Learning parametrised regularisation functions via quotient minimisation
Proceedings in Applied Mathematics and Mechanics
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Benning, M., Gilboa, G., & Schönlieb, C. (2016). Learning parametrised regularisation functions via quotient minimisation. Proceedings in Applied Mathematics and Mechanics, 16 933-936. https://doi.org/10.1002/pamm.201610451
We propose a novel strategy for the computation of adaptive regularisation functions. The general strategy consists of minimising the ratio of a parametrised regularisation function; the numerator contains the regulariser with a desirable training signal as its argument, whereas the denominator contains the same regulariser but with its argument being a training signal one wants to avoid. The rationale behind this is to adapt parametric regularisations to given training data that contain both wanted and unwanted outcomes. We discuss the numerical implementation of this minimisation problem for a specific parametrisation, and present preliminary numerical results which demonstrate that this approach is able to recover total variation as well as second-order total variation regularisation from suitable training data.
MB and CBS acknowledge support from the EPSRC grant EP/M00483X/1 and the Leverhulme grant ’Breaking the non-convexity barrier’. GG acknowledges support from the Israel Science Foundation (grant No. 718/15) and by the Magnet program of the OCS, Israel Ministry of Economy, in the framework of Omek Consortium.
External DOI: https://doi.org/10.1002/pamm.201610451
This record's URL: https://www.repository.cam.ac.uk/handle/1810/260954