Sparse Signal Recovery Model And Algorithm Based On Nonconvex Function Composition

The sparse signal recovery problem is an important basic problem in the compressed sensing theory.Mathematically,the problem is usually described as a7)₀sparse optimization model(referred to as the original model).However,the model is NP-hard problems can usually not be effectively solved.Therefore,it is an important research in this field to construct the equivalent relaxation model of the original model and design an effective solution algorithm.The main research contents of this paper are as follows:1.Based on the idea of deep composition of functionals,a new7)₀approximation function is constructed by combining two kinds of nonconvex sparse functions,and a new sparse signal reconstruction model with constraints is established,and the equivalence between the model and the original model is proved.2.NCCS algorithm is proposed to solve the new reconstruction model.Firstly,MM(major minimization)technology is used to transform the objective function in the model,and the rationality of the transformation is analyzed.Secondly,uncon-strained transformation of the model is realized according to the external penalty function method.Finally,the conjugate gradient method is used to solve the un-constrained optimization problem.In addition,in order to reduce the possibility of the algorithm falling into local extremum,we minimize the solution of7)₁sparse optimization model as the initial value of the algorithm.3.In order to verify the effectiveness and superiority of NCCS algorithm in reconstruction performance,a number of numerical simulation experiments are carried out.The results show that compared with the classical algorithms,such as SL0 algorithm,BP algorithm,IRLS algorithm and SCSA algorithm,the NCCS algorithm has better performance in terms of signal reconstruction error,signal-to-noise ratio,support set recovery success rate,and normalized mean square error.Simultaneously,compared with the SCSA algorithm proposed in the latest literature,the running time of the NCCS algorithm has a further improvement.