Application And Construction Of Orthonormal Symmetric Multiwavelets

We know that except of the Haar wavelet, the characters of compact support, symmetric(anti-symmetric) and orthogonality don't exit in a simple wavelet function at the same time, but it is very disadvantageous in the process of dealing with signals. To solve this question, we study the multiwavelet system. As we know, the theory of multiwavelet that possess the compact support, symmetric (anti-symmetric) and orthogonality is better than scalar wavelet, but there is no a good multiwavlet be found,so far. So, we propose a new method for generating multiwavelet system in this paper. For compactly supported symmetric-antisymmetric orthonormal multiwavelet systems, we first show that any length-(2N+1) multiwavelet system can be constructed from a length-2N multiwavelet system and vice versa. Then we present an example for the construction of the length-3 multiwavelet system directly from length-2 multiwavelet system. For the data preprocessed by prefilter more smooth and non-redundant, a class of prefilter based on approximation order and orthogonality is described in detail, and the construction of this prefilter is given in this paper. At last, we take the multiwavelet system generated by this paper in application on image denoising and obtain a good result compared with GHM multiwavelet and CL multiwavelet.