Wavelet Transform And The Application In Image De-Noising And Compress Coding

Wavelet transform has been looked as a powerful analytic tool and method. It becomes more and more important not only in the theory field—mathematical in which it has built a new division but also in more application fields—signal processing, image processing, model distinguishing, quantum physics and more non-linear processing. This dissertation focuses on the research of wavelet transform and the applications of image de-noise and compress.This dissertation is divided into six chapters. Chapter 1 introduces research background and main work of this paper. Chapter 2 describes the wavelet transform theory in details. In this chapter, three kinds of signal transform methods were compared: Fourier Transform, Gabor Transform and Wavelet Transform. And the property of Guassian Function and Gabor Transform were shown in details. In chapter 3, some important properties of wavelet transform were investigated. Two main kinds of wavelet: orthogonal wavelet and bi-orthogonal wavelet, are used to show the performances of scales function and wavelet function in the time-domain and frequency-domain. Chapter 4 introduces the theory and methods of threshold de-noising in wavelet domain. And in this chapter, some newmethods—Bayes shrink, MDLQ threshold and Context Threshold are shown in details,followed by they were simulated with the computer based on the Matlab. Chapter 5 introduces some compress methods. And the Zerotree method is simulated. Conclusions are drawn in Chapter 6. Some further research on wavelet transform threshold de-noising and compress are also discussed.