Bi-orthogonal filter banks with directional vanishing moments [image representation applications]
In this paper we study 2D nonseparable filter banks that annihilate information along a certain discrete direction. This is done by having filters with directional vanishing moments (DVM). We study the approximation property of such filters and the design problem providing conditions for its solvability. In particular, we completely characterize the solution and propose a design procedure utilizing the mapping technique. Nonlinear approximation experiments with the contourlet transform indicate that compared with the traditional filters, the new filters designed with DVM provide gains in SNR and visual quality due to their short size.