The Wavelets Transform Based On Non-sinusoidal Matrixes And Application

A variety of wavelets are widely used in the fileds of signal processing and image processing as a mature Multi-Resolution Analysis(MRA) method.However,in many situations, traditional wavelets can not meet the entire need.For example,all traditional wavelets except Haar wavelet do not have all qualities of wavelets. Comparing traditional wavelets,the M-bond wavelets and multiwavelets can have all the qualities of wavelets.So they arouse many attentions of the researchers.Walsh matrix and Slant matrix are the non-sinusoidal matrixes which have a close relationship with each other.They are both the wavelet matrixes.We construct two kinds of wavelet.One is M-Band Haar wavelet and Slant Haar Wavelet.The other is M-bond multiwavelet based on parametric slant matrix.The filter banks of these M-bond multiwavelets are conveniently generated by parametric Slant matrixes.The filter banks are very flexible by being choosed some proper parameters.This paper also has two numerical tests.In the first test, the paper decompose texture images into some parts with M-Band Haar wavelet and Slant Haar Wavelet,then extract texture features and classify texture based on the minimum distance classifier.In the other test, the paper apply M-bond multiwavelet base on parametric slant matrix to image denoising based on threshold and get a satisfactory result.