This is usually achieved by making appropriate assumptions of the input to estimate the impulse response by analyzing the output.
Most of the algorithms to solve this problem are based on assumption that both input and impulse response live in respective known subspaces.
In image processing, blind deconvolution is a deconvolution technique that permits recovery of the target scene from a single or set of "blurred" images in the presence of a poorly determined or unknown point spread function (PSF).
Researchers have been studying blind deconvolution methods for several decades, and have approached the problem from different directions.
It is part of audio processing of recordings in ill-posed cases such as the cocktail party effect.
If we are given the original signal, we can use a supervising technique, such as finding a Wiener filter, but without it, we can still explore what we do know about it to attempt its recovery.
Most blind deconvolution techniques use higher-order statistics of the signals, and permit the correction of such phase distortions.
Top left image: NGC224 by
Hubble Space Telescope
. Top right contour: best fit of the
point spread function
(PSF) (a priori).
[
1
]
Middle left image: Deconvolution by
maximum a posteriori estimation
(MAP), the 2nd iteration. Middle right contour: Estimate of the PSF by MAP, the 2nd iteration. Bottom left image: Deconvolution by MAP, the final result. Bottom right contour: Estimate of the PSF by MAP, the final result.
Blurred Image, obtained by convolution of original image with blur kernel. Input image lies in fixed subspace of wavelet transform and blur kernel lies in random subspace.
Recovered image after applying algorithm of blind deconvolution. This algorithm basically solves optimization problem using nuclear norm minimization. L=65536, K=65 and N=44838,
Original image
Blurred image: obtained after the convolution of original image with blur kernel. Original image lies in fixed subspace of wavelet transform and blur lies in random subspace. L=65536, K=200, N=65400
Recovered image: very different from original image, because essential condition for the algorithm of blind deconvolution using nuclear norm minimization is violated. L=65536, K=200, N=65400
