Study On Wavelet Theory And Its Algorithms For Image And Signal Processing

Wavelet analysis is a novel research field in the world. To study the new theory, methods and applications of wavelets is of great theoretical significance and practical value. This paper aims to consummate the wavelet theory, present some new algorithms and develop the new scopes of wavelet applications. The main results include:Two fonns, the matrix form and the convolution form, for the realization of the wavelet fast algorithm are discussed in detail. An analysis is made on the influence of the wavelet bases on practical applications by studying their mathematical properties. A method for constructing orthonormal wavelet bases from tight frames is presented. A rank 3 wavelet basis and its corresponding filter coefficients are constructed by analyzing the properties of rank M wavelet.To overcome the difficulty of reconstructing wavelet coefficients in the modulus maximum denoising, this paper presents a new piecewise cubic spline interpolating (PC SI) algorithm, with which the wavelet coefficients can be reconstructed fast and efficiently. A threshold filtering algorithm based on the region relativity of the wavelet coefficients is presented to overcome the disadvantage of the relativity-based algorithm available which is inaccurate in computing the relativities of the deflected wavelet coefficients. To avoid the discontinuity caused by using the hard-thresholding model and the biased estimation caused by using the sofi-thresholding model, we present three improved models of threshold estimation. These three models are: polynomial interpolating model, compromise model (in between the hard-thresholding and softthresholding models), and the modulus squared model.A variation formula of Poisson noise with the decomposition scale in waveletdomain is derived and then a local wavelet-domain multiple filtering algorithm is presented. According to the property of Film-grain noise, we compute and obtain an optimal filtering operator in transform domain by minimizing the mean square error between the estimated signal and the original signal, which makes the threshold selfadaptive.A peak-value detection algorithm with the wavelet transform is given, which can be used for exact pitch detection and accurate Chinese tone recognition. And the following three algorithms are presented respectively: an embedded and detection algorithm of audio digital water marking with the wavelet transform, a wavelet phase filtering algorithm for image noise removal, and a new method for multiscale imagedata fusion based on the wavelet transfonn. Besides, the wavelet packet method is used, for the first time, to detect the gastric motility and the wavelet transform method is used, for the first time, to remove the grid texture and enhance the image in solar radio bursts. The experimental results show that all the methods presented in this paper are efficient and practical.