کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417631 | 1339300 | 2016 | 37 صفحه PDF | دانلود رایگان |
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 generalised 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 Î converges to the original problem as the smoothing vanishes. All analysis is done in function spaces rather than on the discretised learning problem.
Journal: Journal of Mathematical Analysis and Applications - Volume 434, Issue 1, 1 February 2016, Pages 464-500