Micorlocal filtering using wavelet and local multiresolution analysis

1. 小波和分块奇异值图像处理：提出了一种由离散小波变换和样条分块奇异值图像去噪组成的混合方法，并将其用于去除图像中的高斯噪声。滤波的基础是消除加性高斯白噪声或其他类型噪声引起的奇异值和奇异向量的变化。小波分析在系统辨识中的应用：推导了利用小波变换获取核分布时频信息的公式。提出了一种基于小波的定常线性系统辨识新方法，并利用平稳小波变换将其离散化。采用时频分析的盲源分离：盲源分离问题对应的是一种使计算机能够满意地解决鸡尾酒会问题的方法。讨论了一种基于时频信息的时空混合盲源分离方法。广义Sobolev空间中的多小波：在广义Sobolev空间中引入了一类正则多小波，并给出了相应的符号和定义。得到了正交系统的振荡性质。定义了广义Sobolev空间中多小波的多分辨率分析。

1. Wavelet and block singular value image processing: A new hybrid method consisting of a discrete wavelet transform and a spline block SVD denoising procedure is proposed and used to remove Gaussian noise from images. Filtering is based on eliminating changes in singular values and singular vectors caused by additive Gaussian white noise or other types of noise.2. Applications of wavelet analysis to system identification: Formulae using wavelet transform to access time-frequency information of kernel distributions are deduced. A new wavelet based system identification method for time-invariant linear systems and its discretized formula using stationary wavelet transform are proposed.3. Blind source separation using time-frequency analysis: The blind source separation problem corresponds to a way to enable computers to solve the cocktail party problem in a satisfactory manner. A blind source separation based on time-frequency informations for spatio-temporal mixture problems is discussed.4. Multiwavelets in generalized Sobolev spaces: A class of r-regular multiwavelets is introduced with appropriate notation and definitions in generalized Sobolev spaces. The oscillation properity of the orthonormal system is obtained. A multiresolution analysis for multiwavelets is defined in generalized Sobolev spaces.