Binary Deterministic Sensing Matrix Construction Using Manifold Optimization

Binary deterministic sensing matrices are highly desirable for sampling sparse signals, as they require only a small number of sum-operations to generate the measurement vector. Furthermore, sparse sensing matrices enable the use of lowcomplexity algorithms for signal reconstruction. In this paper, we propose a method to construct low-density binary deterministic sensing matrices by formulating a manifold-based optimization problem on the statistical manifold. The proposed matrices can be of arbitrary sizes, providing a significant advantage over existing constructions. We also prove the convergence of the proposed algorithm. The proposed binary sensing matrices feature low coherence and constant column weight. Simulation results demonstrate that our method outperforms existing binary sensing matrices in terms of reconstruction percentage and signal to noise ratio (SNR).