Study On New Methods Of Signal Processing Based On Stable White Noise

This dissertation briefly introduces the statistical characteristics of stable distribution and proposes a new spectral density different from power spectrum density of second order processes. Thus a new concept of stable white noise and a method of whitening based on covariation sequence and the fractional order spectrum--covariation spectrum under alpha-stable conditions are obtained. According to parameter model of stable distribution, we discuss a new frequency domain whitening method based on alpha spectrum. Methods of whitening based on generalized Yuler-Walker equation and prediction deconvolution and PAR nonlinear model are also get.A new adaptive mixed moments filtering algorithm and a new adaptive generalized recursive least p-norm filtering algorithm based on SaSG noise model are obtained. This dissertation discusses a new adaptive generalized recursive least p-norm Kalman filtering algorithm based on innovation process with infinite variances and improves and analyzes its robustness and performances. A new adaptive filtering algorithm based on median orthogonality criterion and adaptive recursive least mean p-norm lattice filtering algorithm and a new adaptive filtering algorithm based on minimum error entropy criterion are also discussed.This dissertation discusses a new generalized least mean p-norm beamforming method based on the matrix diagonal loading and the leakage iteration. What's more, a new beamforming method based on the fractional lower order covariance matrix under alpha-stable interference conditions is analyzed. Furthermore, a new method of DOA estimation based on the fractional order correlation is discussed. The dissertation also discusses a new method of 2-D direction finding for underwater 2-D source localization using a vector hydrophones array under alpha-stable noise conditions.Identifying algorithm of the independent components of an alpha-stable random vector for under-determined mixtures is discussed and the method is based on an estimate of the discrete spectral measure for the characteristic function of an alpha-stable random vector. The dissertation proposes neural network structures related to multilayer feed-forward networks for performing BSS based on fractional lower order statistics and subspace technique. This a new EP estimation algorithm based on minimum dispersion (MD) criterion and Givens matrix is obtained.This dissertation uses shot noise to model the speckle noise, analyzes and modeled the coefficients of 2-D multi-resolution wavelet decomposition of logarithmically transformed images using alpha stable distribution. Consequently, we obtain a new function of classifying the coefficients and a new noise-removal method based on multi-resolution wavelet decomposition and alpha stable model.