Sparsity Adaptive Joint Greedy Algorithm for Dual Signal Estimation

This paper presents two novel joint greedy algorithms for signal reconstruction in the case of impulsive noise. The performance of most existing greedy algorithms based on the assumption of Gaussian noise significantly deteriorates when the noise is impulsive noise that has heavy tails. To address the impulsive noise, in this work, it is modeled as α-stable distribution and formulated as a sparse signal in the time domain. Therefore, the noise suppression problem becomes an estimation one. With this reformulation, two methods by simultaneously estimating the signal of interest and noise are developed based on sparsity adaptive matching pursuit (SAMP). The numerical studies demonstrate that the proposed approaches provide excellent performance in both the signal recovery and noise suppression.