skills assessment. Some states also have rules about necessary number of training hours. Even after tattoo artists receive their license, they may be required to attend continuing education classes.


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Despite the pervasiveness of drug advertisements, you might still be confused about whether a certain drug treats restless leg syndrome, erectile dysfunction, anxiety, or insomnia (or maybe all four?). Certain names, like Viagra, have gained enough cultural cachet to be widely recognized, but most, though familiar sounding, don't reveal their intended use.
According to The Merck Manuals, "When a drug is approved by the Food and Drug Administration ... it is given a generic (official) name and a trade (proprietary or brand) name. The trade name identifies it as the exclusive property of a particular company."
The United States Adopted Names (USAN) Council is responsible for selecting a drug's generic name and approving the drug's trade name, as proposed by the pharmaceutical company. Click below for insight into drug naming schemes, and a list of names currently under consideration (anyone for a little lebrilizumab?).
United States Adopted Names Council
FDA Approved Drug Products (Drugs@FDA)
Photo: Cheap Pharmaceuticals in Cabo San Lucas by Nelson Minar.

subset: commoncrawl


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anonymous on 12/08/2011
After having the apt treated and the whole building checked by a pest control company, there has been no sighting of bugs at all. Management is keeping a close eye.
Anonymous on 11/14/2011
Can anyone tell me if this building still has bedbugs? I'm desperate to find out.
Anonymous on 09/26/2011
I currently live in the building and have not had any encounters with bedbugs. The building does have a disgusting silverfish infestation though, http://en.wikipedia.org/wiki/Silverfish maybe thats what was encountered.
anonymous on 09/20/2011
from the moment i went to see the suite, rented it, i was mislead and lied to. i was told certain things would be done when they get to it. they are still not getting to it. also building has issues, old, sound and noise, and guess what.... bed bugs... just to top things off. i am suspect of the postings that sound just so darn happy. tenants who get bed bugs are not happy, but really traumatized. and have to throw away all their personal stuff. my experience... really bad.
Anonymous on 09/08/2010
I found the landlords helpful. I had a problem with one of my appliances and the very next day someone was here to fix it. The building is taken care of, someone is always cleaning the elevator, lobby, outside intercom etc. I feel safe, like there are no sketchy crack heads wandering the hallways or anything. And the bed bug issue was dealt with painlessly (And believe me I was freaking out about it!)
And no, this isn't the landloard writing this either-I'm just very happy with my apartment,
the building and the location.
Anonymous on 06/18/2010
as of June 17. the infected suite was treated twice and has been tested with a bedbug sniffing dog. All surrounding suites have been cleared. Management in is the process of having the dog check every suite in the building. Manament responded immediately.
Anonymous on 04/30/2010
My boyfriend's apartment recently got bedbugs, about a month and a half ago. I react really badly to bug bites, so I eventually scoured his bedroom and found them under the mattress. They're really developed, big ones -- according to what I've read, that means they're probably a few months old. Meaning they probably came in from another apartment. Just a guess, though.
517 bedbug reports near this address:
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Handmade lampwork glass pendant on sterling silver - Daisies on fresh green
A Posy Necklace is a little bunch of flowers that will last for ever!
Each one of these pendants will be unique, they start out life as rods of coloured glass which I melt and shape in a gas flame. Once I have the shape I add dots of glass and manipulate them to form the little flowers - this particular style remind me of orchids.. When the bead has been annealed and carefully cooled it is finished with sterling silver before being hung on a sterling silver chain - all ready to wear!
The sterling silver chains are Belcher (rolo) chains with bolt ring clasps. You can choose a 16" (short) or 18" (standard) length.
Dimensions (approx):
Glass Pendant 13 x 13mm
Total drop including bail 25mm
Bail size 6mm (solid ring)
The pendant will be delivered to you in gift box.
To view the rest of my exclusive Posy Necklace range click here
I make each glass bead individually so there will be some variation in composition between beads, that's what makes them unique!
All my beads are annealed in a digitally controlled kiln which makes them extremely durable. However, it should be remembered that they are glass and it is possible to break them. All beads should be kept away from small children and pets.
1-3 business days
I'll do my best to meet these shipping estimates, but can't guarantee them. Actual delivery time will depend on the shipping method you choose.
Buyers are responsible for any customs and import taxes that may apply. I'm not responsible for delays due to customs.
Just contact me within: 14 days of delivery
Ship items back to me within: 30 days of delivery
Request a cancellation within: 2 days of purchase
But please contact me if you have any problems with your order.
Because of the nature of these items, unless they arrive damaged or defective, I can't accept returns for:
Buyers are responsible for return shipping costs. If the item is not returned in its original condition, the buyer is responsible for any loss in value.
Please contact me if you have any problems with your order.
A Little Trinket is here to make Little Trinkets for you to treasure and not to bombard you with unwanted emails. We do like to keep in touch with our valued followers but we are not here to sell, rent or trade email lists with other companies or businesses. This Privacy Policy explains what we do with your information.
When you place an order
As above, your shipping and billing addresss, and contact information will only be used
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This Privacy Policy was written April 2018 and will be reviewed within one year from then.
I am happy to discuss wholesale availability with you, just drop me a line and we'll start chatting
I'd love to create something unique especially for you. Just get in touch and we can discuss the options.
Niobium is an element (formerly known as Colombium) which can be anodised, and therefore coloured, just like Aluminium. It is light and strong which is important for jewellery but possibly more important is that it is hypoallergenic. This makes it suitable for those with sensitivity to other metals.
Aluminium (or Aluminum if you prefer) can be anodised by submerging it in acid and subjecting to an electrical current. This results in a microscopic, almost honeycomb surface. Colour added to that surface is sealing into the chambers with heat and the result is permanently coloured metal - The colours you see on my anodised Aluminium cannot wash or rub off.
Aluminium is extremely light which makes is perfect for comfortable jewellery. It cannot be soldered, like Silver for example, so you will find items like my Pansy Stud earrings can be separated into the studs (Sterling Silver or Niobium) and the anodised Aluminium flower. This means you can wear the studs alone if you wish - two pairs for the price of one!


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Saturday, 30 March 2013
Battlefield Earth (2000)
Now this film wanted to be epic, it really tried, Travolta put millions of his own fortune into it and pushed people into helping him create it. These type of catastrophic alien invasion films were all the rage around this time after the success of 'Independence Day'. The films title alone sounds epic, a thundering statement...BATTLEFIELD EARTH!, it sounds like the ultimate sci-fi action film, so what's wrong with it?.
First and foremost it looks like, and for all intense and purposes, is an extended 'Star Trek' episode. The plot is very dull and plays out like a dull episode of 'Star Trek', one involving lots of dialog about mining for minerals (gold, for what reason? I dunno), slave trading and general alien politics. The mistake made with the alien race (with the rather stupid name of 'Psychlos', is that the best Hubbard could come up with??) in this film is that they are dissected too much. We hear about all sorts of trivial background stuff that isn't required, in the end they just seem like large humans, there is no mystery.
On top of the really overly laboured plot is the simple fact that these aliens look crap. Putting aside the obvious 'Klingon' like appearance, they look like huge platform wearing transvestites with dreadlock-like hair in campy goth space suits. As if they belong in some fetish club or one of those freaky bizarre goth circus's.
Then there's the simple question of why Travolta's face isn't the same as the rest of the alien race? why do all of them have devil/vampire-like faces but Travolta's is normal?. Is this because Travolta didn't wanna be hidden behind makeup?. Who's decision was it to let Travolta have/keep his little goatee? that kinda detracts from the whole alien design don't you think, a humanoid goatee. And who are these really old looking alien politicians with the flabby necks? is that what 'Psychlos' look like with age? why don't they look like the other 'Psychlos' facially?.
Other minor issues spring to mind also such as the fact these guys don't feel pain, Travolta's arm gets blown off yet it doesn't really faze him. Whitaker seems to be the only black alien in the entire race. Then there's the amusing observation that most of the cast clearly can't walk too well in the stilts they are on, no running by these aliens hehe.
Then we have the human element, or what's left of them. OK so humans are almost extinct and the 'Psychlos' have been ruling them for 1000 years apparently. So why has humankind completely forgotten everything about their past? the ability to use their brains, know what basic objects like glass or weapons are, names of places etc...they have forgotten everything which makes no sense. Mankind has been enslaved by aliens but why have they gone backwards to primitive cavemen? they don't know what a city is or what stars in the sky are, they worships Gods like ancient humans once did and they all scream and yelp like monkeys. But they still wear trousers.
The plot totally loses it once the rebellion begins, the last humans led by Pepper conveniently find apparent secret military bases still stocked to the gills with weapons, Harrier jets and power it seems. Little bit of training and many of them are now proficient in guns and even better...can fly Harrier Jump jets no probs!! just like that. So much so that they are able to engage alien ships in a fancy ass dogfight.
There really are so many plot holes and question marks I can't possibly mention them all or remember them all!. I do recall the effects being somewhat bigged up at the time, they were suppose to be pretty neat for the day. I guess they aren't too bad to be honest, some shots look nice, mainly ruined cityscape's, the alien ships are a reasonable design as is some of the ship flight sequences. Sets are pretty bland and uninspired, just faceless metallic facilities whilst the whole film has this quite ugly blue/grey/green tint/hue to it which is unusual.
So for a film called 'battlefield earth' there actually isn't that much in the realms of mega earthbound conflicts going on, its all based in one location. On a certain silly level the film can be enjoyable with its action sequences, it totally jumps on the 'Independence Day' bandwagon that's for sure, but it can still be minor fun.
Had this been a few half hour episodes of a TV sci-fi series then it could be looked on more favourably. I mean the film really isn't much better than a TV show, but I must admit to liking Travolta's wickedly evil campy performance. That and the 'Psychlos' females that we get a glimpse of, a kind of fetish wearing gothic Cenobite with very very long tongues, film highlight for me.
Posted by Phil Hubbs at 18:24
Labels: Review Classic/Cult Sci-fi Movie Reviews
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I think I could probably have her done within a week or two if I just sit down and get busy. Then I have the fun of deciding what my next project will be!
Marilyn commented on my last post that she was looking forward to the goodies I received/bought on my trip, so I finally got around to taking some pictures; now I just have to squirrel everything away!
Here's a picture of what was in our retreat goody bags:
The wonderful free gifts that Casa Cenina gave to us:
A couple pictures of what I bought at Casa Cenina:
In case you couldn't tell from previous blog posts, I am a major cat person! ;)
Finally, all my Primitive Hare purchases:
Isi had her display up all week, so this was the result of about three separate expeditions.
I guess I won't have to look far to find my next project!
Hope everyone has a great stitchy week!


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DUBAI, United Arab Emirates — Actor Tom Cruise is literally hanging around Dubai as he films scenes for a new movie.
Cruise proved how much he really loves doing most of his own stunts as he dangled almost 2,717 feet in the air from the tallest building in the world.
The actor spent this past weekend filming near the top of the Burj Kahlifa in Dubai for scenes for the fourth "Mission: Impossible" movie, London's Daily Mail reported.
On Saturday, the actor was photographed hanging from the observation deck of the building, which is 124 floors high, as fans gathered below watched in amazement.
Dressed all in black, the 48-year-old Cruise dashed from window-to-window as the film crew taped the scene from an open window above him.
Cruise is well-known for doing his own stunts in all his movies, especially the "Mission: Impossible" films.
"I love having the camera right there in front of me, where you can see me holding a shot all the way through," he told The Daily Mail in an interview over the summer. "I think it adds to the excitement for an audience. It's something that is challenging to do and fun for me."
"Mission Impossible: Ghost Protocol" is slated to hit theaters in 2011.
With AP


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What a fun Christmas we had! Noah is at that super fun age where you can get him next to nothing (though we probably still got him too much) and he loves it no matter what!
Here's Noah in his new jammies with his stash...
Gotta love the bed head and puffy eye pics! Abe and I showing off our Christmas socks...
And then... the day after Christmas is one of my fav's because this is what it looks like:
A complete disaster! I LOVE the messy house right after the celebrations! That may sound strange, but those are some of the best memories of growing up. Playing with all your new toys amongst boxes and wrapping paper. He played there for at least two hours!
Certainly one of the happiest kids I know. I'm such a lucky mom!
I hope everyone's Christmas was as joyful as mine. :)
Happy New Year!


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Susie Lupert
Vice President at Housing Works
By Penny Gray
Avice president at nonprofit Housing Works, Susie Lupert talks to us about the Housing Works Bookstore Café at 126 Crosby St., as well as the other business ventures that Housing Works has going in its fight to end homelessness and AIDS through relentless advocacy, lifesaving services and entrepreneurial businesses.
How did you land at Housing Works?
I have a background in not-for-profits and a master's in not-for-profit policy, so I've been dedicated to the field for a long time. I've been here for eight years now, so it's been the crux of my career.
How would you describe Housing Works?
Housing Works is a grassroots organization dedicated to helping homeless people who are HIV-positive. We're a unique nonprofit because we believe that profitability isn't bad. An efficiently run company isn't bad. I can't imagine another nonprofit like us. We're running businesses to raise money to help people.
You're a vice president-what does that mean in terms of day-to-day practice?
A lot! My job is to generate long-term visionary ideas about our businesses. I run several of the small businesses for Housing Works, and we're always thinking about how to be profitable while remaining true to our core values. It's a unique balance of brainstorming about revenue generation while also developing a board of directors, all the while leaving enough space to think about new ways to raise money for the HIV-positive homeless of New York, which is our ultimate purpose and mission. The Bookstore and Café are only two of the businesses I'm responsible for running.
How does the Housing Works Bookstore Café on Crosby Street relate to Housing Works' wider mission?
We've been at 126 Crosby St. since 1996, so it's been quite a while-long enough that we're a Downtown institution. We're really one of the last community spaces left in Soho, and we pride ourselves on being part of the Downtown community. We've got many supporters who are die-hard Downtown artists, and we hope that people see us as part of the Downtown infrastructure.
What's it like being Downtown at the moment?
It's tough because the rent is high and we have a large staff to support. We've started doing private events to subsidize the cost of staying open. People just don't buy as many books as they used to. It's a real sacrifice to us to close early to fund the location, but the space just can't be a used bookstore anymore because we don't sell enough books. One interesting fact that most folks don't know is that we actually run another business underneath the Bookstore Café in the basement. It's our online bookshop, and it generates about $1 million in revenue every year, equal to the bookstore's revenue. We provide skills and full-time jobs to those who have come through our job-training program-it's an amazing incubator to make money and provide jobs. It's also a great form of outreach to let people know about Housing Works all around the world. We put a bookmark in every book we ship out, and we hear from folks all the time who are so excited to learn about us and visit us when they come to New York City.
Do you think the Housing Works Bookstore Café could exist elsewhere in the city?
Sure; it's replicable, but it wouldn't be the same. It would probably be purely an events space. People aren't buying books anymore, which may be sad, but it's the way things are. The private events keep us open and part of the community, which is what we want to be and do. We couldn't replace the Downtown community somewhere else in the city, that's for sure!
What upcoming events is Housing Works Bookstore Café hosting?
Every Friday night we have a happy hour with cheap drink specials and board games. We really want to create a community space for people-what better way to do that than to provide a space where people can economically have a glass of wine before dinner and get to know other? Or, even better, just read and drink. We also host two Moth Story Slams every month. [The Moth is a nonprofit dedicated to telling stories about true life.] We've enjoyed that collaboration very much. Dec. 18 is a special day for us as we'll be hosting "What the Dickens?" a Christmas Carol marathon in which authors and celebrities come and read throughout the day, starting at 1 p.m. That's not to be missed, and it's an excellent way to celebrate the holiday season.
What do you love most about your job?
My job is totally unique. I love it because not another one exists like it in the world. Every year I'm taking on projects and job elements I haven't done the year before. It's a position that is constantly in flux. And that's a lot of fun.
Photo courtesy of housing works


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Feature-specific imaging
- Michael Lewis
- 3 years ago
- Views:
1 Feature-specific imaging Mark A. Neifeld and Premchandra Shankar We analyze the performance of feature-specific imaging systems. We study incoherent optical systems that directly measure linear projects of the optical irradiance distribution. Direct feature measurement exploits the multiplex advantage, and for small numbers of projections can provide higher feature-fidelity than those systems that postprocess a conventional image. We examine feature-specific imaging using Wavelet, Karhunen Loeve KL, Hadamard, and independent-component features, quantifying feature fidelity in Gaussian-, shot-, and quantization-noise environments. An example of feature-specific imaging based on KL projections is analyzed and demonstrates that within a high-noise environment it is possible to improve image fidelity via direct feature measurement. A candidate optical system is presented and a preliminary implementational study is undertaken Optical Society of America OCIS codes: , , , , The authors are with the Department of Electrical and Computer Engineering, Optical Sciences Center, University of Arizona, Tucson, Arizona Received 30 October 2002; revised manuscript received 21 February $ Optical Society of America 1. Introduction Imaging is an important component of many applications in both the government and commercial sectors. Defense-related imaging applications are concerned with a broad range of tasks from navigation to threat assessment and targeting; while commercial applications include such diverse tasks as parts inspection, medical imaging, and security surveillance. It is important to realize that nearly all of these important applications include, as part of the overall system goal, some quantitative diagnostic process. As an example we can consider an astronomical imaging system for which the goal might be to answer the question: Does the imager field-ofview contain any previously unknown celestial objects and if so, what are their characteristics? Another example can be found within a target recognition environment for which the overall system goal may be to label the objects in a scene as either target or nontarget objects. These two examples serve to illustrate a common disconnect between imaging system design and the diagnostic task for which the image measurements will be used. Namely, nearly every imaging system attempts to form, either directly or as an intermediate result, a visually appealing representation of the scene; however, without any additional specifications, it is not clear that such a representation is necessary to achieve the goal. It is not uncommon therefore to find imager hardware performance quantified by using a metric e.g., visual quality that bears little relevance to the eventual use of the measured data. The above discussion suggests a need for taskspecific imaging system design strategies. Taskspecific image quality metrics along with their associated hardware software co-design procedures would facilitate the manipulation of both optical and algorithmic degrees of freedom toward the optimal solution to a specific imaging system goal. These observations have been made by several authors before us and have given rise to important nontraditional imaging systems and system design metrics. 1 Task-specific ideal-observer performance metrics have had an important impact on the techniques used to manipulate various forms of medical imagery, while information theoretic metrics have been applied to optical-imaging systems for applications ranging from storage to astronomy. 2 4 The joint design of imager hardware and software has been demonstrated through the use of cubic phase masks for extended depth of field, aberration correction, etc. 5 Recent demonstrations of novel tomographic, holographic, and interferometric imaging systems provide additional platforms upon which these novel solutions might be tested. 6 8 In this paper we consider a form of task-specific imaging for which overall system performance is determined by the fidelity of linear object features. The next section presents our analysis of such a 10 June 2003 Vol. 42, No. 17 APPLIED OPTICS 3379
2 Fig. 1. Schematic diagram of a a conventional imager, b a feature-specific imager. feature-specific imaging system, and we elucidate the important role that photon count plays in defining the comparison with conventional imaging. This analysis demonstrates that the direct measurement of linear features can be fundamentally superior to their extraction via postprocessing from a conventional image. The novelty of our approach resides in our attention to feature fidelity subject to a fixed photon budget, and results in the conclusion that fidelity can be improved via direct feature measurement. Section 3 quantifies the feature fidelity obtained from a feature-specific imager for various types of noise, while Section 4 presents a design example of feature-specific imaging for the case of Karhunen Loeve KL features and demonstrates some important tradeoffs in the context of hardware software co-design. Section 5 presents a candidate optical architecture for a photon-efficient featurespecific imager along with a sensitivity analysis of this candidate implementation. 2. Feature-Specific Imaging Framework In this section we will present a framework for the design and analysis of task-specific imagers. Our approach will be suitable for those problems that can be described in terms of linear object features. This defines a very broad class of tasks, each of which will have a preferred set of features. For example, if the imager is required to transmit or store its imagery, then features might be selected to optimize compression efficiency. We will consider wavelet features in this regard. 9 If a coding decoding problem underlies the deployment of the imager, then Hadamard features may be required. 10 Alternately, if image mean-squared error MSE is the relevant taskspecific metric, then KL features i.e., principal components may be best, while for the extraction of maximum image information the so-called independent component features are optimal. 11,12 Although we will describe feature-specific imaging in a general way, examples of feature-specific imaging will be limited to the four types of features mentioned above. Figure 1 presents schematic representations of the two optical systems that we will compare. We will limit our study to incoherent optical systems, and we will seek to measure linear projections of the object irradiance distribution. Objects are assumed to be spatially discrete without loss of generality. Figure 1 a depicts a conventional imager that measures the object irradiance on a two-dimensional detector array. The object is treated as a set of K disjoint object blocks, each of which is assumed to contain N N pixels. Features will be computed independently on different object blocks so that each block may be treated as a vector g i with dimension N, where i 1, 2,... K. The use of object blocks instead of full objects allows us to consider both local and global features within a common framework, and because each block is treated independently, we can often drop the subscript without producing any confusion. The measurement of each object block g is corrupted by noise to yield the estimate ĝ. We first consider the case of additive white Gaussian noise AWGN so that ĝ g n, where n represents a zero-mean AWGN process with variance 2. Shot noise and quantization noise are considered in the next section. In Fig. 1 a the linear object features are computed as a postprocessing step by using the 3380 APPLIED OPTICS Vol. 42, No June 2003
3 M N projection matrix P to yield the feature estimates fˆc R M. We quantify the feature fidelity by use of the MSE criterion as MSE c f fˆc 2 M, where f is the desired noise free feature vector and represents statistical expectation. Assuming that the noise variables are independent and identically distributed iid and further assuming that the rows of the projection matrix are normalized, we find that MSE c 2. This simple result demonstrates that the fidelity of features computed via postprocessing a conventional image is limited by the detector noise alone. Figure 1 b depicts the operation of a featurespecific imager. Instead of measuring the object irradiance distribution in preparation for later electronic feature computation, this optical system is responsible for computing the desired projections and measuring them directly. It is simple to imagine an optical system based on transparencies that will accomplish this goal. 13,14 More photon-efficient solutions based on diffractive and or reflective optics can also be envisioned. In Section 5 we will present a novel polarization-based optical solution. Regardless of the specific hardware realization, however, we can consider the detected signal in our featurespecific imager to be a corrupted version of the desired feature vector. In the case of AWGN we can write the M-dimensional measurement vector as m Pˆ g n, where Pˆ is the projection matrix that is realized by the optical hardware. There are many reasons why P Pˆ e.g., imperfect optical components, finite optical bandwidth, misalignment, etc. and most of these will depend upon the specifics of the hardware implementation, however, there are two aspects of the optics that are unavoidable. The first unavoidable aspect of the optical solution derives from the conservation of energy. In particular, no column in the Pˆ matrix can sum in absolute value to greater than one. This constraint ensures that for a given object irradiance distribution and measurement time, the same number of photons are used in both the conventional and the feature-specific measurements. The mathematical implication of this photon-count constraint is a scaling of the measurement so that Pˆ P C, where C is the maximum absolute column sum of P. The actual feature estimate is thus obtained by multiplying the measurement m by the constant C to produce fˆm Pg Cn. We see that the photon-count constraint has resulted in an effective noise scaling for the direct feature measurement. The second unavoidable aspect of an optical feature-specific imaging solution is the need for dualrail signaling. Because negative quantities cannot be represented directly in an incoherent optical system, two complementary arms will be required to realize a projection matrix with bipolar quantities: One arm uses the positive values of P to generate the measurement m kp g C n and the other arm uses the negative values to compute m 1 k P g C n, where k is the power-splitting ratio of the dual-rail system, the ijth element of P is given by P ij P ij if P ij 0 and P ij 0 otherwise, and C is the maximum column sum of P. P and C are defined in an analogous way. In the case of a dualrail implementation, the final feature estimate is produced by subtracting the scaled outputs of the two arms: fˆm C m k C m 1 k. We can once again use the MSE criterion to quantify the performance of this feature-specific imager. We define MSE m f fˆm 2 M and in the case of AWGN, this can be reduced to MSE m C k 2 C 1 k 2 2. Because in general C C we find that k 0.5 is often not the optimal splitting ratio for minimizing MSE in a dual-rail feature-specific imager. Throughout the remainder of this paper all results will use the optimal projection-matrix dependent splitting ratio. In contrast with a conventional imager, the above discussion of feature-specific imaging indicates that the feature MSE depends on both the measurement noise and the characteristics of the projection matrix. In the next section we will see that because C and C depend on the number of rows in P, in cases for which relatively few features are required C k 2 C 1 k 2 1 and a multiplex advantage can be obtained from the feature-specific imager Feature Fidelity Results The feature-specific imager depicted in Fig. 1 b provides two potential advantages over the conventional imager shown in Fig. 1 a. First is the reduced detector count required to accomplish some overall system goal. If the task for which an imager has been deployed requires M features, then the featurespecific imager makes 2M measurements per block as compared with the N often 2M measurements made by a conventional imager. This reduction in detector count can impact both the complexity and maximum frame rate of the resulting imager. Second is the multiplex advantage described in the previous section. The potential reduction in MSE that accompanies the use of a feature-specific imager derives from the increase in the number of photons incident on each detector relative to the fixed measurement noise. This increase in measurement signal-to-noise ratio SNR translates directly into a reduction in feature MSE. Because the MSE reduction depends on the projection matrix we will quantify it for four cases of interest. The first projections that we will consider are the so-called Hadamard projections. A Hadamard matrix of order N is a N N orthogonal matrix of positive and negative ones. Figure 2 shows two example Hadamard matricies of size 8 8. The black squares indicate 1 and the white squares indicate 1. The rows in the matrix can be ordered in one of two ways. Figure 2 a represents the natural ordering dictated by the recursive use of a Hadamard matrix of size 2, i.e., 1 1; 1 1. Figure 2 b, in contrast, is generated by a sequential ordering for which the number of sign changes increases by one with each row. It is sometimes convenient to use the 10 June 2003 Vol. 42, No. 17 APPLIED OPTICS 3381
4 Fig. 2. Hadamard projection matricies of order 8 with: a natural ordering, b sequential ordering. sequential ordering because the features measured by using this version of the Hadamard matrix are generated in order of increasing frequency. Hadamard matrices are important for many reasons. Although their use in multiplex measurement originates with the derivation of optimal weighing designs, they are also used in spectroscopy to achieve the multiplex advantage. 16,17 Hadamard projections have also been used in picture processing, coding, and transmission to achieve bandwidth reduction. 18 We also consider feature-specific imaging by using wavelet projections. The wavelet transform is a multiresolution analysis tool that exploits the ability of certain classes of function to localize in both space and spatial frequency. Wavelets are widely used for image compression, signal image analysis, and to facilitate the fast solution of certain linear systems. 9,19 In this work we will use two wavelet families: integer-valued Haar wavelets and real-valued Daubechies DAUB4 wavelets. A wavelet decomposition can be expressed with a single unitary matrix transformation P, where the rows of P are the wavelet projections arranged in order of increasing spatial frequency. Figures 3 a and 3 b show example 8 8 projection matricies for Haar and DAUB4 wavelets respectively. The third linear features that we will consider here are KL features. KL features are optimum in the sense that they provide dimensionality reduction with the smallest possible MSE. This optimality results from their energy compaction property: A Fig. 3. Wavelet projection matricies of order 8: a Integervalued Haar wavelets, b real-valued DAUB4 wavelets. large percentage of energy in a zero-mean object can be concentrated into a small number of KL features. The KL transform also minimizes the correlation among features, providing information-optimal compression for Gaussian sources. For these reasons KL projections are often used for data compression, pattern recognition, and signal de-noising The KL projections are computed from training data and are given by the eigenvectors of the data covariance matrix. Figure 4 a shows the ten faces that were used as training data for this work. Each face in this set was decomposed into N N blocks and the resulting set of N-dimensional vectors was used to compute the data covariance matrix. The eigenvectors of the covariance matrix were then sorted in decreasing order of their corresponding eigenvalues. Figure 4 b depicts the first 16 KL features for the training data shown in Fig. 4 a for the case N 64. Each eigenvector has been independently scaled into the range to generate a gray-scale image for display purposes. The last type of features that we will consider are the so-called independent components. 12 Independent component analysis ICA provides features that are statistically independent for any source distribution, converging to KL features for Gaussian sources. The ICA defines a linear transformation that is optimal in that it minimizes the mutual information among the transform coefficients. ICA has been used for various types of feature extraction as well as statistical applications such as blind source separation. 23,24 ICA features can be ordered in terms of their information content to produce a projection matrix P. Using the training data shown in Fig. 4 a, we have computed ICA features using an algorithm described in Ref. 25. The first 16 ICA features are shown in Fig. 4 c for the case of N 64. We know from Section 2 that the relative performance of feature-specific imaging can be written as MSE m MSE c C k 2 C 1 k 2 and that the values of C and C as well as the optimal value of k will depend on a the feature set of interest and b the number of features used to define the P matrix. Each of the feature sets described above has a natural ordering. For example, if M N KL features are desired then the M projections corresponding to the largest eigenvalues of the data covariance matrix are generally used. Using this natural ordering we can plot as a function of the number of features M, for each of the four feature sets described above. We will use optimal power splitting into each arm of the dual-rail system throughout this exercise. The result is shown in Fig. 5 a for the case N 64. It is important to notice that all points for which 1 correspond to configurations for which featurespecific measurements produce higher feature fidelity than can be achieved via postprocessing a conventional image. From the data in Fig. 5 a we see that 1.0 for M 2 for ICA and KL features, M 3 for Hadamard and Haar wavelet features, and M 4 for DAUB4 wavelet features. From this data we conclude that for applications in which relatively 3382 APPLIED OPTICS Vol. 42, No June 2003
5 Fig. 4. a Ten faces used for training the KL and ICA features, b first 16 KL features computed using N 64. Each 64-dimensional feature appears as an 8 8 image, c first 16 ICA features computed using N 64. These features are rendered as in b. few features are required to meet the overall system goal, feature-specific multiplex imaging can be superior to conventional imaging. The diversity of feature sets included here gives us confidence that the general behavior represented by the data in Fig. 5 a will persist for other feature sets as well. The value of M for which each of these features sets achieves 1.0 represents a small fraction of the total N 64 possible features. It is interesting to examine how the 1.0 condition depends upon the block size N. We will consider the example of KL features. In Fig. 5 b we plot versus the fractional number of KL features M N for several values of N. From this data we see that the use of larger blocks will indeed increase the number of features that can be measured in a feature-specific imager while maintaining 1.0; however, the fraction of feature dimensions at which the 1.0 condition occurs is found to be approximately 5%, decreasing slightly with increasing N. It is also possible to investigate feature-specific imaging under non-awgn noise models. We have considered two such models: shot noise and quantization noise. In the case of shot-noise limited imaging we do not expect an increase in the number of photons reaching a detector to provide any improvement in SNR. This is because the shot-noise-limited SNR is inherent in the irradiance collected by the instrument and does not depend on the energy incident on any particular detector. Thus we expect no multiplex advantage for feature-specific imaging in the presence of shot noise. Simulation results for this case are shown in Fig. 5 c, which uses the same feature sets N 64 as were used to generate the data in Fig. 5 a. Because MSE m MSE c cannot be written in a simple form as it was for AWGN, we use Monte Carlo simulation to generate the data in Fig. 5 c. From this data we see that 1 for all values of M confirming our intuition and demonstrating that feature-specific imaging provides no advan- 10 June 2003 Vol. 42, No. 17 APPLIED OPTICS 3383
6 Fig. 5. a Relative feature fidelity i.e., versus number of features M under AWGN noise model described in the text for N 64. b versus fractional number of KL features under AWGN model for N 36, 49, 64, and 81. versus M under c shot-noise, and d quantization noise models described in the text for N 64. tage under a shot noise model. For the case of quantization noise the situation is quite different. Once again we investigate the behavior of as a function of M; however, in this case we assume that 8-bit quantization limits the MSE of the conventional image measurement. Features are then computed from the measured image to generate some feature error MSE c. We consider bandwidth to be the constrained resource for this case, and we note that 8-bit quantization results in a data rate that scales like 8N. This suggests that more precise analog to digital converters can be used in a feature-specific imager while maintaining the same data rate. In particular we assume that the word length used for each feature is given by min 24, 8N M, where the minimum function is used to upper bound e.g., to limit implementational complexity the number of bits allocated to direct feature measurements. The results of this study are shown in Fig. 5 d. From this data we see that a large range of M values produce 1 suggesting that feature-specific imaging can be a powerful technique within a quantizationnoise limited environment such as the one described above. 4. Karhunen Loeve Imaging The preceding discussion has been quite general and has quantified the potential benefit of direct feature measurements in terms of feature fidelity. We have seen from this discussion that a trade-off exists between feature fidelity and the number of measured features, and that this tradeoff is governed by the photon-count constraint. In this section we will consider an example of feature-specific imaging in which we demonstrate the utility of direct feature measurements toward some overall imaging system goal. We select KL features for this example because a this feature set is familiar to a broad audience, b the system goal for which these features are optimal i.e., minimum reconstruction MSE is intuitive and can be represented visually, and c we find the somewhat surprising result that even when the system goal is to produce a pretty picture there are cases in which it 3384 APPLIED OPTICS Vol. 42, No June 2003
7 Fig. 6. Reconstructed images obtained with a conventional imaging MSE d 500, b feature-specific imaging MSE kl 154. AWGN corrupts all measurements with and the featurespecific imager used M 4 and N 64. is preferable to measure features than to measure a conventional image. We begin by considering a conventional imaging system that is subject to additive white Gaussian measurement noise with variance 2. Such a system produces the object estimate ĝ d g n, where n represents the AWGN. The pixelwise MSE associated with an image obtained via such a direct imaging system is simply MSE d g ĝ d 2 N 2. An example of a measured image with 22 is given in Fig. 6 a. Alternately, a feature-specific imager might measure some number M of KL features fˆi : i 1,...,M to produce the object estimate ĝ kl M i 1 fˆip i where p i is the ith row of P and is defined by the normalized ith largest eigenvector of the KL training-data covariance matrix. See figure 4b for an example of the first 16 eigenvectors computed using the training faces shown in figure 4a. It is important to note that the pixelwise MSE associated with ĝ kl, specifically MSE kl g ĝ kl 2 N contains two components. One of these arises from discarding N M terms from the full KL expansion of the image. The other arises from the AWGN associated with the feature measurements. Including both of these components we can write MSE kl as N i M 2 i M 1 N C 2 k C 2 1 k, MSE kl 1 N (1) where i is the ith-largest eigenvalue of the KL training-data covariance matrix. From this expression it is clear that a tradeoff exists between these two sources of error. Increasing the number of features decreases the first term while it increases the second. Figure 7 a shows a plot of MSE kl versus M for 22 and several values of N. From this graph we can see that there is indeed an optimum number of features for each blocksize. This optimum choice of M balances the error arising from the truncated KL expansion against the error arising from the measurement process. We also notice that for all values of N considered here, the optimal value of MSE kl is less than 2, which indicates that the feature-specific approach can be superior to conventional imaging for this example. Extracting the minimum MSE from each curve in Fig. 7 a we can plot the optimal MSE versus N as shown in Fig. 7 b. This figure reflects a trade-off with the blocksize N. We can understand this trade-off in terms of a balance between image energy and feature fidelity. In particular we recall that increasing blocksize results in improved feature fidelity at constant M see Fig. 5 b, however, the fraction of image energy contained in that fixed number of features goes down with increasing N. The result shown in Fig. 7 b suggests that N 121 is optimal for this example. Figure 6 b shows the reconstructed image associated with the optimal KL feature-specific imager for 22. It uses M 6 and N 121 and achieves MSE kl 132. Because the relative performance of the feature-specific approach will be sensitive to the value of 2,wecan repeat the analysis that gave rise to the graphs of Figs. 7 a and 7 b for many values of noise, extracting only the optimal performance. The result is shown in Figure 7c. This graph presents the MSE performance of both conventional open squares and KL feature-specific open circles imaging versus noise. From this figure we see that the KL feature-specific approach offers significant advantages in high-noise environments i.e., A convenient way to quantify the value of a KL imager is represented by the crossover point for these two curves. This is the value of noise above which KL imaging is superior to conventional imaging. From Fig. 7 c we see that this crossover point is x 8.5. The second term in Eq. 1 depends on the fidelity of the optical feature measurement process. In the previous section we discussed how this process is influenced by two physical constraints: a the positive-valued nature of optical irradiance resulted in the need for dual-rail signaling and b the conservation of energy required the scaling of the dual-rail projection matricies by their respective maximum column sums. Constraint a provided us with an additional degree of freedom in our optical-system design. We can optimize the fraction of collected photons that enter each arm of the dual-rail system via the parameter k. This optimization has in fact been performed for all data presented thus far. It is possible to carry this idea one step further, optimizing the fraction of photons that participate in each feature measurement. Consider scaling the ith row of the projection matrix P P by a constant a i b i. This results in a linear scaling of the corresponding feature measurements so that fˆi f i C a n a i and fˆi f i C b n b i, where a a 1, a 2,...,a M and b b 1, b 2,...,b M and n is the AWGN process. Note that the presence of these new feature scaling factors will change the values of the maximum column sums so that C a and C b are now written as explicit functions of a and b. If we implement such a scaling operation within a KL imaging system, 10 June 2003 Vol. 42, No. 17 APPLIED OPTICS 3385
8 Fig. 7. Reconstruction MSE for KL feature-specific imaging corrupted by AWGN. a MSE versus number of features for and N 16, 36, and 64. b Minimum MSE versus blocksize for c Optimum KL feature-specific imaging performance versus noise standard deviation. the resulting MSE in the image estimate MSE kl, can now be written as MSE kl 1 N C b N i 2 M i M 1 N i 1 b i 2 C a a i 2. (2) From this equation we can see that it is possible to exploit the additional degrees of freedom in a and b to further minimize the MSE of the KL imaging system. The complex dependence on a and b that is represented by the maximum column sums C a and C b, makes this a challenging optimization problem. We use a modified gradient search method for each value of M to find the optimal a and b vectors. From these optimized system designs we can select the best value of M for each value of noise. The result of this process is shown by the curve with open diamond symbols in Fig. 7 c. We notice that the optimal allocation of photons has resulted in a crossover point that is slightly lower x 8.25, indicating a performance improvement of 10 log db. KL imaging uses projection matricies P and P that are based on the eigenvectors of the trainingdata covariance matrix. This guarantees optimal noise-free performance for test images that are selected from the same underlying image distribution as the training data. The previous results in this section are based on a test image that is similar to but not contained in the training data. In cases for which the testing data is dissimilar from the training data, we expect KL imaging performance to degrade. Using the same KL imaging system as we used to generate the optimal data in Fig. 7, we have quantified this degradation for the five test images shown in Fig. 8. In all five cases the crossover noise value is increased as compared with the optimal crossover value from Fig. 7 c x Table 1 shows the crossover noise cost in db for each of these test images APPLIED OPTICS Vol. 42, No June 2003
9 Fig. 8. Test images for evaluating training-set-sensitivity of KL feature-specific imaging: a Man, b Dog, c Desk, d Car, and e Goldhill. Table 1. Crossover Noise Cost a Image Man Dog Desk Car Goldhill Crossover noise cost a For test images that differ from the training set. 5. Polarization-Based Optical System for Feature-Specific Imaging Figure 9 shows a candidate optical architecture for feature-specific imaging. It is a polarization-based dual-rail optical pipeline processor. The system shown in this figure is suitable for the measurement of two features, however, additional processing stages can be cascaded as shown. Because the performance of feature-specific imaging as compared with conventional imaging so critically depends on the efficient use of all the collected photons, this system is designed to be photon efficient. Its operation will first be described for the case of a single feature. We assume that light entering the feature-specific Fig. 9. Candidate feature-specific imaging architecture: PBS polarizing beamsplitter, SPM spatial polarization modulator, D1 and D1 are detectors for the positive and negative components of the 1st feature measurement and D2 and D2 are for the 2nd feature. 10 June 2003 Vol. 42, No. 17 APPLIED OPTICS 3387
10 imager is unpolarized. This unpolarized incident light first passes through a polarizing beamsplitter PBS as shown. The PBS separates the incident light into s- and p-polarizations, directing each into a separate arm of the dual-rail system. The light in each arm is imaged onto a spatial polarization modulator SPM that rotates the polarization at each pixel of the optical irradiance pattern by an angle given by the desired projection p 1. The rotations in the positive arm are given by 1 i sin 1 p 1 i C if p 1 i 0 and 1 i 0 otherwise. For the negative arm we have the complementary scheme: 1 i sin 1 p 1 i C if p 1 i 0 and 1 i 0 otherwise. Notice that normalization by the maximum column sums C and C ensures that the maximum rotation imparted by any pixel is 90. These rotations can be imparted for example by using an electrically addressable device such as a liquid-crystal LC modulator, or by using a fixed device such as a surface-relief profile etched into an optically active crystal. In either case the orthogonal component of polarization generated by the SPM in each arm is re-directed by use of polarizing beamsplitters and is integrated onto the photodetectors as shown in Fig. 9. Now we describe the operation of this system in the case of two features. The prescription for the rotation angles 1 i and 1 i remains unchanged in this case, however, it is important to note two things. First, note that the un-rotated light propagates past the PBS elements and can be used for the computation of additional features. Second, note that the normalization of P and P by their respective maximum column sums ensures that there are sufficient photons for the computation of these successive features. The prescription for the rotation angles in stage two, however, must be modified to account for the reduced irradiance at each pixel of the stage 2 SPMs. Specifically we have 2 i sin 1 p 2 i C p 1 i if p 2 i 0 and 2 i 0 otherwise. A complementary scheme is used for the negative arm. From Fig. 9 we see that the light exiting each arm of stage 1 is reimaged onto the SPMs in each arm of stage 2 so that feature 2 may be computed via the induced polarization rotations described above. Additional stages operate in the same way. The optical system described above is photonefficient by design; however, there are unavoidable implementational imperfections that will impact the performance of such a feature-specific imager. To quantify the impact of these imperfections we have formed a computer model of the system shown in Fig. 9. The model includes various sources of imperfection, such as 1 imperfect PBS devices with 98% transmission and 2% leakage, 2 imperfect coatings that give rise to surface reflections all surfaces in our model are taken to be 99% transmissive, 3 LC SPM elements subject to a uniform noise term 0.05V in their applied voltage, and of course AWGN at each detector. We have also included a logistic response function shown in Fig. 10 to model each SPM; however, many other sources of experimental Fig. 10. SPM response function used in optical system tolerancing study. error have been overlooked in this preliminary analysis. We expect for example that SPM devices will not have a 100 areal fill-factor, and or may not have a uniform response at all pixels or for all incident angles. These SPM characteristics have not yet been included in our model. The results of our preliminary implementational study are shown by the asterisk curve in Fig. 7 c. We see from this data that the presence of these device system imperfections have degraded the performance of the KL imager, generating a crossover noise cost of 1.34 db. We also notice that this degradation is most deliterious in low-noise environments and that significant MSE advantage is still provided by KL imaging when the detector noise level is high. 6. Conclusions This paper has presented an analysis of featurespecific imaging. An imager is often deployed as part of a larger system designed to achieve some diagnostic task. In cases for which the overall system goal can be described in terms of linear projections of the object irradiance distribution, we consider the possibility of direct optical feature measurement. We have quantified the fundamental limits of such an approach. We have compared the feature fidelity associated with direct feature measurements to the fidelity achieved by postprocessing a conventional image, and we find a tradeoff between the number of features and the corresponding feature fidelity. In both AWGN and quantization-noise limited imaging environments this tradeoff results in higher fidelity for direct feature measurements as compared with processing a conventional image in cases for which relatively few features are necessary to adequately meet the goals of the overall system. A common alternate approach to the measurement of linear object features is the optical correlator. It is instructive to consider the photon inefficiencies that result from the use of optical correlation within the feature-specific imaging environment described here. Two observations can be made in this regard APPLIED OPTICS Vol. 42, No June 2003
11 First, a correlator is shift invariant so that the blockwise linear projections that we describe are obtained at the center of each block in the correlation plane. Photons arriving at other locations are unused resulting in poor feature fidelity. Second, a single correlator implements a Toeplitz projection matrix that depends upon only a single feature. Multiple correlators are therefore required one for each row in the desired projection matrix to realize the desired computation. Division of photons among these multiple correlators represents another source of photon inefficiency. In this paper we have shown that the use of a single projection matrix, augmented to optimize the efficient utilization of photons, can result in featurespecific imaging with high fidelity. A specific example of feature-specific imaging based on KL projections was analyzed and yielded the important result that it is possible to improve image MSE via direct feature measurement in high AWGN environments. A candidate optical system was presented and a preliminary implementational study demonstrates that such a system can efficiently measure linear object features and can provide improved performance as compared with conventional imaging. This work is continuing along several important dimensions. In the course of this work we have noticed that KL features are suboptimal for minimum MSE image reconstructions when feature measurements are corrupted by noise. We are now seeking a new formulation for the optimum feature set in this case. Extension of the techniques described here to include multispectral imaging is also underway so that correlation among wavelength bands can be exploited to generate more efficient use of photons in these systems. We are also working to improve our implementational model with the eventual goal of constructing an optical system for feature-specific imaging. References 1. M. P. Christensen, G. W. Euliss, M. J. McFadden, K. M. Coyle, P. Milojkovic, M. W. Haney, J. van der Gracht, and R. A. Athale, Active-eyes: an adaptive pixel-by-pixel imagesegmentation sensor architecture for high-dynamic-range hyperspectral imaging, Appl. Opt. 41, E. Clarkson and H. H. Barrett, Approximations to idealobserver performance on signal-detection tasks, Appl. Opt. 39, W. C. Chou, M. A. Neifeld, and R. Xuan, Information-based optical design for binary-valued imagery, Appl. Opt. 39, S. Prasad, Information capacity of a seeing-limited imaging system, Opt. Commun. 177, S. Tucker, W. T. Cathey, and E. Dowski, Extended depth of field and aberration control for inexpensive digital microscope systems, Optics Express 4, D. L. Marks, R. Stack, A. J. Johnson, D. J. Brady, and D. C. Munson, Cone-beam tomography with a digital camera, Appl. Opt. 40, Z. Liu, M. Centurion, G. Panotopoulos, J. Hong, and D. Psaltis, Holographic recording of fast events on a CCD camera, Opt. Lett. 27, P. Potuluri, M. Fetterman, and D. Brady, High depth of field microscopic imaging using an interferometric camera, Opt. Express 8, M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, Image coding using wavelet transform, IEEE Trans. Image Process. 1, M. Harwit and N. J. A. Sloane, Hadamard Transform Optics, Academic, New York, 1979, pp K. I. Diamantaras and S. Y. Kung, Principal Components Neural Networks: Theory and Applications, Wiley, New York, 1996, pp R. Stephen and E. Richard, Independent Component Analysis: Principles and Practice, R. Stephen and E. Richard, eds. Cambridge University, Cambridge, UK, 2001, Chap. 1, C. J. Oliver, Optical image processing by multiplex coding, Appl. Opt. 15, R. D. Swift, R. B. Wattson, J. A. Decker, R. Paganetti, and M. Harwit, Hadamard transform imager and imaging spectrometer, Appl. Opt. 15, P. B. Fellgett and E. H. Linfoot, On the assessment of optical images, Philos. Trans. R. Soc. London 247, T. J. Vickers, C. K. Mann, and J. Zhu, Hadamard Multiplex Multichannel Spectroscopy to Achieve a Spectroscopic Power Distribution Advantage, Appl. Spectrosc. 45, A. G. Marshall and M. B. Comisarow, Fourier and Hadamard transform methods in spectroscopy, Anal. Chem. 47, H. J. Landau and D. Slepian, Some computer experiments in picture processing for bandwidth reduction, Bell Syst. Tech. J. 50, I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inf. Theory 36, H. Feng and M. Effros, On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression, IEEE Trans. Image Process. 11, S. J. Lee, S. B. Jung, J. W. Kwon, and S. H. Hong, Face detection and recognition using PCA, TENCON 99 Proc. IEEE Region 10 Conference 1, A. Aysin, L. F. Chaparro, I. Grave, and V. Shusterman, Denoising of Non-Stationary Signals Using Optimized Karhunen-Loeve Expansion, Proc. IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, A. Hyvarinen, Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces, Neural Comput. 12, H. Saruwatari, T. Kawamura, and K. Shikano, Fastconvergence algorithm for ICA-based blind source separation using array signal processing, Proc. IEEE 11th Signal Processing Workshop on Statistical Signal Processing, A. Hyvarinen, Fast ICA by a fixed-point algorithm that maximizes non-gaussianity, Independent Component Analysis: Principles and Practice, R. Stephen and E. Richard, eds. Cambridge University, Cambridge, UK, 2001, Chap. 2, pp June 2003 Vol. 42, No. 17 APPLIED OPTICS 3389
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