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