Abstract Conventional compressive sampling (CS) primarily assumes light-tailed models for the underlying signal and/or noise statistics. Nevertheless, this assumption is abolished when operating in impulsive environments, where non-Gaussian infinite-variance processes arise for the signal and/or noise components. This drives traditional linear sampling operators to failure, since the gross observation errors are spread uniformly over the generated compressed measurements, whilst masking the critical information content of the observed signal. To address this problem, this paper exploits the power of symmetric alpha-stable (S α S) distributions to design a robust nonlinear compressive sampling operator capable of suppressing the effects of infinite-variance additive observation noise. Specifically, a generalized alpha-stable matched filter is introduced for generating compressed measurements in a nonlinear fashion, which achieves increased robustness to impulsive observation noise, thus subsequently improving the accuracy of traditional sparse reconstruction algorithms. This filter emerges naturally in the case of additive observation noise modeled by S α S distributions, as an effective mechanism for downweighting gross outliers in the noisy signal. The theoretical justification along with the experimental evaluation demonstrate the improved performance of our nonlinear CS framework when compared against state-of-the-art CS techniques for a broad range of impulsive environments.

中文翻译：

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使用对称 Alpha 稳定分布的稳健非线性压缩采样

摘要 传统的压缩采样 (CS) 主要假设基础信号和/或噪声统计数据的光尾模型。然而，当在脉冲环境中运行时，该假设被废除，其中信号和/或噪声分量出现非高斯无限方差过程。这导致传统的线性采样算子失败，因为总观测误差均匀分布在生成的压缩测量值上，同时掩盖了观测信号的关键信息内容。为了解决这个问题，本文利用对称 alpha 稳定 (S α S) 分布的能力来设计一个鲁棒的非线性压缩采样算子，能够抑制无限方差加性观测噪声的影响。具体来说，引入了广义 alpha 稳定匹配滤波器，用于以非线性方式生成压缩测量，从而提高了对脉冲观测噪声的鲁棒性，从而提高了传统稀疏重建算法的准确性。在由 S α S 分布建模的加性观测噪声的情况下，该滤波器自然出现，作为降低噪声信号中总异常值的有效机制。理论论证和实验评估证明了我们的非线性 CS 框架在广泛的脉冲环境中与最先进的 CS 技术相比性能有所提高。从而提高了传统稀疏重建算法的准确性。在由 S α S 分布建模的加性观测噪声的情况下，该滤波器自然出现，作为降低噪声信号中总异常值的有效机制。理论论证和实验评估证明了我们的非线性 CS 框架在广泛的脉冲环境中与最先进的 CS 技术相比性能有所提高。从而提高了传统稀疏重建算法的准确性。在由 S α S 分布建模的加性观测噪声的情况下，该滤波器自然出现，作为降低噪声信号中总异常值的有效机制。理论论证和实验评估证明了我们的非线性 CS 框架在广泛的脉冲环境中与最先进的 CS 技术相比性能有所提高。