Regularization by Architecture: A Deep Prior Approach for Inverse Problems

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 aim...

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Bibliographic Details
Published inJournal of mathematical imaging and vision Vol. 62; no. 3; pp. 456 - 470
Main Authors Dittmer, Sören, Kluth, Tobias, Maass, Peter, Otero Baguer, Daniel
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Computer Science
Ill posed problems
Image processing
Image Processing and Computer Vision
Inverse problems
Linear operators
Mathematical Methods in Physics
Optimization
Regularization
Signal,Image and Speech Processing
Deep learning
Deep image prior
Inverse problems
Regularization by architecture
Deep inverse prior
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Summary: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.
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ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-019-00923-x