The Theory Of Multiwavelet On The Interval And Its Application In Image Compression

Multiwavelet theory is the new development of wavelet theory. Multiwavelet can satisfy orthogonality, symmetry, compact support and high-vanish moment at the same time, so it has better properties than those of traditional wavelet. Compared with the multiwavelet in L2[R], multiwavelet on the interval [0,1] can process the signals defined on the interval more efficiently. As the supplementary to the multiwavelet theory, in this paper, we firstly get some basic results about the construction of multiwavelet, then we emphasize to study the parameterized construction of multi-scaling functions and multi-wavelet functions, and discuss their properties such as orthogonality, symmetry and balance. In the end, we get some bananced multiwavelets on the interval.The most important aspect of multiwavelet application is using it for image compressing. Multiwavelet is corresponding to vector filter, therefore, it has its own characteristic in image processing. In the fourth chapter, we compress some Lenna image using our wavelets on the interval, the results of experiments indicatethat the multiwavelets constructed by us are correct and their properties are good.