Sensing Matrix Sensitivity to Random Gaussian Perturbations in Compressed Sensing
Sensing Matrix Sensitivity to Random Gaussian Perturbations in Compressed Sensing
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DOI：
10.23919/eusipco.2018.8553575
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
A. Lavrenko;F. Roemer;G. D. Galdo;R. Thomä
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文献类型：
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作者：
A. Lavrenko;F. Roemer;G. D. Galdo;R. Thomä
在压缩传感中，传感矩阵的选择起着至关重要的作用：它定义了所需的硬件工作并确定了可实现的恢复性能。最近的研究表明，与随机集合相比，通过优化传感矩阵，可以潜在地提高系统性能。在这项工作中，我们分析了传感矩阵设计对随机扰动（例如由硬件缺陷引起的随机扰动）相对于总（平均）矩阵相干性的敏感性。我们推导了存在高斯扰动时总相干性平均恶化的精确表达式，作为扰动方差和传感矩阵本身的函数。然后我们用数字评估它对恢复性能的影响。
In compressed sensing, the choice of the sensing matrix plays a crucial role: it defines the required hardware effort and determines the achievable recovery performance. Recent studies indicate that by optimizing a sensing matrix, one can potentially improve system performance compared to random ensembles. In this work, we analyze the sensitivity of a sensing matrix design to random perturbations, e.g., caused by hardware imperfections, with respect to the total (average) matrix coherence. We derive an exact expression for the average deterioration of the total coherence in the presence of Gaussian perturbations as a function of the perturbations' variance and the sensing matrix itself. We then numerically evaluate the impact it has on the recovery performance.