Non-Cartesian Spiral Binary Sensing Matrices

Binary sensing matrices can offer rapid multiplier-less data acquisition, owing to their binarization structure and competitive sampling efficiency, which promise to promote compressive sensing from theory to application. However, the size of existing binary constructions is often limited, and the generating strategies require extensive computational complexity. In this work, we propose a trivial strategy to deterministically construct non-Cartesian spiral binary sensing matrices (SbMs) with arbitrary size for compressive sensing. The mutual coherence of SbMs is proven to satisfy the Welch bound, i.e., optimal theoretical guarantee. Moreover, the simulation results show that the proposed SbMs can not only outperform their counterparts in sampling performance but also facilitate reconstruction speed.