Newly deterministic construction of compressed sensing matrices via singular linear spaces over finite fields

Abstract

A valuable opportunity is provided by compressed sensing (CS) to accomplish the tasks of high speed sampling, the transmission of large volumes of data, and storage in signal processing. To some extent, CS has brought tremendous changes in the information technologies that we use in our daily lives. However, the construction of compressed sensing matrices still can pose substantial problems. In this paper, we provide a kind of deterministic construction of sensing matrices based on singular linear spaces over finite fields. In particular, by choosing appropriate parameters, we constructed binary sensing matrices that are superior to existing matrices, and they outperform DeVore's matrices. In addition, we used an embedding manipulation to merge our binary matrices with matrices that had low coherence, thereby improving such matrices. Compared with the quintessential binary matrices, the improved matrices possess better ability to compress and recover signals. The favorable performance of our binary and improved matrices was demonstrated by numerical simulations.