Multiscaling Functions And Multivariate Wavelet Frames

It is well-known that compactly supported orthogonal symmetric waveletwith dilation factor d=2 is Haar basis. There does exist multiwavelet whichsatisfy all this properties. At present, constructing multiwavelet with nice prop-erties becomes hot. But the approach is not as mature as the classical wavelet.This paper presents an algorithm for the construction of compactly supportedorthogonal symmetric multiwavelet. It can reach desired vanishing moments.By applying dual convolution, we obtain nice multivariate wavelet frames. Theapproximation order is higher than respect convolution.In Chapter 1, we brie?y introduce the history and the international situa-tion of the research in wavelet analysis, and the main results of this paper.In Chapter 2, we focus on the basic theories of wavelet, multiwavelet andrelated notions.In Chapter 3, with the help of a special mask and polynomial, construc-tion of compactly supported orthogonal symmetric multiwavelet with vanishingmoments becomes simple and practicable.In Chapter 4, based on MEP, we give an approach to construct multivari-ate bi-frames using dual convolution.