Volume 20, Issue 3 (9-2023)
jor 2023, 20(3): 19-32 |
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Alamdari M S, Fatemi M, Ghaffari A. The Recovery of Sparse Signals by Sequential Quadratic Programming Approach. jor 2023; 20 (3) :19-32
URL: http://jamlu.liau.ac.ir/article-1-2174-en.html
URL: http://jamlu.liau.ac.ir/article-1-2174-en.html
Department of Mathematics, K. N. Toosi University of Technology, Teharn, Iran , m.s.alamdari69@gmail.com
Abstract: (1063 Views)
In this article, with the idea of the sequential quadratic programming method and using the smoothed l0 norm as the objective function, a modified sequential quadratic programming method is presented to solve the problem of finding sparse solutions of the system of underdetermined linear equations. We provide a new approach for solving quadratic subproblems, which leads to the less complexity and simplicity in solving quadratic subproblems. The proposed method starts with an initial guess and in each iteration to calculate the search direction, a specific quadratic optimization problem is solved. The quadratic approximation of the objective function and the linear approximation of the constraints of the original problem are used to design the subproblem. Then, theoretical analysis of the method is presented and its convergence is proved. The results obtained from the implementation of the proposed method on sensor matrices of different dimensions show that the efficiency of the method does not depend on the dimensions of the input matrix. Finally, the comparison of the reported SNR regarding to the proposed method with the most frequent thin signal recovery algorithms shows the high efficiency and performance of the proposed method.
Keywords: Sparse Signal Recovery, Nonlinear Programming, Smoothed Norm, Sequential Quadratic Programming
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