A New Method of Measurement Matrix Optimization for Compressed Sensing Based on Alternating Minimization

Mathematics

Biao Wu¹  Renjie Yi²  Chen Cui²  Yang Gong² 

[1] Huayin Ordnance Test Center, Weinan 714000, China;Institute of Electronic Countermeasure, National University of Defense Technology, Hefei 230000, China;

关键词: compressed sensing;    measurement matrix;    Equiangular Tight Frame;    mutual coherence;   

DOI  :  10.3390/math9040329

来源: DOAJ

【 摘 要 】

In this paper, a new method of measurement matrix optimization for compressed sensing based on alternating minimization is introduced. The optimal measurement matrix is formulated in terms of minimizing the Frobenius norm of the difference between the Gram matrix of sensing matrix and the target one. The method considers the simultaneous minimization of the mutual coherence indexes including maximum mutual coherence ${\mu }_{max}$, t-averaged mutual coherence ${\mu }_{ave}$ and global mutual coherence ${\mu }_{all}$, and solves the problem that minimizing a single index usually results in the deterioration of the others. Firstly, the threshold of the shrinkage function is raised to be higher than the Welch bound and the relaxed Equiangular Tight Frame obtained by applying the new function to the Gram matrix is taken as the initial target Gram matrix, which reduces ${\mu }_{ave}$ and solves the problem that ${\mu }_{max}$ would be larger caused by the lower threshold in the known shrinkage function. Then a new target Gram matrix is obtained by sequentially applying rank reduction and eigenvalue averaging to the initial one, leading to lower. The analytical solutions of measurement matrix are derived by SVD and an alternating scheme is adopted in the method. Simulation results show that the proposed method simultaneously reduces the above three indexes and outperforms the known algorithms in terms of reconstruction performance.

【 授权许可】

Unknown