Reconstruction of Sparse Signals in Impulsive Disturbance Environments

Sparse signals corrupted by impulsive disturbances are considered. The assumption about disturbances is that they degrade the original signal sparsity. No assumption about their statistical behavior or range of values is made. In the first part of the paper, it is assumed that some uncorrupted signal samples exist. A criterion for selection of corrupted signal samples is proposed. It is based on the analysis of the first step of a gradient-based iterative algorithm used in the signal reconstruction. An iterative extension of the original criterion is introduced to enhance its selection property. Based on this criterion, the corrupted signal samples are efficiently removed. Then, the compressive sensing theory-based reconstruction methods are used for signal recovery, along with an appropriately defined criterion to detect a full recovery event among different realizations. In the second part of the paper, a case when all signal samples are corrupted by an impulsive disturbance is considered as well. Based on the defined criterion, the most heavily corrupted samples are removed. The presented criterion and the reconstruction algorithm are applied on the signal with a Gaussian noise.