dc.creator | de, los Reyes JC | |
dc.creator | Schönlieb, CB | |
dc.creator | Valkonen, T | |
dc.date.accessioned | 2018-11-24T23:18:23Z | |
dc.date.available | 2015-09-16T10:41:44Z | |
dc.date.available | 2018-11-24T23:18:23Z | |
dc.date.issued | 2015-09-16 | |
dc.identifier | https://www.repository.cam.ac.uk/handle/1810/250589 | |
dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3266 | |
dc.description.abstract | We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general type of regulariser is considered, which encompasses total variation (TV), total generalized variation (TGV) and infimal-convolution total variation (ICTV). We prove that under certain conditions on the given data optimal parameters derived by bilevel optimisation problems exist. A crucial point in the existence proof turns out to be the boundedness of the optimal parameters away from 0 which we prove in this paper. The analysis is done on the original -- in image restoration typically non-smooth variational problem -- as well as on a smoothed approximation set in Hilbert space which is the one considered in numerical computations. For the smoothed bilevel problem we also prove that it Γ converges to the original problem as the smoothing vanishes. All analysis is done in function spaces rather than on the discretised learning problem. | |
dc.language | en | |
dc.publisher | Elsevier | |
dc.publisher | Journal of Mathematical Analysis and Applications | |
dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
dc.rights | Creative Commons Attribution 4.0 International License | |
dc.subject | total variation | |
dc.subject | total generalised variation | |
dc.subject | bi-level optimisation | |
dc.subject | optimality | |
dc.subject | parameter choice | |
dc.title | The structure of optimal parameters for image restoration problems | |
dc.type | Article | |