Regularization Theory of the Analytic Deep Prior Approach

The analytic deep prior (ADP) approach was recently introduced for the theoretical analysis of deep image prior (DIP) methods with special network architectures. In this paper, we prove that ADP is in fact equivalent to classical variational Ivanov methods for solving ill-posed inverse problems. Besides, we propose a new variant which incorporates the strategy of early stopping into the ADP model. For both variants, we show how classical regularization properties (existence, stability, convergence) can be obtained under common assumptions.