# Regularization by architecture: A deep prior approach for inverse problems

## TL;DR

This paper explores deep image prior (DIP) methods for inverse problems, providing theoretical insights by interpreting DIP as Tikhonov functional optimization and validating findings with numerical experiments.

## Contribution

It introduces a novel interpretation of DIP as Tikhonov functional optimization, offering analytical results and bridging theory with practical inverse problem solutions.

## Key findings

- DIP can be viewed as Tikhonov regularization.
- Theoretical analysis of specific network designs and operators.
- Numerical experiments support the analytical results.

## Abstract

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.