自寻优阈值小波去噪方法

Wavelet Based De-noising Self-optimizing Method

  • 摘要: 针对阈值去噪方法中难以选取最优阈值的问题,提出了一种自寻优的最优阈值去噪方法。先论述了最优阈值是由信号与阈值函数共同决定的概念。在此概念上给出了自寻优方法的具体步骤,自寻优方法是把阈值作为从零到某一终值离散化的一组数,并从这些离散化的阈值中寻得最优的阈值。但此方法中终值的选取和阈值离散化带来过大的计算量成为其方法的难点。基于此问题,本文给出了解决方案并予以证明。通过试验中观察得到的高频死去值现象确定终值,通过单峰值现象及多分辨率中各空间独立原理等进行了计算量的简化。试验结果表明,此算法得到了更高的信噪比、更低的均方根误差和更光滑的外观。

     

    Abstract: According to threshold de-noising algorithm to select the problem of proper threshold, this paper put forward a self-optimizing algorithm of optimal threshold. This paper discusses the optimum threshold concept and the optimum threshold is decided by signal and threshold function. Based on this concept, this paper provides the optimal method concrete steps, optimization method discrete threshold from zero to final value and from these discretization threshold can be found the optimal threshold. However, large calculated amount become the problem of the method. Based on this problem, this paper gives the solvable methods and proves it. Through the dead value of high frequency phenomenon that is observed by experiment fix the final value, and through single peak phenomenon and multi-resolution analysis simplify the method. Experiments show that the proposed method improves the signal-to-noise ratios and reduce the root mean square error. Moreover, the de-noising signals have smooth and visual appearance.

     

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