In the past decade, compressed sensing (CS) has provided an efficient framework for signal compression and recovery as the intermediate steps in signal processing. The well‐known greedy analysis algorithm, called Greedy Analysis Pursuit (GAP) has the capability of recovering the signals from a restricted number of measurements. In this article, we propose an extension to the GAP to solve the weighted optimization problem satisfying an inequality constraint based on the Lorentzian cost function to modify the EEG signal reconstruction in the presence of heavy‐tailed impulsive noise. Numerical results illustrate the effectiveness of our proposed algorithm, called enhanced weighted GAP (ewGAP) to reinforce the efficiency of the signal reconstruction and provide an appropriate candidate for compressed sensing of the EEG signals. The suggested algorithm achieves promising reconstruction performance and robustness that outperforms other analysis‐based approaches such as GAP, Analysis Subspace Pursuit (ASP), and Analysis Compressive Sampling Matching Pursuit (ACoSaMP).

中文翻译：

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一种增强的加权贪婪分析追踪算法在脑电信号重建中的应用

在过去十年中，压缩感知 (CS) 为作为信号处理中间步骤的信号压缩和恢复提供了有效的框架。众所周知的贪婪分析算法，称为贪婪分析追踪（GAP），能够从有限数量的测量中恢复信号。在本文中，我们提出了 GAP 的扩展，以解决基于洛伦兹成本函数的不等式约束的加权优化问题，以在存在重尾脉冲噪声的情况下修改 EEG 信号重建。数值结果说明了我们提出的算法的有效性，称为增强加权 GAP (ewGAP)，以增强信号重建的效率，并为 EEG 信号的压缩感知提供合适的候选者。