A general approach for analysis and application of discrete multiwavelet transforms

This paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms, particularly to image compression. First, we establish the concept of an equivalent scalar (wavelet)filter bank syst em in which we present an equivalent and sufficient representation of a mul tiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks. This relationship motivates a new measure called the good mu ltifilter properties (GMP's), which define the desirable filter characteris tics of the equivalent scalar filters. We then relate the notion of GMP's d irectly to the matrix filters as necessary eigenvector properties for the r efinement masks of a given multiwavelet system. Second, we propose a genera lized, efficient, and nonredundant framework for multiwavelet initializatio n by designing appropriate preanalysis and post-synthesis multirate filteri ng techniques. Finally, our simulations verified that both orthogonal and b iorthogonal multiwavelets that possess GMP's and employ the proposed initia lization technique can perform better than the popular scalar wavelets such as Daubechies'D8 wavelet and the D(9/7) wavelet, and some of these multiwa velets achieved this with lower computational complexity.