Multichannel restoration of single channel images us in g a wavelet d eco m p 0 sit ion

TLDR: In this article, a new matrix structure for the separable 3-D wavelet transform is presented, which allows the transformation of block circulant operators, found in 2-D linear filtering problems, into semi-block diagonal matrices in the wavelet-frequency domain, and an adaptive Wiener filter is implemented in this domain, which utilizes the cross correlations between subbands in the decomposition to subst antially improve the restoration of noisy-blurred images over that found with single channel filtering.

Abstract: In this paper, multichannel linear filt.ering is applied to the restoration of single channel images t.hrough the use of a wavelet decomposition. A new matrix structure for the separable 3-D wavelet transform is present.ed which allows the transformation of block circulant operat,ors, found in 2-D linear filtering problems, into semi- block circulant operators, which are defined here. These operators are easily treated as block diagonal matrices in the wavelet-frequency domain. An adaptive Wiener filter is implemented in t,his domain, which utilizes the cross correlat,ions between subbands in the decomposition to subst antially improve the restoration of noisy-blurred images over that found with single channel filtering. This improvement is especially evident when the power spectrum of the original image is available.