基于无偏风险估计方法的信号稀疏性分析

Signal Sparseness Analysis Based on Unbiased Risk Estimation Methods

信号的稀疏表示已成为信号处理中的重要方法.利用统计学中的无偏风险估计方法,提出了确定零化阈值δ的方法,使得我们能够根据实际问题,科学合理地把小于δ的元素视为零,从而计算其稀疏度并判别是否稀疏.通过大量的数值实验,结果表明,该方法对规范和统一信号稀疏表示的度量问题以及解决大数据问题具有重要意义.

Signal sparse representation has become an important method of signal processing.In this paper,using unbiased risk estimation methods in statistics,the method to determine zero thresholdδis proposed,which allows us to regard the less thanδelement as zero scientifically and legitimately according to practical problems.Thus the signal sparsity can be calculated and whether sparsity can be distinguished.Through a large number of numerical experiments,the results show that the proposed method is important to measurement problems of standardized and uniform signal sparse representation and problem solving big data.