Optimized Structured Sparse Sensing Matrices for Compressive Sensing
This addresses the problem of efficient signal acquisition in compressive sensing applications, though it appears to be an incremental improvement over existing structured sensing matrix designs.
The paper tackles the problem of designing efficient sensing matrices for compressive sensing by proposing a robust structured sparse sensing matrix that minimizes distance to target Gram matrices with small mutual coherence and adds regularization for robustness to sparse representation errors. Numerical experiments show this approach achieves higher signal reconstruction than random dense sensing matrices.
We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix.