Large-scale sparse signal recovery by modified HS conjugate gradient method

Abstract The \ (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 \ (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