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D. S. Pham and S. Venkatesh. Improved image recovery from compressed data contaminated with impulsive noise. IEEE Transactions on Image Processing, 2011. (to appear).

Compressed sensing (CS) is a new information sampling theory for acquiring sparse or compressible data with much fewer measurements than are otherwise required by the Nyquist/Shannon counterpart. This is particularly important for some imaging applications such as magnetic resonance imaging or in astronomy. However, in the existing CS formulation, use of the l2 norm on the residuals is not particularly efficient when the noise is impulsive. This could lead to an increase in the upper bound of the recovery error. To address this problem, we consider a robust formulation for compressed sensing to suppress outliers in the residuals. We propose an iterative algorithm for solving the robust CS problem that exploits the power of existing CS solvers. We also show that the upper bound on the recovery error in the case of non-Gaussian noise is reduced, and then demonstrate the efficacy of the method through numerical studies.

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30th April 2012