# A Variational Approach to Remove Outliers and Impulse Noise

@article{Nikolova2004AVA, title={A Variational Approach to Remove Outliers and Impulse Noise}, author={Mila Nikolova}, journal={Journal of Mathematical Imaging and Vision}, year={2004}, volume={20}, pages={99-120} }

We consider signal and image restoration using convex cost-functions composed of a non-smooth data-fidelity term and a smooth regularization term. We provide a convergent method to minimize such cost-functions. In order to restore data corrupted with outliers and impulsive noise, we focus on cost-functions composed of an ℓ1 data-fidelity term and an edge-preserving regularization term. The analysis of the minimizers of these cost-functions provides a natural justification of the method. It is…

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