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.

Publication Date



"Operator decomposition using the wavelet transform: fundamental properties and image restoration," Proceedings of the 1994 IEEE International Conference on Image Processing (ICIP '94). The Institute of Electrical and Electronics Engineers. Held in Austin, Texas: 13-16 November 1994. ©1994 Institute of Electrical and Electronics Engineers (IEEE). Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.ISBN:0-8186-6952-7Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

Chester F. Carlson Center for Imaging Science (COS)


RIT – Main Campus