Semi-tensor compressed sensing

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.