# American Institute of Mathematical Sciences

2007, 1(4): 661-672. doi: 10.3934/ipi.2007.1.661

## Signal recovery from incomplete measurements in the presence of outliers

 1 Institute of Mathematics, University of Mannheim, 68131 Mannheim, Germany, Germany, Germany

Received  May 2007 Published  October 2007

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.
Citation: Björn Popilka, Simon Setzer, Gabriele Steidl. Signal recovery from incomplete measurements in the presence of outliers. Inverse Problems & Imaging, 2007, 1 (4) : 661-672. doi: 10.3934/ipi.2007.1.661
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