Factoring M-band wavelet transforms into reversible integer mappings and lifting steps

In this paper, a matrix factorization method is presented for reversible integer M-band wavelet transforms. Based on an algebraic construction of orthonormal M-band wavelets with perfect reconstruction, the polyphase matrix can be factorized into a finite sequence of elementary reversible matrices that map integers to integers reversibly. We show that the reversible integer mapping is essentially equivalent to the lifting scheme, thus we extend the classical lifting scheme to a more flexible framework.