Regularization by Architecture: A Deep Prior Approach for Inverse Problems

Author:

Dittmer SörenORCID,Kluth Tobias,Maass Peter,Otero Baguer DanielORCID

Abstract

Abstract The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for applying DIP to inverse problems have been reported. This paper aims at discussing different interpretations of DIP and to obtain analytic results for specific network designs and linear operators. The main contribution is to introduce the idea of viewing these approaches as the optimization of Tikhonov functionals rather than optimizing networks. Besides theoretical results, we present numerical verifications.

Funder

Deutsche Forschungsgemeinschaft

European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Geometry and Topology,Computer Vision and Pattern Recognition,Condensed Matter Physics,Modelling and Simulation,Statistics and Probability

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