Application Of Three-terms Conjugate Gradient Method And Absolute Smoothing In Signal Reconstruction

In this paper,the problem of signal recovery in compressed sensing is studied.For the problem of regularization of l_p-norm,it is smoothed by continuous weighting technique and smooth approximation function of absolute value function,and the smoothed model is solved by three-terms conjugate gradient method.The boundedness of level set,Lipschitz continuity of objective function gradient,and the global convergence of the algorithm are proved.Numerical experiments are carried out under four kinds of observation matrices,and compared with NESTA,FPCBB.The experimental results show the effectiveness of the algorithm.For the l₁-norm regularization model,the smoothing function of the absolute value function is used to approximate the l₁-norm,and the three-terms conjugate gradient method is used to solve it.The boundedness of the level set,Lipschitz continuity of the function gradient and the global convergence of the algorithm are proved.Numerical experiments are carried out and numerical are given.