Bilevel Image Denoising Using Gaussianity Tests
- Cite this paper as:
- 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
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.
KeywordsBilevel programming Image denoising Gaussianity tests Convex optimization
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