Workshop on Structure Adapting Methods - Abstract
We consider the problem of recovery of a sparse signal, observed the noisy environment when nuisance is present. We propose the recovery routines which are based on L1 minimization constrained or penalized with contrasts which depend on the geometry of the nuisance sets. We show that such routines outperform some known methods, e.g. Lasso estimator and Dantzig selector. We discuss the link between the theory of linear estimation and L1-recovery and show how this theory allows to construct optimal contrast matrices.