一种基于组合赋权法的小波去噪质量评价方法  

A quality evaluation method for wavelet denoising based on combinatorial weighting method

作　　者：李晋斐 赵冬青[1] 王栋民 蔡聪聪 贾晓雪 张乐添 LI Jinfei;ZHAO Dongqing;WANG Dongmin;CAI Congcong;JIA Xiaoxue;ZHANG Letian(Institute of Geospatial Information,Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]信息工程大学地理空间信息学院,郑州450001

出　　处：《北京航空航天大学学报》2023年第3期718-725,共8页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金(41774037)。

摘　　要：针对传统质量评价指标在小波阈值去噪中理论依据不足的问题,提出了一种基于组合赋权法的小波去噪质量评价方法,能够为小波去噪参数的选择提供有效评价。通过分析在真值未知情况下均方根误差(RMSE)、信噪比(SNR)、平滑度等单项指标的特点,选取RMSE与平滑度作为小波去噪指标,对其进行归一化处理,采用信息熵权与变异系数的方法进行组合赋权,将归一化指标与对应权值线性组合,得到一种新的指标即为复合评价指标,其值越小,说明去噪效果越好,所选参数越优。仿真实验表明,在真值已知情况下,该评价指标具有更高的准确性,能够适用于不同的分解层数与小波基函数,具有比传统方法更好的适用性;实测数据表明,所提方法得出的小波去噪峰值域更加光滑,波形更加平稳,去噪效果更佳。Addressing such a problem with the traditional indicator system for quality evaluation as an insufficient theoretical basis for wavelet threshold denoising,a combination weighting approach-based method for evaluation of wavelet denoising quality is proposed with the expectation of effectively evaluating the selection of wavelet denoising parameters.Through analysis of characteristics of individual indicators such as root-mean-square error(RMSE),signal-noise ratio(SNR)and smoothness with the truth-value unknown,RMSE and smoothness are selected as wavelet denoising indicators.They are first normalized,then processed with information entropy and coefficient of variation for combination weighting,and,in the end,linearly combined with the corresponding weights to produce a new indicator,i.e.,the composite index.A smaller composite index indicates better denoising effect and better parameters selected.According to a simulated experiment,the index outperforms the conventional approach in terms of accuracy given the truth-value and is applicable to various decomposition levels and wavelet base functions.According to experimental data,this method achieves smoother wavelet denoising peak regions,steadier waveforms,and a better denoising effect.

关 键 词：小波阈值去噪 质量评价指标 均方根误差 平滑度 组合赋权 惯性元件随机误差 

分 类 号：V249.3[航空宇航科学与技术—飞行器设计] P227.9[天文地球—大地测量学与测量工程]