On aliasing effects in the contourlet filter bank

The pyramidal directional filter bank (PDFB) for the contourlet transform is analyzed in this paper. First, the PDFB is viewed as an overcomplete filter bank, and the directional filters are expressed in terms of polyphase components of the pyramidal filter bank and the conventional DFB. The aliasing effect of the conventional DFB and the Laplacian pyramid to the equivalent directional filters is then considered, and the conditions to reduce this effect are presented. Experiments show that the designed PDFBs satisfying these requirements have the equivalent filters with much better frequency responses. The performance of the new PDFB is verified by non-linear approximation of images. It is found that improvement of 0.2 to 0.5 dB in PSNR as compared to the existing PDFB can be achieved.