基于单纯形-模拟退火算法的小波阈值去噪研究

Wavelet Thresholding Denoising Based On Simplex-Simulated Annealing Algorithm

阐述了小波分析去除信号噪声的原理和方法,其中阈值的选取将直接关系到信号去噪的质量。本文基于广义交叉验证准则(GCV)求解阈值的基础上,提出了利用单纯形—模拟退火算法来求得小波变换各子带最优阈值,计算时无需噪声方差等先验信息,同时该方法不依赖初始阈值的选取,既获得了全局最优解,又提高了搜索效率。最后通过Matlab程序实现了小波变换的噪声抑制仿真分析,实验结果表明,与常规的4种阈值选择方法(Rigrsure、Sqtwolog、Heursure、Minimaxi)相比,本文算法确定的阈值进行小波去噪,其去噪效果无论是在信噪比(SNR)增益还是在均方根误差(RMSE)意义上均是最佳的。

Expounding the basic theory and method of removing noises from signals with wavelet analysis, the determination of the threshold has an impact on the quality of removing noises from signals. This paper presents an new method based on generalized cross validation （GCV）, it can get optimal thresholds of every wavelet subband by using the method of simplex-simulated annealing algorithm without requiring the prior knowledge of the noise variance, at the same time this method is independent of the choice of initial threshold, and it not only gets the global optimum, but also enhances searching efficiency. And then using Matlab to realize simulation of wavelet denoising by programming, the results show that the threshold in this paper is excellent compared with four threshold selection rules （Rigrsure,Sqtwolog. Heursure,Minimaxi）, and it gives better SNR gains and RMSE performance of denoising effects.