Two-Dimensional Orthogonal Filter Banks with Directional Vanishing Moments

We present two-dimensional filter banks with directional vanishing moments. The directional-vanishing-moment condition is crucial for the regularity of directional filter banks. However, it is a challenging task to design orthogonal filter banks with directional vanishing moments. Due to the lack of multidimensional factorization theorems, traditional one-dimensional methods cannot be extended to higher dimensional cases. Kovačević and Vetterli investigated the design of two-dimensional orthogonal filter banks and proposed a set of closed-form solutions called the lattice structure, where the polyphase matrix of the filter bank is characterized with a set of rotation parameters. Orthogonal filter banks with lattice structures have simple implementation. We propose a method of designing orthogonal filter banks with directional vanishing moments based on this lattice structure. The constraint of directional vanishing moments is imposed on the rotation parameters. We find the solutions of rotation parameters have special structure. Based on this structure, we find the closed-form solution for orthogonal filter banks with directional vanishing moments.