Gao J B, Yang H, Hu X Y, Hu D C
Department of Automation, Tsinghua University, Beijing 100084, China.
Guang Pu Xue Yu Guang Pu Fen Xi. 2001 Oct;21(5):620-2.
In the filed of wavelet denoising, an essential problem is how 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 probability 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.
在小波去噪领域，一个关键问题是如何确定小波系数的截止阈值，该阈值能分别划分出对应信号和噪声的系数。这里讨论的小波去噪方法通过运用信息论的最大熵原理（MEP）来确定此阈值。从概率论的基本原理可以推断出，任意分布的随机噪声序列的小波细节系数序列服从正态分布。基于这一结论，利用最大熵原理确定一个最优阈值。使得绝对值小于该阈值的系数服从正态概率分布。从统计学角度看，这个阈值是区分信号和噪声的小波系数的最优值。使用光谱数据的仿真分析以及与其他方法的比较表明，该方法能实现信噪比的最佳提升，并且其性能对信噪比变化的敏感度最低。
