基于自适应阈值函数的小波阈值去噪方法

摘要

De-noising is an important application field of the wavelet analysis. It has advantage over the traditional filtering methods for its well localized time and frequency property. A central issue in the signal de-nosing research is how to obtain a good balance between shrinking noise and preserving the signal singularity features. This paper presents a wavelet de-noising method based on an adaptive threshold function. By tuning the parameter of the threshold function, the noise wavelet coefficients are shrunk while the signal details are preserved as much as possible on the small scales of the wavelet transform, and on the other hand, the noise coefficients are removed to their maximum extent on a large scale. The simulation results of the blocks, bumps and signals corresponding to the sonar returns from underwater targets, demonstrate that the signal singularity features by adopting the proposed method are better preserved with significant advantage than the traditional threshold filtering method.%去噪是小波分析的一个重要应用领域，相对于其它方法，小波变换具有对信号时频局部性详细刻画的优势。在信号的去噪处理过程中，如何在削弱噪声的同时又最大限度的保留信号的奇异性特征是信号去噪研究的一个核心问题。该文提出一种基于自适应阈值函数的小波去噪方法，通过调整阈值函数实现在信号小波分解的细尺度上去除噪声的同时又尽量保留信号细节系数，而在宽尺度上最大限度地滤除噪声部分的小波系数。通过对blocks, bumps和水下目标回波信号的仿真实验证明，该方法和现有的阈值去噪方法相比，具有显著的优势，能够在滤除噪声的同时很好地保留信号的奇异性特征。