Robust greedy algorithms for compressed sensing

The problem of sparse signal reconstruction in the presence of possibly impulsive noise is studied. The state-of-the-art greedy algorithms, Iterative Hard Thresholding (IHT), Orthogonal Matching Pursuit (OMP), and Compressive Sampling Matching Pursuit (CoSaMP) are robustified in order to cope with impulsive noise environments and outliers. We employ robust weighting of the residuals and replace the least-squares estimates by M-estimates of regression. Also a robust M-estimation based ridge regression is considered and shown to possess high potential when utilized in CS algorithms.