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.

中文翻译：

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模糊熵及其在增强子空间过滤中的应用


模糊熵（FuzzyEn）利用模糊概率来表征向量之间的相似性，是一种鲁棒的非线性统计量，用于量化非线性时间序列的复杂性或规律性。本研究的目的是研究 FuzzyEn 的统计特性并使用 FuzzyEn 改进子空间去噪技术。我们首先展示 FuzzyEn 的渐近正态性并导出其有限样本行为的方差。然后，我们从模糊逻辑的角度分析了子空间去噪中两个悬而未决的基本问题，即取决于所谓的“本底噪声”和信号子空间中存在的未改变的噪声。提出了一种FuzzyEn辅助的子空间迭代软阈值(FESIST)去噪方法，该方法可以有效克服现有子空间滤波(SSF)技术的不足。该方法的有效性首先在两个合成混沌序列上得到证明，然后在真实的生物信号上进行测试。结果证明了该方法相对于现有 SSF 技术以及经验模态分解和小波分解方法的优越性。