New Construction of Deterministic Compressed Sensing Matrices via Singular Linear Spaces over Finite Fields

摘要

As an emerging approach of signal processing, not only has compressed sensing (CS) successfully compressed and sampled signals with few measurements, but also has owned the capabilities of ensuring the exact recovery of signals. However, the above-mentioned properties are based on the (compressed) sensing matrices. Hence the construction of sensing matrices is the key problem. Compared with the intensive study of random sensing matrices, only a few deterministic constructions are known. In this paper, we provide a family of new construction of deterministic sensing matrices via singular linear spaces over finite fields, and show its better performance than Devore's construction using polynomials over finite fields.