随机过程的小波变换及其在信号处理中的应用

We do the research of wavelet transform of nonstationary 1/f fractal stochastic.processes and its application which based on the engineering background of.stochastic signal processing in electronic information.Because wavelet transform is an approximate whitening filters for 1/f Processes ,we use this principle to estimate the waveform of nonstationary 1/f fractal stochastic signal with color noise.We found.that wavelet basic function have very strong influence on the effect of Kalman Filtering. The correlation of wavelet coefficients of orthogonal wavelet basis with high order.disappeared moments decay fast, thus wavelet filter has better whitening effect and the effect of Kalman Filtering is better too. On the other hand, we note that the variance of.wavelet coefficients is an energy of nonstationary 1/f fractal stochastic signal in local frequency domain. By using the infrared catatrophe phenomena of 1/f fractal stochastic signal, we present an optimum threshold method based on the minimum mean-square to.compare with Kalman Filtering. This threshold method do not need to estimate variance of signal when estimate the waveform of nonstationary 1/f fractal stochastic signal At the same time, we provide a method of determining the wavelet decomposition. This method makes signal estimation more easily. Besides, we use the stability of Order Statistics to study parameter estimation of stochastic processes , to construct nonlinear.Order Statistic Filter and applied it to image processing. Relevant papers have register by SCI(1paper)and EI(3papers) respectively.

以随机过程理论为基础的随机信号处理是数学与信息科学的重要交叉领域，具有自相似性及长程相关性的非平稳1/f类分形随机过程在信号处理中有着广泛应用。本项目旨在将1/f类分形布朗运动纳入经典白噪声分析框架，通过广义函数的小波变换探索无穷维高斯空间按频谱特征进行的分解，为实施相关观测噪声中随机信号的检测与估计提供一个高起点的理论框架。