ITERATIVELY REWEIGHTED SPARSE RECONSTRUCTION IN IMPULSIVE NOISE

Most of the existing sparse recovery methods are based on the squared error criterion, i.e., l(2)-norm metric, by appropriately adding to a sparsity-promoting regularizer. This criterion is, however, statistically optimal only when the noise are Gaussian distributed. In fact, non-Gaussian impulsive noise with heavy tailed distribution has been reported in a variety of practical applications. To guarantee outlier-resistant sparse reconstruction for impulsive noise, in this paper we instead employ the generalized l(p)-norm (1 <= p < 2) to quantify the residual error metric. By heuristically leveraging the sparsity-encouraging log-sum penalty, two iteratively reweighted algorithms are proposed for approximately solving the l(p) - l(0) sparse recovery problem, where the reweighted matrices constructed from the previous iterative solution are considered both for l(p) and l(0) metrics. Simulation results demonstrate the efficiency and robustness of the proposed algorithms.