Optimization Design of M-Channel Oversampled Graph Filter Banks via Successive Convex Approximation

Abstract

This letter presents an efficient algorithm to design an M-channel oversampled graph filter bank, whose overall performance is governed by the spectral characteristic of the filters and the reconstruction error. The design of the filters is formulated into a constrained optimization problem that minimizes the stopband energy of the filters subject to the reconstruction error constraint. The problem is a non-convex quadratically constrained quadratic program (QCQP), which is typically NP-hard. In order to overcome this challenge, we apply the successive convex approximation to successively solve it. At each iteration, the non-convex QCQP is approximately transformed into the convex one by linearizing the constraint. Numerical examples and comparison are included to show that the proposed approach can lead to the oversampled graph filter banks with satisfactory overall performance, particularly good spectral selectivity.