  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.
