Semi-Tensor Product Compressed Sensing With Its Applications: A Review

Recently, as an emerging signal processing technology, the semi-tensor product compressed sensing (STP-CS) has attracted widespread attention in the fields of image processing, communications, and bioinformatics. This article reviews the theoretical foundations, algorithmic designs, and practical applications of STP-CS. It begins by revisiting the basic concepts of compressed sensing (CS) and the definition of the semi-tensor product (STP), followed by a detailed discussion on the theoretical model of STP-CS, optimization of the measurement matrix, and reconstruction algorithms. Furthermore, the article explores the practical applications of STP-CS in areas such as sensor nodes, visual security, image encryption, and spectrum sensing, analyzing its performance advantages and potential challenges in these fields. A comprehensive analysis indicates that STP-CS offers significant benefits in saving storage space, reducing computational complexity, and enhancing data security, making it a promising technology in the field of signal processing.

I. Introduction

With the rapid development of information technology, data acquisition and processing in the field of signal processing have increasingly become a focal point of research in recent years. Traditional signal acquisition methods follow the Nyquist sampling theorem, which states that the sampling frequency must be at least double the highest frequency of the signal to ensure its integrity and reconstructability [1]. However, this theory faces significant challenges in practical applications, especially in resource-constrained sensor networks and large-scale data processing scenarios. To address this issue, compressed sensing (CS) technology that is proposed by Donoho [2], Candes et al. [3], and Candes and Tao [4] provides a new perspective for signal acquisition and reconstruction. It allows the acquisition and reconstruction of sparse or compressible signals at a sampling rate far less than the Nyquist frequency, greatly reducing the demands for storage and transmission resources. The essence of CS theory lies in the sparsity of signals, meaning that they can be expressed with a relatively small number of non-zero coefficients in some transform domain. By designing an appropriate measurement matrix, CS can compress high-dimensional signals into low-dimensional measurements, and then reconstruct the original signals through optimization algorithms [5], [6]. This process not only reduces sampling costs but also improves data processing efficiency.