Critically sampled graph filter banks with polynomial filters from regular domain filter banks

Graph signal processing deals with the processing of signals defined on irregular domains and is an emerging area of research. Graph filter banks allow the wavelet transform to be extended for processing graph signals. Sakiyama and Tanaka (2015) [22] recently proposed a technique to convert linear-phase biorthogonal filter banks for regular domain signals to biorthogonal graph filter banks. Perfect reconstruction is preserved using the technique but the resulting spectral filter functions are transcendental and not polynomial. Polynomial function filters are desired for the localization property and implementation efficiency. In this work we present alternative techniques to perform the conversion. Perfect reconstruction is preserved with the proposed techniques and the resulting spectral filters are polynomial functions.