Sensing Matrix Design via Mutual Coherence Minimization for Electromagnetic Compressive Imaging Applications

Abstract

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.