Research Of Morphological Wavelets And Its Application

Because of a well time-frequency quality and transform mechanism according to Human Vision System, Wavelet transform has acquired a great deal of applications in image processing, image denosing, pattern recognition and many other research fields. But classical wavelet transform is a tool of linear signal analysis, the linear approximation cannot describe its primary characters in many cases, so the theoretic importance and application potentiality of nonlinear multi-resolution analysis in signal processing have been recognized recently. J.Goutsias introduced the concept of morphological wavelets in 2000, Morphological wavelets based on mathematical morphology is a new research direction in the theory of nonlinear wavelets,which unified most of linear and nonlinear wavelets and formd a uniform multi-resolution analysis frame.This dissertation funded by National Natural Science Foundation (60473015)――Research on fast algorithms in high-performance computation and its applications, emphasizes the research of morphological wavelets and its application to the problems that are not well solved in image processing. We give a brief reminder of basic concepts of mathematical morphology and of the pyramid transform and non-linear multi-resolution analysis, and then present an axiomatic framework to wavelet multi-resolution signal decomposition schemes.We construct and extend the algorithem of morphological wavelets based on these theories mentioned above and non-linear character of morphological operactor. At last, the paper introduces a new morphological wavelets based on slant transform, it provides a more vivid way to handle image. According to the numerical experiment in Matlab and VC, the result of the image compressing shows that this scheme is more satisfactory and efficient contrast to the wavelet introduced by existing literatures.