The Application Of Conjugate Gradient Method For Signal Recovery

Compressive sensing theory is a new type of signal acquisition and processing method proposed by Donoho,Candès and Tao in 2006.Inhomogeneous and indirect sampling method is used for the original signal.Compared with the traditional Nyquist uniform and direct sampling method,compressed sensing can greatly reduce the number of samples and improve the sampling efficiency,which saves transportation,calculation,storage and other resources and reduce the waste of time.It has broad prospects in signal/image processing,medical treatment and other fields.In this paper,the conjugate gradient method for the problem of signal recovery is studied.The main results are as follows:Firstly,a new smooth approximate function ofl₀-norm is proposed and the model ofl₀-norm is smoothed.The Lipschitz continuity of the gradient of the objective function is proved.Based on this,the PRP conjugate gradient method is used to solve the problem of signal recovery.The global convergence of the algorithm is proved under appropriate assumptions.A lot of numerical experiments are carried out,and the experimental results show that the algorithm is effective.Secondly,thel₁-regularized least squares problem is transformed into unconstrained optimization problems by using complementary functions.Then the HS conjugate gradient method is used to solve the signal recovery.The Lipschitz continuity of the gradient of the objective function is proved.The global convergence of the algorithm is proved under appropriate assumptions.Numerical experiments are carried out.The results show that the algorithm is effective.