{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learned-convex-regularizers-for-inverse","title":"Learned convex regularizers for inverse problems","arxiv_id":"2008.02839","date":"2020-08-06","proceeding":null,"authors":["Subhadip Mukherjee","Sören Dittmer","Zakhar Shumaylov","Sebastian Lunz","Ozan Öktem","Carola-Bibiane Schönlieb"],"abstract":"We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially to discern ground-truth images from unregularized reconstructions. Convexity of the regularizer is desirable since (i) one can establish analytical convergence guarantees for the corresponding variational reconstruction problem and (ii) devise efficient and provable algorithms for reconstruction. In particular, we show that the optimal solution to the variational problem converges to the ground-truth if the penalty parameter decays sub-linearly with respect to the norm of the noise. Further, we prove the existence of a sub-gradient-based algorithm that leads to a monotonically decreasing error in the parameter space with iterations. 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