Abstract
The \({\ell _1}\) regularization based methods for sparse signal reconstruction is a topic of considerable interest recently,which is widely employed in basis pursuit denoising, compressed sensing and other related fields.These problems can be cast as \({\ell _1}\)-regularized least-squares programs (LSPs).But it is challenging due to the non-smoothness of the regularization.Inspired by Nesterov's smoothing technique, we smoothed the regularization term.Hence this paper proposed a new modified HS conjugate gradient algorithm for solving common recovery problems in signal processing.Numerical experiment shows that our algorithm is effective and suitable for solving large-scale sparse signal recovery problems. CCS CONCEPTS Mathematics of computing ~ Mathematical analysis ~ Mathematical optimization