Semi-tensor compressed sensing

Abstract

In compressed sensing (CS), sparse or compressible signals can be reconstructed with fewer samples than the Nyquist–Shannon theorem requires. Over the past ten years, CS has developed into a relatively mature theory and this brand-new technique has been widely used in many fields such as image processing, wireless communication and medical imaging. In this paper, we propose a new model for signal compression and reconstruction based on semi-tensor product, called STP-CS, which is a generalization of traditional CS. Like traditional CS, we investigate some reconstruction conditions of STP-CS in terms of the spark, the coherence and the restricted isometry property (RIP). The experimental results show that STP-CS has the flexibility to choose a lower-dimensional sensing matrix for signal compression and reconstruction.