Construction And Application Of Four - Band Wavelet - Tight Frame

The research of wavelets construction method has always been an important issue for wavelet analysis theory. This article will discuss the construction of the four-band wavelet tight frame, and focus on a improved method of constructing the tight frame wavelet through PR conditions and the filter structure, in addition,we study its application in Graphics and Image Processing combining the image fusion technolo-gy. The thesis is divided into five parts:Chapter1is the introduction, in which it describes the current development of wavelet analysis and the basic concepts of wavelet analysis theory.Chapter2outlines the concepts and related properties of the wavelet frames,frame multiresolution analysis (FMRA),the relationship between the two scales, four-band wavelet tight frame and the multi-band wavelet frame.It will lay a theoretical foundation of constructing four-band wavelet tight frame.In chapter3,we will concentrate in how to construct a four-band wavelet tight frame,and propose a approach of constructing the four-band wavelet tight frame filterbanks of eight filters by the perfect reconstruction condition,and then we generate wavelets.Chapter4is the application of the four-band wavelet tight frame.In this section,we describe some of the main applications and advantages of the four-band wavelet tight frames,and focus on the application in image fusion techniques.Chapter5is a summary and outlook of the article, it gives a new direction to explore on the basis of the conclusion.