Design of nonsubsampled directional filter banks with arbitrary number of channels

This paper studies a novel method for creating M-channel nonsubsampled directional filter banks (DFBs). It is based on the pseudo-polar Fourier transform (PPFT) which evaluates the Fourier transform at points along rays equispaced in slope. We take some modifications on the arrangement of the euqispaced rays, making the two-dimensional (2D) PPFT grid to the Cartesian 2D discrete-Fourier transform grid. Then we apply one-dimensional (1D) filter banks (FBs) to the arranged PPFT along the slope direction. This can perform the decomposition of images into arbitrary directionally-oriented subbands. By using this method, the design of DFBs is reduced to that of 1D FBs, leading to the low design complexity and good design flexibility. Furthermore, by combining the proposed DFBs with Laplacian pyramid, we can achieve a multiscale and multidirection system. Experimental result is given to illustrate the proposed approach.