基于改进奇异谱分析的信号去噪方法

传统的去噪方法，比如小波阈值去噪，它只对高斯噪声有效，对于脉冲噪声却无能为力.近年来发展起来的奇异谱分析方法可以在高信噪比的条件下很好地滤除上述两类噪声，但该方法降噪过程涉及了一定的主观因素，并且受矩阵扰动理论的限制，该方法随着信噪比的降低，去噪能力也随之下降.针对上述情况，提出一种改进算法，将矩阵秩最小化理论应用于奇异谱分析方法中.仿真结果表明，改进算法去噪效果明显，能够最大限度降低信号均方误差，提高信噪比，增强奇异谱分析方法的通用性. 

Signal Denoising Method Based on Improve Singular Spectrum Analysis

The traditional denoising method, such as wavelet threshold, is only valid for Gaussian noise, but is powerless for pulse jamming. Singular spectrum analysis developed in recent years can be a good filter at high SNR conditions of these two types of noises, but the process of noise reduction involves a certain subjective factors, and is subject to restrictions of matrix perturbation theory. Moreover, the ability of denoising will decrease with the lower SNR. For the above situation, an improved algorithm was proposed, which applied rank minimization theory to singular spectrum analysis. Simulation results show that denoising effect of the improved algorithm is obvious, which can maximize the reduction of the mean square error of the signals and improve signal to noise ratio; enhance versatility of singular spectrum analysis.