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Minimax design of orthogonal filter banks with sparse coefficients

In this paper, we propose a new method for the design of a class of orthogonal filter banks with sparse coefficients in the minimax sense. We first formulate a design problem based on the minimization of the reweighted L1-norm of the filter bank coefficients subject to the perfect reconstruction (PR) and vanishing moments (VM)). As the PR constraint is nonconvex, we initialize the coefficients of the filter bank to transform the design problem into a convex one. Finally, we give several examples to illustrate the effectiveness of the proposed sparse design method as opposed to the nonsparse version.