The Elastic Unconstrained Algorithms Of The Signal Recovery

This paper mainly studies the Elastic unconstrained algorithms for signal recovery.The results,obtained in this dissertation,are summarized as follows:First,as the l₁ norm and l_q norm are more likely to promote sparsity,the elastic unconstrained l_q-l₁ minimization model is proposed.We use the smoothing strategy to obtain the smoothing model.The first-order optimization conditions are used to transform the problem into a reversible system of linear equations,and then an iterative algorithm is proposed to solve the system of equations.We prove the boundedness and asymptotic regularity of the iterative sequence,and the global convergence of the algorithm.The error bound between the limit point and the real solution is analyzed.Under the four observation matrices,numerical experiments were carried out and compared with the L₁-magic,IRL1,HALF,and FPCBB.The experimental results show the effectiveness of the algorithm.Second,for the signal recovery problem,a l₁-l₀ unconstrained minimization model is constructed.The smoothing function of l₁ norm and l₀ norm is used to obtain the smoothing model.We use the optimality condition and the previous step information of the algorithm to transform the problem to a linear equation system with a unique solution,and give an algorithm for solving the equation system.The boundedness of the level set and the global convergence of the algorithm are proved.Under the four observation matrices,numerical experiments were carried out and compared numerically with the L₁-magic,IRL1,FISTA,and FPCBB.