AN ELLIPSOID BASED, TWO-STAGE SCREENING TEST FOR BPDN

Consider the Basis Pursuit De-Noising (BPDN) estimator for recovery of unknown, sparse parameters. This note presents an ellipsoid-based, two-stage screening test method which aims to reduce a-priori the dimensionality of the resulting optimization problem. The new elements of the proposed method are given by (i) using an efficient ellipsoid approximation scheme in both stages and (ii) making better use of the information which has been calculated during the first stage. A comparative experiment indicates that this procedure can lead to better overall time complexity compared to known screening tests, while screening away more irrelevant variables in a preprocessing stage.