Binary Deterministic Sensing Matrix Construction Using Manifold Optimization

Binary deterministic sensing matrices are attractive for sampling sparse signals due to their reliance only on sum operations for generating measurement vectors. Additionally, their sparsity facilitates the use of low-complexity reconstruction algorithms. In this paper, we present a novel approach for constructing low-density binary deterministic sensing matrices by formulating an optimization problem on the statistical manifold. Unlike many existing methods, the proposed construction supports arbitrary matrix sizes, offering greater flexibility. We also establish the convergence of the proposed algorithm. The resulting matrices exhibit low coherence and regular column weight. Simulation results demonstrate that our method outper forms existing approaches in terms of reconstruction accuracy.