An Algorithm Based On Interior Point Approach For Sparse Signal Reconstruction

This article firstly describes an interior point method for large scale l1-regularized least squares. As the solution of l1-regularized least squares canbe sparse, the interior point method can be applied to reconstruct sparsesignal in compressive sensing. In order to improve the quality of recon-structed signal, we embed the above algorithm in a continuation processby assigning a varying sequence of values to regularized parameter, anduse the warm start technology to accelerate the speed of our algorithm.Our numerical experimentations show that good reconstructed signal canbe achieved by gradually decreasing the regularized parameter, and theprimal interior point method would use more time to reconstruct a signalif independently regulating the regularized parameter. We also observed inour experiments an approximate lower bound of the regularized parameterthat afects the quality of the reconstructed signal and the sparsity of asignal with some specific compression ratio for good reconstruction.