Wavelet Denoising Based On Adjacent Dependencies

Recently, wavelet denoising has been widely used in many fields of theory and application. As a new denoising method, there still exist some issues. In this dissertation, based on the stationary wavelet transform (SWT), different dependencies among wavelet coefficients are studied in denoising. The fast algorithm of SWT and new wavelet denoising methods are developed and proposed respectively. The main contributions are as follows:1. The factorizing algorithm of SWT using lifting scheme is implemented. SWT can be obtained with a finite number of alternating lifting and dual lifting steps starting from the lazy wavelet, using the equivalent relation of position-swapping between up (down) sampler and filter. Furthermore, we present that the lifting factorization can reduce almost a half of computational burden of the standard algorithm. Moreover, SWT possessing arbitrary vanishing moments can be constructed by lifting and some examples are presented.2. Considering joint inter- and intrascale dependencies of wavelet coefficients, multiscale product in cone of influence is constructed. For magnitude and different multiscale products, we compare their abilities to distinguish between noise and useful signal by using statistical decision theory. Further analyses show that the performances of significant measures depend on the energy ratio of noise to signal. For relatively high ratio, the multiscale product can provide a better separation between noise and useful signal, whereas the opposite is true for small ratio.3. Regarding noisy items of multiscale product as the convolution of noise wavelet coefficient and a certain filter, then using the linear filter theory, the variance of noisy items of mutiscale product can be obtained. Thus the threshold applying to multiscale product is determined. According to the formation of multiscale product the soft thresholding method is proposed. The analyses of the mean square error (MSE) characteristics show that the MSE of the hard thresholding method will be larger than that...