New biorthogonal multiwavelets for image compression

Abstract

There has been a growing research interest in the areas of construction and application of multiwavelets over the past few years. In a previous paper, we introduced a class of symmetric-antisymmetric orthonormal multiwavelets which were constructed directly from orthonormal scalar wavelets. These multiwavelets were shown to perform better than existing orthonormal multiwavelets and scalar wavelets in terms of image compression performance and computational complexity. However, their performance still lags behind some popular biorthogonal scalar wavelets such as Daubechies' D(9/7) and Villasenor's V(10/18). This paper aims to address this shortcoming by extending our earlier work to the biorthogonal setting. Two methods of construction are introduced; thus resulting in previously unpublished symmetric-antisymmetric biorthogonal multiwavelet filters. Extensive simulations showed that these multiwavelet filters can give an improvement of up to 0.7 dB over D(9/7) and V(10/18), and yet require only comparable but often lower computational cost. More importantly, better preservation of textures and edges of the reconstructed images was also observed.