Abstract
We propose a new methodology based on bilevel programming to remove additive white Gaussian noise from images. The lower-level problem consists of a parameterized variational model to denoise images. The parameters are optimized in order to minimize a specific cost function that measures the residual Gaussianity. This model is justified using a statistical analysis. We propose an original numerical method based on the Gauss-Newton algorithm to minimize the outer cost function. We finally perform a few experiments that show the well-foundedness of the approach. We observe a significant improvement compared to standard TV-\(\ell ^2\) algorithms and show that the method automatically adapts to the signal regularity.
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Fehrenbach, J., Nikolova, M., Steidl, G., Weiss, P. (2015). Bilevel Image Denoising Using Gaussianity Tests. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_10
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DOI: https://doi.org/10.1007/978-3-319-18461-6_10
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