Multiresolution Image Restoration in the Wavelet Domain

This paper proposes an image restoration approach in the wavelet domain that directly associates multiresolution with multichannel image processing. We express the formation of the multiresolution image as an operator on the image domain that transforms block-circulant structures into partially-block-circulant structures. We prove that the stationarity assumption in the image domain leads to the suppression of cross-band correlation in the multiresolution domain. Moreover, the space invariance assumption leads to the loss of cross-band interference and interaction. In addition to the rigorous explanation of these effects, our formulation reveals new correlation schemes for the multiresolution signal in the wavelet domain. In essence, the proposed implementation relaxes the stationarity and spaceinvariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms that take advantage of the correlation structure in the wavelet domain. We provide a rigorous study of these effects for both the equal-rate subband decomposition and the multiresolution pyramid decomposition. Several image restoration examples on the Wiener-filtering approach show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation.