Compactly supported matrix valued wavelets-biorthogonal unconditional bases

摘要

This paper introduces the concept of biorthogonal matrix valued wavelet bases. By elaborating on perfect reconstruction matrix filter banks which are assembled by matrix FIR filters, we form matrix valued wavelet functions with compact support such that they constitute unconditional bases for the space of matrix valued signals. To validate the theory, a class of unconditional biorthogonal and orthonormal matrix valued wavelets is given. The links of the present scheme with the multiwavelets' frame are also explored.