A Research On LASSO Problem Based On Signal Recovery

Compressed sensing theory breaks through the limitations of traditional sampling meth-ods and shows its great advantage of low sampling rate.Sparse signal reconstruction is a core problem of compressed sensing theory.With the increasing of data scale,fast and robust algorithms for large-scale signal reconstruction has become a new challenge to be solved.In this paper,we focus on algorithms based on l₁regularization models especially lasso model in signal recovery problems.The algorithm we described is a semismooth Newton augmented Lagrangian(in short,S_snal)method,which developed for general convex com-posite optimization problems.In S_snalalgorithm,the literature^[1]uses error bound condi-tion and metric subregularity as a tool to study the asymptotic superlinear convergence of the augmented Lagrangian algorithm(ALM),then presents a semismooth Newton method(SNCG)to handle the subproblem at each ALM iteration.We shall adapt the results in it-erature^[2,3]to analyze the convergence of SNCG algorithm.Under mild conditions,SNCG algorithm could get a fast superlinear or even quadratic convergence.In addition,by ex-ploring the second-order sparsity of the augmented Lagrangian functions,we can greatly reduce the computational cost of searching Newton direction.In the end,we conduct ex-tensive numerical experiments to evaluate the performance of S_snalalgorithm,comparing with mf IPM algorithm and TNIPM algorithm.S_snalalgorithm has a hight-performance in signal recovery problems.Numerical results have demonstrated the superior efficiency and robustness of S_snalalgorithm in solving large-scale sparse problems.