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Signal recovery from incomplete measurements in the presence of outliers

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  • We study the restoration of a sparse signal or an image with a sparse gradient from a relatively small number of linear measurements which are additionally corrupted by a small amount of white Gaussian noise and outliers. We minimize $\l_1-\l_1$ and $\l_1-TV$ regularization functionals using various algorithms and present numerical results for different measurement matrices as well as different sparsity levels of the initial signal/image and of the outlier vector.
    Mathematics Subject Classification: 94A08, 68U10, 65K10, 49J55.


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