Symmetric Construction of Biorthogonal Multiwavelets with Short Sequences

This paper presents a novel approach for constructing symmetric compactly supported biorthogonal multiwavelets with short sequences. Starting from the symmetric properties of scaling and wavelet functions, parameterized symmetric forms of the polyphase matrices can be derived, which greatly simplify the construction problem of compactly supported biorthogonal multiwavelets. Moreover, according to the perfect reconstruction matrix equations, the parameters of polyphase matrices can be reduced, which finally leads to our proposed algorithm for the construction of symmetric compactly supported biorthogonal multiwavelets with short sequences.