中南大学 交通运输工程学院,长沙 410075
School of Traffic and Transportation Engineering,Central South University,Changsha 410075,China
Compressed sensing provides an 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 extracts the relationships between variables from the constraint of the underdetermined system of equations, and divides 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.