Two-dimensional nonseparable multiwavelet transform and its application

Two-dimensional compactly supported, orthogonal non-separable multiwavelets and filter-banks are presented. We investigate the general subset of multiwavelets with a corresponding polyphase matrix that can be factored as a product of degree-1 factors in one variable. We consider in particular multiwavelets with vanishing moments. The number of vanishing moments that can be achieved increases with the increase in the McMillan degrees of the multiwavelet polyphase matrix. We design multiwavelets with vanishing moments by solving a set of nonlinear constraints on the free parameters defining the multiwavelet polyphase matrix. Design examples are given for the quincunx sampling scheme. We also show that imposing the requirement of linear phase in the case of order-factorable multiwavelets, imposes a simple constraint on each of its polynomial order-1 factors. We thus obtain a simple and complete method of constructing orthogonal order-factorable multiwavelets with linear phase. Finally, the application of the multiwavelet transform in image coding and compression is presented