Design and Application of a New Multiscale Multidirectional Non-subsampled Filter Bank

We propose a new method for design of computationally efficient nonsubsampled multiscale multidirectional filter bank with perfect reconstruction (PR). This filter bank is composed of two nonsubsampled filter banks, for multiscale decomposition and for directional expansion. For multiscale decomposition, we transform the 1-D equivalent sub band filters directly into 2-D equivalent sub band filters. The computational cost is considerably reduced by avoiding the computation of 2-D convolutions. The multidirectional decomposition utilizes fan filters. A new method for design of 2-D zero phase FIR fan filter transformation function is developed. This method also aids the transformation of a 1D filter bank to a 2-D multidirectional filter bank. The potential application of the proposed filter bank is illustrated by comparing the image denoising performance of the proposed filter bank with other design method that exist in available literature.