Optimal lifting wavelet filter bank design and image compression application

Abstract

The lifting scheme is an efficient tool to construct second-generation wavelets. It has been used to realize Daubechies wavelet transform in image compression standard JPEG-2000. Daubechies wavelets can provide better image coding performance than discrete cosine transform (DCT) which is used in JPEG because the wavelets can present signal more efficiently than DCT. However, for high compression rate, the details of the decompressed images in JPEG-2000 are degraded. The reason is that Daubechies filters are maximally flat while their frequency selectivity is very poor. In this paper, we present an efficient method for the optimal design of filter banks and wavelets based on the lifting structure. The design problem is expressed as an optimization problem where the frequency selectivity of filters is optimized for a given regularity order. The simulation results show that the filter banks designed by our proposed method can offer the coding performance improvement  compared to Daubechies filters in JPEG-2000.