Regularization theory of the analytic deep prior approach

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