Robust Sampling and Reconstruction Methods for Sparse Signals in the Presence of Impulsive Noise
Robust Sampling and Reconstruction Methods for Sparse Signals in the Presence of Impulsive Noise
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DOI：
10.1109/jstsp.2009.2039177
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发表时间：
2010-04-01
影响因子：
7.5
通讯作者：
Aysal, Tuncer C.
中科院分区：
文献类型：
--
作者：
Carrillo, Rafael E.;Barner, Kenneth E.;Aysal, Tuncer C.
压缩感知的最新研究结果表明，稀疏或可压缩的信号可以从一些不相干的测量重建。由于噪声总是存在于实际的数据采集系统，传感和重建方法的开发假设高斯（光尾）模型的腐败噪声。然而，当潜在的信号和/或测量被脉冲噪声破坏时，通常采用的线性采样算子与当前的重建算法相结合，无法恢复信号的接近近似。在本文中，我们提出了鲁棒的方法采样和重构稀疏信号中存在的脉冲噪声。为了解决脉冲噪声在测量过程之前嵌入到潜在信号中的问题，我们提出了一种基于加权无数估计的鲁棒非线性测量算子。此外，我们引入了一个几何优化问题的基础上L-1最小化采用洛伦兹范数约束的残余误差恢复稀疏信号从噪声测量。分析表明，在脉冲环境中，当噪声的方差无穷大时，我们有一个有限的重建误差，而且这些方法产生成功的重建所需的信号。仿真结果表明，所提出的方法显着优于常用的压缩感知采样和重构技术在脉冲环境中，同时提供了相当的性能要求不高，轻尾环境。
Recent results in compressed sensing show that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Since noise is always present in practical data acquisition systems, sensing, and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with current reconstruction algorithms, fail to recover a close approximation of the signal. In this paper, we propose robust methods for sampling and reconstructing sparse signals in the presence of impulsive noise. To solve the problem of impulsive noise embedded in the underlying signal prior the measurement process, we propose a robust nonlinear measurement operator based on the weighed myriad estimator. In addition, we introduce a geometric optimization problem based on L-1 minimization employing a Lorentzian norm constraint on the residual error to recover sparse signals from noisy measurements. Analysis of the proposed methods show that in impulsive environments when the noise posses infinite variance we have a finite reconstruction error and furthermore these methods yield successful reconstruction of the desired signal. Simulations demonstrate that the proposed methods significantly outperform commonly employed compressed sensing sampling and reconstruction techniques in impulsive environments, while providing comparable performance in less demanding,light-tailed environments.