A novel optimization design approach for Contourlet directional filter banks

Abstract

A Contourlet transform, an expansion of a wavelet transform, is a double filter bank structure composed of Laplacian Pyramid and directional filter banks. Several wavelet filters of preferable performance have been developed for wavelet transforms, e.g. CDF (Cohen, Daubechies and Feauveau) 9/7 filter. However, there is still only a limited number of wavelet filters applicable for Contourlet transforms. Therefore, it has become an urgent issue to find effective contourlet filters and design methods in the field of multiscale geometric analysis. In order to design a new directional filter bank for Contourlet transforms, this paper uses parametric modeling to obtain a novel PKVA (See-May Phoong, Chai W. Kim, P. P. Vaidyanathan, and Rashid Ansari) filter, by first implementing Chebyshev best uniform approximation, and then reaching the optimal solution by means of Parks-McClellan algorithm. Using Brodatz standard texture image database for test images, and using image denoising treated with hidden Markov tree (HMT) models in the Contourlet domain, the optimal PKVA filter was obtained on the basis of the peak signal to noise ratio (PSNR) maximum criterion with human visual properties considered. Experiment results show that the image denoising performance of our filter is better than that of Po and Do’s. The PSNR obtained from the experiment is 1.011449 higher than that of Po and Do’s in average. Therefore, Contourlet transforms using the proposed PKVA filter as DFB can ensure that the local error in images is of a uniform minimum value, and that good overall visual effect can be achieved.