A Robust Primal Dual Active Set Algorithm With Continuation For Compressed Sensing With Outliers

This thesis mainly studies a sparse algorithm solving compressed sensing with outliers names a Robust Primal Dual Active Set Algorithm with Continuation.Com-pressed sensing techniques are widely applied in signal processing or other large scale linear regression problems with sparsity,and the existence of outliers often invalidates algorithms which are effective in traditional compressed sensing problems.Robust com-pressed sensing techniques are proposed to solve this challenge,and make it possible to obtain nice estimation of real signals as well as outliers even if a portion of observations are corrupted.The article firstly talks about the background,applications,and theoretical foun-dation of compressed sensing problems.Afterwards,it introduces a Primal Dual Active Set Algorithm with Continuation(PDASC).As a penalty-based least square algorithm,PDASC admits good accuracy as well as high efficiency when solving traditional com-pressed sensing problems,and in the paper,l~0andl~1penalty-based versions are mainly illustrated.Then we give the definition of robust compressed sensing,and its represen-tative model under the penalty background.After discussing conditions and properties of measurement matrix which are required,we finally put forward a Robust Primal Dual Active Set Algorithm with Continuation(Robust PDASC).Not only do we show the algorithm and its derivation,we also give the analysis of convergence,which proves that under certain conditions,the algorithm would lead to a good estimation of the ex-act signal and outliers.We provide experimental simulations at last,prove numerically the effectiveness of the algorithm.