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The analytic deep prior (ADP) approach was recently introduced for thetheoretical analysis of deep image prior (DIP) methods with special networkarchitectures. In this paper, we prove that ADP is in fact equivalent toclassical variational Ivanov methods for solving ill-posed inverse problems.Besides, we propose a new variant which incorporates the strategy of earlystopping into the ADP model. For both variants, we show how classicalregularization properties (existence, stability, convergence) can be obtainedunder common assumptions.

Regularization Theory of the Analytic Deep Prior Approach