Linear-phase M-band wavelets with application to image coding

This paper investigates the design of M-band linear phase wavelet filter banks (M>2), and explores their application to image coding. The generalized LOT description of M-band linear-phase paraunitary filter banks is used to parametrize the M-band linear-phase orthogonal wavelets. It is proven that an M-band linear-phase orthogonal wavelet of even length cannot have more than one vanishing moment. Since this limits the effectiveness of the resulting wavelet filters, we next suggest methods for the construction of linear-phase biorthogonal M-band wavelet lowpass filters, generalizing prior 2-band constructions. However, one cannot guarantee that an arbitrary lowpass filter pair can be completed to a full perfect-reconstruction filter bank. Finally, the new linear-phase orthogonal wavelet filter banks are compared with known wavelet filters with regard to their performance in a transform-based image coder.