Sensing Matrix Design via Mutual Coherence Minimization for Electromagnetic Compressive Imaging Applications
Sensing Matrix Design via Mutual Coherence Minimization for Electromagnetic Compressive Imaging Applications
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DOI：
10.1109/tci.2017.2671398
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发表时间：
2017-02
影响因子：
5.4
通讯作者：
R. Obermeier;J. Lorenzo
中科院分区：
文献类型：
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作者：
R. Obermeier;J. Lorenzo
压缩感知 (CS) 理论指出，只要感知矩阵满足受限等距属性 (RIP)，就可以使用 $\ell _1\text{-}$ 范数最小化技术从少量线性测量 $y=Ax$ 中恢复稀疏信号。不幸的是，RIP 很难在电磁成像应用中验证，其中传感矩阵是确定性计算的。尽管它提供的重建保证比 RIP 弱，但互相干性是评估确定性矩阵的 CS 恢复特性的更实用的指标。在本文中，我们描述了一种最小化电磁成像应用中传感矩阵相互相干性的方法。该设计方法的数值结果针对简单的多单站成像应用给出，其中每次测量的传感器位置作为设计变量。这些结果证明了该算法能够降低相干性并生成具有改进的 CS 恢复能力的传感矩阵。
Compressive sensing (CS) theory states that sparse signals can be recovered from a small number of linear measurements $y=Ax$ using $\ell _1\text{-}$ norm minimization techniques, provided that the sensing matrix satisfies a restricted isometry property (RIP). Unfortunately, the RIP is difficult to verify in electromagnetic imaging applications, where the sensing matrix is computed deterministically. Although it provides weaker reconstruction guarantees than the RIP, the mutual coherence is a more practical metric for assessing the CS recovery properties of deterministic matrices. In this paper, we describe a method for minimizing the mutual coherence of sensing matrices in electromagnetic imaging applications. Numerical results for the design method are presented for a simple multiple monostatic imaging application, in which the sensor positions for each measurement serve as the design variables. These results demonstrate the algorithm's ability to both decrease the coherence and to generate sensing matrices with improved CS recovery capabilities.