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

Authors:
Tony Lin;Pengwei Hao;Shufang Xu
Affiliations:
National Laboratory on Machine Perception, Peking University, Beijing, China;National Laboratory on Machine Perception, Peking University, Beijing, China and Department of Computer Science, Queen Mary, University of London, London, UK;School of Mathematical Sciences, Peking University, Beijing, China
Venue:
Signal Processing - Special section: Advances in signal processing-assisted cross-layer designs
Year:
2006

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Abstract

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.