Operator decomposition using the wavelet transform: fundamental properties and image restoration applications

A novel formulation of image processing operations in the wavelet domain is presented which directly associates multiresolution with multichannel image processing. The formation of the multiresolution image is expressed as an operator on the image domain that transforms block-circulant structures into partially-block-circulant structures. The proposed implementation relaxes the stationarity and space-invariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms which take advantage of the correlation structure in the wavelet domain. Based on this structure, the authors discuss the estimation of the power spectrum in the wavelet domain. Image restoration examples using the linear minimum mean square error filter show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation