Sufficient Conditions on Stable Recovery of Sparse Signals With Partial Support Information

Abstract

In this letter, we study signal reconstruction from compressed sensing measurements. We propose new sufficient conditions for stable recovery when partial support information is available. Weighted l(1)-minimization is adopted to recover the original signal under three noise models. The proposed approach is to use Ozeki's inequality and shifting inequality in order to bound the errors in the associated weighted l(1)-minimization. Our result offers generalized performance bounds on recovery capturing known support information. Improved sufficient conditions for recovery are derived based on our results, even for the cases where the accuracy of prior support information is arbitrarily low.