A Simple Method for Designing 2D M-Channel Near-PR Filter Banks with Linear Phase Property

摘要

Two dimensional (2D) nonseparable filter banks with linear phase (LP) are desired for image sub-band coding and compression. In this paper, we propose a method for designing 2D nonseparable filter banks with the LP and near perfect reconstruction (near-PR) properties. By combining the unimodular transformation and a separable |M|-channel LP filter bank, the design problem is simplified to that of two one-dimensional (1D) LP filter banks. For 1D case, a novel method by employing partial cosine modulation is used to design near-PR filter banks with LP analysis and synthesis filters. For 2D case, we cascade two 1D near-PR LP filter banks in the form of tree structure to design a separable LP filter bank. With the unimodular transformation, a nonseparable LP filter bank is obtained. In addition, the filter bank achieves the near-PR property without sophisticated nonlinear optimization procedures. Design example shows the efficiency and simplicity of the proposed method.