Multichannel Restoration of Single Channel Images Using a Wavelet-Based Subband Decomposition

In this paper, we present a new matrix vector formulation of a wavelet-based subband decomposition. This formulation allows for the decomposition of both the convolution operator and the signal in the subband domain. With this approach, any single channel linear space-invariant filtering problem can be cast into a multichannel framework. We apply this decomposition to the linear space-invariant image restoration problem and propose a family of multichannel linear minimum mean square error (LMMSE) restoration ffiters. These filters explicitly incorporate both within and between subband (channel) relations of the decomposed image. Since only within channel stationarity is assumed in the image model, this approach presents a new method for modeling the nonstationarity of images. Experimental results are presented which test the proposed multichannel LMMSE filters. These experiments show that if accurate estimates of the subband statistics are available, the proposed multichannel filters provide major improvements over the traditional single channel filters.