Study On Wavelet Analysis And Its Application To Signal And Image De-noising

Wavelet analysis is a rapidly developing and novel subject. Nowadays, it has been widely used in practical applications. To study the new theory, methods and applications of wavelets is of great theoretical significance and practical value. This dissertation aims to consummate the wavelet theory, present some new wavelet de-noising algorithms and develop the new scopes of wavelet applications. The thesis mainly includes the following aspects:The fundamental theories of wavelet analysis are discussed in detail. Continuous wavelet transform, discrete wavelet transform and dyadic wavelet transform are introduced. The fast algorithm of discrete dyadic wavelet transform is given. Finally, an analysis is made on the influence of the wavelet bases on practical applications by studying their mathematical properties.The principles of wavelet transform modulus maxima de-noising method are introduced in detail , an analysis of the choice of some parameters in the process of de-noising is made in detail,and some choice grounds are given. Some key problems on de-noising method based on wavelet threshold are discussed in detail , and some improvement schemes are proposed, and the simulation testing has proved the effectiveness of the schemes. A combination de-noising algorithm based on the spatial correlation-based algorithm is presented, the experimental results show that the filtered wavelet coefficients in the proposed algorithm have the advantages of good continuity, high accuracy and convenience for signal reconstruction.An image de-noising method of wavelet thresholding based on generalized cross validation (GCV) is discussed in detail. And an image de-noising method of Adapt Bayes Shrink threshold based on Bayes Shrink threshold is presented.The experimental results show that both the methods above-presented are efficient and practical.