Matrix factorizations for reversible integer implementation of orthonormal M-band wavelet transforms

This paper presents a matrix factorization method for implementing orthonormal M-band wavelet reversible integer transforms. Based on an algebraic construction approach, the polyphase matrix of orthonormal M-band wavelet transforms can be factorized into a finite sequence of elementary reversible matrices that map integers to integers reversibly. These elementary reversible matrices can be further factorized into lifting matrices, thus we extend the classical lifting scheme to a more flexible framework. r 2005 Elsevier B.V. All rights reserved.