On the Performance of Sensing Matrix Design-Based Alternating Minimization Approach for Compressive Sensing

The iterative alternating minimization approach has gained increasing attention for the development of sensing matrix design algorithms. However, relying solely on the mutual coherence index as a single evaluation metric does not guarantee optimal sensing matrix performance. To enhance Compressed Sensing (CS) recovery accuracy, it is crucial to simultaneously minimize multiple coherence metrics (<tex>$\mu_{m x}, \mu_{\text{ave}}$</tex>, and <tex>$\mu_{\text{all}}$</tex>), particularly by leveraging Equiangular Tight Frame (ETF) properties. In this paper, we propose a novel iterative alternating minimization method for designing an optimized sensing matrix that reduces mutual coherence values. Our approach incorporates a simple yet effective shrinkage function, which enables the approximation of an ideal ETF structure during the updating phase while maintaining computational efficiency. Experimental results demonstrate that the sensing matrix designed using the proposed algorithm achieves superior performance in terms of both signal reconstruction accuracy and coherence reduction, outperforming existing methods.