Fuzzy Entropy and Its Application for Enhanced Subspace Filtering

Fuzzy entropy (FuzzyEn), which employs the fuzzy probability to characterize the similarity between vectors, is a robust nonlinear statistic to quantify the complexity or regularity of nonlinear time series. The aim of this study is to investigate the statistical properties of FuzzyEn and improve the subspace denoising technique using FuzzyEn. We first show the asymptotic normality of FuzzyEn and derive its variance for finite sample behavior. We then analyze the two pending and fundamental issues in subspace denoising, i.e., depending on the so-called "noise floor" and the unaltered noise existing in signal subspace, from the point of view of fuzzy logic. A FuzzyEn-assisted subspace iterative soft threshold (FESIST) denoising method, which can effectively overcome the deficiency in the existing subspace filtering (SSF) techniques, is presented. The effectiveness of the method is first demonstrated on two synthetic chaotic series and then tested on real biological signals. The results demonstrate the superiority of the proposed method over existing SSF techniques, as well as the empirical mode decomposition and wavelet decomposition approaches.