Numerous recent approaches attempt to remove image blur due to camera shake, either with one or multiple input images, by explicitly solving an inverse and inherently ill-posed deconvolution problem. If the photographer takes a burst of images, a modality available in virtually all modern digital cameras, we show that it is possible to combine them to get a clean sharp version. This is done without explicitly solving any blur estimation and subsequent inverse problem. The proposed algorithm is strikingly simple: it performs a weighted average in the Fourier domain, with weights depending on the Fourier spectrum magnitude. The method can be seen as a generalization of the align and average procedure, with a weighted average, motivated by hand-shake physiology and theoretically supported, taking place in the Fourier domain. The method’s rationale is that camera shake has a random nature, and therefore, each image in the burst is generally blurred differently. Experiments with real camera data, and extensive comparisons, show that the proposed Fourier burst accumulation algorithm achieves state-of-the-art results an order of magnitude faster, with simplicity for on-board implementation on camera phones. Finally, we also present experiments in real high dynamic range (HDR) scenes, showing how the method can be straightforwardly extended to HDR photography.
@cite_35: We use a Lucky Imaging system to obtain I -band images with much improved angular resolution on a 2.5 m telescope. We present results from a 10-night assessment campaign on the 2.56 m Nordic Optical Telescope and quantify the performance of our system in seeings better than 1.0 '' . In good seeing we have acquired near diffraction-limited images; in poorer seeing the angular resolution has been routinely improved by factors of 2.5–4. The system can use guide stars as faint as @math with full performance and its useful field of view is consistently larger than 40 '' diameter. The technique shows promise for a number of science programmes, both galactic (e.g. binary candidates, brown dwarfs, globular cluster cores) and extragalactic (e.g. quasar host galaxies, damped Lyman- α absorbers).
@cite_40: In short-exposure imaging through turbulence, there is some probability that the image will be nearly diffraction limited because the instantaneous wave-front distortion over the aperture was negligible. A number of years ago in a rather brief paper, Hufnagel (1966) argued heuristically that the probability of getting a good image would decrease exponentially with aperture area. This paper undertakes a rigorous quantitative analysis of the probability. We find that the probability of obtaining a good short-exposure image is Prob ≈ 5.6 exp[−0.1557 (D r0)2] (for D r0 ≥ 3.5), where D is the aperture diameter and r0 is the coherence length of the distorted wave front, as defined by Fried (1967). A good image is taken to be one for which the squared wave-front distortion over the aperture is 1 rad2 or less. The analysis is based on the decomposition of the distorted wave front over the aperture, in an orthonormal series with randomly independent coefficients. The orthonormal functions used are the eigenfunctions of a Karhunen-Loeve integral equation. The integral equation is solved using a separation of variables into radial and azimuthal dependence. The azimuthal dependence was solved analytically and the radial, numerically. The first 569 radial eigenfunctions and eigenvalues were obtained. The probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion. It is equal to the probability that a randomly chosen point in the hyperspace will lie within a hypersphere of unit radius, the points in the hyperspace being randomly chosen in accordance with the product of independent Gaussian probability distribution—one distribution for each dimension. The variance of these distrbutions is directly proportional to the eigenvalues of the Karhunen-Loeve equation. This hyperspace integral (involving up to several hundred dimensions) has been evaluated using Monte Carlo techniques.
A popular technique in astronomical photography, known as or , is to take a series of thousands of short-exposure images and then select and fuse only the sharper ones @cite_35 . Fried @cite_40 showed that the probability of getting a sharp lucky short-exposure image through turbulence follows a negative exponential. Thus, when the captured series or video is sufficiently long, there will exist such a frame with high probability.