Novel designs for nonsubsampled multiresolution directional filter banks and an extra finer directional wavelet transform

This paper presents two novel multirate tree-structure designs for a class of nonsubsampled, perfect reconstruction (PR) multiresolution directional filter banks (MDFBs). The proposed designs are simple and efficiently obtained from a combination of 2-D nonseparable filters and 2 by 2 upsampling matrices. The proposed MDFBs having one lowpass and six highpass directional subbands represent the oriented image features non-adaptively with complete shift-invariance. We also propose nonsubsampled design of an extra finer directional wavelet transform (EFiDWT), with one lowpass and twelve highpass directional subbands. The proposed designs can have efficient implementations with the notion of generalized separability. The efficacy of the proposed designs are tested for image denoising application that uses simple hard thresholding technique.