Biorthogonal unconditional bases of compactly supported matrix valued wavelets

In this paper, we introduce the concept of biorthogonal matrix valued wavelets. We elaborate on perfect reconstruction matrix filter banks which are assembled by matrix FIR filters and we deduce that the resulting matrix valued wavelet functions have compact support. Moreover, we form biorthogonal unconditional bases for the space of matrix valued signals. To validate the theory, a class of biorthogonal and orthonormaI matrix valued wavelets are given. The connection of the present scheme with the theory of multiwavelets are also explored.