Signal recovery from incomplete measurements in the presence of outliers

Björn Popilka; Simon Setzer; Gabriele Steidl

doi:10.3934/ipi.2007.1.661

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2007, Volume 1, Issue 4: 661-672. Doi: 10.3934/ipi.2007.1.661

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Signal recovery from incomplete measurements in the presence of outliers

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

Received: April 30, 2007

Published: October 2007

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Abstract

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.

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Mathematics Subject Classification: 94A08, 68U10, 65K10, 49J55.

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