We propose a method for signal recovery in compressed sensing when measurements can be highly corrupted. It is based on ℓp minimization for 0 <; p ≤ 1. Since it was shown that ℓp minimization performs better than ℓ1 minimization when there are no large errors, the proposed approach is a natural extension to compressed sensing with corruptions. We provide a theoretical justification of this idea, based on analogous reasoning as in the case when measurements are not corrupted by large errors. Better performance of the proposed approach compared to ℓ1 minimization is illustrated in numerical experiments.
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)