DRIP: deep regularizers for inverse problems

Moshe Eliasof, Eldad Haber, Eran Treister

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most appropriate solution, in the sense that it contains a-priori information, were developed. However, they suffer from several shortcomings. First, most techniques cannot guarantee that the solution fits the data at inference. Second, while the derivation of the techniques is inspired by the existence of a valid scalar regularization function, such techniques do not in practice rely on such a function, and therefore veer away from classical variational techniques. In this work we introduce a new family of neural regularizers for the solution of inverse problems. These regularizers are based on a variational formulation and are guaranteed to fit the data. We demonstrate their use on a number of highly ill-posed problems, from image deblurring to limited angle tomography.

Original languageEnglish
Article number015006
JournalInverse Problems
Volume40
Issue number1
DOIs
StatePublished - 1 Jan 2024

Keywords

  • deep neural networks
  • inverse problems
  • proximal methods
  • variational methods

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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