Micorlocal filtering using wavelet and local multiresolution analysis

1.小波和块奇异值图像处理：提出了一种新的混合方法，包括离散小波变换和样条块SVD去噪过程，并用于去除图像中的高斯噪声。滤波是基于消除由加性高斯白色噪声或其他类型的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。提出了一种新的基于小波变换的线性定常系统辨识方法，并给出了基于平稳小波变换的离散化公式.使用时频分析的盲源分离：盲源分离问题对应于使计算机能够以令人满意的方式解决鸡尾酒会问题的方法。讨论了一种基于时频信息的空时混合信号盲分离方法.广义Sobolev空间中的多小波：在广义Sobolev空间中引入了一类r-正则多小波，并给出了相应的符号和定义。得到了该正交规范系统的振动性。在广义Sobolev空间中定义了多小波的多分辨分析。

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.