Regularization Theory of the Analytic Deep Prior Approach

TL;DR

This paper provides a theoretical analysis of the analytic deep prior (ADP) approach, establishing its equivalence to classical variational methods and proposing a new variant with early stopping, demonstrating regularization properties.

Contribution

It proves the equivalence of ADP to Ivanov regularization and introduces a new ADP variant with early stopping, enhancing understanding of deep prior regularization.

Findings

ADP is equivalent to classical variational Ivanov methods.

A new ADP variant with early stopping is proposed.

Regularization properties are established for both variants.

Abstract

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.