Multichannel restoration of single channel images using a wavelet decomposition

Abstract

Multichannel linear filtering is applied to the restoration of single-channel images through the use of a wavelet decomposition. A novel matrix structure for the separable 2-D wavelet transform is presented which allows the transformation of block circulant operators, found in 2-D linear filtering problems, into semiblock 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 this domain, which uses the cross-correlations between subbands in the decomposition to improve substantially 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.