贝叶斯估计和尺度空间滤波相结合的滤波方法

提出了一种贝叶斯估计和尺度空间滤波相结合的滤波方法。信号的小波系数表现出很强的非高斯统计特性，其密度函数可以用推广的拉普拉斯先验分布建模。利用贝叶斯估计能够较好地提取出信号的小波系数，再由小波逆变换恢复信号。贝叶斯估计较好地保留了信号的边缘信息，但滤波信号尚不够平滑。尺度空间滤波在保留信号边缘的同时，还有很好的平滑作用。两者相结合有很好的滤波效果。

A Method of Denoising Using Jointing Bayes Estimation and Scale Space Filtering

This paper proposes a method of denoising by the use of jointing Bayes estimation and scale space filtering. The wavelet coefficients of signals have highly non-Gaussian statistics that may be modeled with generalized Laplacian distributions. At first the noisy signal is decomposed by orthogonal wavelet transform, and Bayes estimators can extract the wavelet coefficients of original signal. Then an inverse wavelet transform is used to reconstruct signal. The denoised signal can preserve the edge's location and shape of the original signal, but it is not smooth enough. To overcome the deficiency, the scale space filtering is used in subsequence. This method can smooth the denoised signal estimated by Bayes estimator, and also preserve edges. By jointing these two methods, the performance of denoising is excellent.