1.湖南省自然科学杰出青年基金，基于智能优化算法的对地观测网络资源优化调度理论与方法，2019JJ20026, 主持，2019-2022 2.国家自科基金面上项目，空天地一体化对地观测网络资源协同优化调度，62073341, 主持，2021-2024
Central South University
Compressed sensing provides effective support for processing large scale signal data. The problem of sparse signal representation and sparse signal reconstruction in compressed sensing is essentially a sparse optimization problem, which aims to find the sparsest solution from the infinite solutions that satisfy the constraint of underdetermined system of equations. This paper proposes an algorithm based on variable reduction to solve the sparse optimization problem in compressed sensing (VRSO). Variable reduction extract the relationships between variables from the constraint of the underdetermined system of equations, and divide variables into core variables and reduced variables. During the calculation, the core variables are always used to represent the reduced variables. By setting the elements in the core variables to be 0, the minimization problem in the whole variable solution space is simplified to the solution space of reduced variables. This algorithm updates core variables in terms of the inner product of atoms and observation signal, so as to find a group of sparse solutions. According to the experimental results, the reconstruction error and sparsity error of VRSO are better than other comparative algorithms such as Matching Pursuit, Orthogonal Matching Pursuit and Iterative Hard Thresholding. The results show that the signal obtained by VRSO has higher precision and better sparsity.