Blind deconvolution
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Blind Deconvolution is a technique which permits recovery of the target object from set of "blurred" images in the presence of a poorly determined or unknown Point Spread Function (PSF). Regular linear and non-linear deconvolution techniques require a known PSF. For the "blind" case a set of multiple images (data cube) of the same target object is preferable, each having dissimilar PSF's. The blind deconvolution algorithm is then able to restore not only the target object but also the PSF's. A good estimate of the PSF is helpful for quicker convergence but not necessary.
Iterative methods include Richardson-Lucy deconvolution, and Expectation-maximization algorithms.
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[edit] Concept
Suppose we have a signal transmitted through a channel. Usually the channel can be modelled as a linear system, so the receptor receives the convolution between the original signal and the impulse response of the channel. If we want to reverse the effect of the channel, and obtain the original signal, we must process the recorded signal by another linear system with the inverse response of the channel. This system is generally known as an equaliser.
If we know the original signal, we can use a supervised technique such as finding a Wiener filter. If we don't know the original signal, we still can explore what we know about the original signal to try to find it. For example, we can filter the received signal to obtain a filter with the desired spectral power density. This is what happens when the original signal has no autocorrelation, and we whiten the received signal.
Whitening usually leaves some phase distortion on the results. Most blind deconvolution techniques depend on higher-order statistics of the signals, and have the possibility to correct phase distortions. What happens is that we can optimize the equaliser to obtain a signal with a PDF closer to what we know about the original PDF.
[edit] High Order Statistics
Blind deconvolution algorithms often make use of high-order statistics, with moments higher than two. This can be implicit or explicit.
[edit] Gaussianity
The output of a linear system usually have a gaussian output, because of the central limit theorem. Blind deconvolution algorithms try to find an equaliser that maximizes the "non-gaussianity" of the recovered signal. Because of that, the techniques usually don't work with gaussian signals, since they have higher cumulants equal to zero.
[edit] Algorithms
Important algorithms for blind deconvolution are: Constant modulus algorithm decision directed shalvi weinstein
