基于最大熵原理的小波去噪方法  

Maximal Entropy Principle Wavelet Denoising

作　　者：高建波[1] 杨恒[1] 胡鑫尧[2] 胡东成[1] 

机构地区：[1]清华大学自动化系,北京100084 [2]清华大学化学系,北京100084

出　　处：《光谱学与光谱分析》2001年第5期620-622,共3页Spectroscopy and Spectral Analysis

基　　金：清华大学博士论文基金 (编号 :980 7)

摘　　要：小波变换去噪中最关键的问题是如何确定小波系数的阈值 ,使其能够将与噪声和信号相对应的小波系数合理地区分开来。根据概率论的基本原理可以推断 ,随机序列的细节小波变换系数符合正态分布。基于此结论 ,可以利用最大熵原理确定一个阈值 ,使得绝对值小于此阈值的小波系数组成的序列符合正态分布。该阈值在统计意义下能够最佳地区分信号与噪声的小波系数。采用光谱数据的仿真分析以及与其他方法的对比实验证明 ,这种最大熵小波去噪方法不仅在提高信噪比方面显示出了其优势 ,而且去噪效果不易受信噪比变化的影响。In the filed of wavelet denoising, an essential problem is haw to determine the cutting threshold of wavelet coefficients that divides the coefficients corresponding to signal and noise respectively. The wavelet denoising method discussed here determines this threshold by using the maximal entropy principle (MEP) of information theory. From the basic principle of probalility theory, it can be deduced that the detailed wavelet coefficients sequence of an arbitrary distributed random noise sequence satisfies a normal distribution. Based on this conclusion, an optimal threshold is determined using MEP. Such that the coefficients whose absolute values are less than the threshold satisfies a normal probabilistic distribution. This threshold is an optimal value that distinguishes the wavelet coefficients of signal and noise in view of statistics. The simulation analysis using spectral data and the comparison with other methods showed that this method provides a best improvement of signal-to-noise ratio, and its performance is least sensitive to the change of signal-to-noise ratio.

关 键 词：小波系数 阈值 信噪比 红外光谱 最大熵原理 小波变换 信号处理 去噪 

分 类 号：O657.3[理学—分析化学] O174.2[理学—化学]