Robust Recovery Of Sparse Signal Using Generalized Partial Nonconvex Regularization

Sparse optimization method has attracted a great deal of interest in sparse reconstruction,signal estimation,face recognition,machine learning,bioinformatics and so on.The researchers create suitable sparse optimization model according to the data structure of practical problem background,transfrom it's formulation and design the corresponding sparse optimization al-gorithm to solve this model in order to make it more efficient to solve the sparse solution of optimization problem.This paper mainly studies the sparse solution of an undetermined linear system.Because l0 norm is an discontinuous,nonconvex and integer-valued function,the sparse solution of the optimization problem is NP-hard.This paper substitutes l1 norm for l2 norm of residual error for descending the error by missing data,data outliers and noise intensity in the process of sig-nal generation and transmission.At the same time,in order to neutralize some bias incurred by some large entries(in magnitude)of the vector,this paper uses less biased relaxation partial reg-ularizers of l0-norm for recovering a sparse solution of the linear system.We indicate existence of the optimal solutions of x minimization subproblem model and solve it by using the general partial nonconvex alternating direction method of multipliers.We prove any accumulation point of the sequence generated by the algorithm is first-order ?-stationary point of the model and it converges to the first-order optimality condition.Numerical results show the sparse recovery effect of our algorithm is not worse than corresponding the general nonpartial and nonconvex algorithm in Gaussian noise,Gaussian-mixture noise and SaS noise.It has better recovery performance in Gaussian-mixture noise and SaS noise than Gaussian noise,and is batter than YALL1,TL1,Lq-L1-ADMM algorithm in some conditions.