Spectrally Sharpened Two Channel Graph Filter Bank and Its Polyphase Structure

Graph filter banks allow for the spectral analysis of signals defined over graph domains. We consider the construction of two channel biorthogonal filter banks with outputs that are critically sampled. A method that sharpens the frequency response of an existing filter bank will be presented. The method is based on the use of sharpening kernels, and an analytical technique for constructing the kernels will be developed. Polyphase analysis of the sharpened filters will be performed, and the relationship between the original and sharpened polyphase structures will be derived. The polyphase structure allows the filter bank to be implemented efficiently using lifting steps. We will show that the number of lifting steps of the sharpened structure is unchanged, compared to the original structure. Application to nonlinear approximation of images will also be considered.