Regularization by architecture: A deep prior approach for inverse problems
This work provides a theoretical framework for DIP in inverse problems, but it is incremental as it builds on existing experimental results.
The paper tackles the problem of solving ill-posed inverse problems using deep image prior (DIP) techniques by interpreting them as Tikhonov functional optimization, and it presents theoretical results and numerical verifications.
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.