基于空域相关的优化阈值函数滤波算法及其虚拟实现

A Filtering Algorithm of Optimal Threshold Function Based on Spatial Correlation and Its Virtual Realization

基于静态小波变换,将小波系数间的相关性应用于阈值滤波,提出并虚拟实现了基于空域相关的优化阈值函数滤波算法.在构造出基于空域相关的显著性函数和基于显著性函数的阈值滤波过程的基础上,提出了基于空域相关的优化阈值函数,并把极小化广义交叉验证得到均方差意义下的最优阈值用于该优化阈值函数.仿真和实验结果表明,基于空域相关的优化阈值函数滤波算法不仅能够有效去除噪声,而且也能完好地保留信号的重要特征,适用范围宽,滤波效果好,在很大程度上抑制了噪声和谐波,具有良好的滤波性能.

A correlation among wavelet coefficients based on stationary wavelet transform was applied to thresholding filtering. A filtering algorithm of optimal threshold function based on spatial correlation was presented, and its virtual realization was achieved. In the process of construction, based on significance measure function of spatial correlation and the threshold function filtering of significance measure function, an optimal threshold function on the basis of spatial correlation was proposed. The optimal threshold function, in the sense of mean square error （MSE） obtained through minimizing generalized cross validation （GCV）, was applied to this optimal threshold function. The simulations and experiments show that this method can not only remove noises effectively, but also preserve the original features of the signal. As a result, it inhibits noises and harmonics to a great extent with good filtering effects and it will have a broad range of applications.