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 decompos ition of both the convolution operator and the signal in the subband d omain. With this approach, any single channel linear space-invariant f iltering problem can be cast into a multichannel framework. We apply t his decomposition to the linear space-invariant image restoration prob lem and propose a family of multichannel linear minimum mean square er ror (LMMSE) restoration filters. 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 nonstation arity of images. Experimental results are presented which test the pro posed multichannel LMMSE filters. These experiments show that if accur ate estimates of the subband statistics are available, the proposed mu ltichannel tilters provide major improvements over the traditional sin gle channel filters.