University of Oulu

S. Mukherjee, A. Hauptmann, O. Öktem, M. Pereyra and C. -B. Schönlieb, "Learned Reconstruction Methods With Convergence Guarantees: A survey of concepts and applications," in IEEE Signal Processing Magazine, vol. 40, no. 1, pp. 164-182, Jan. 2023, doi: 10.1109/MSP.2022.3207451.

Learned reconstruction methods with convergence guarantees : a survey of concepts and applications

Saved in:
Author: Mukherjee, Subhadip1; Hauptmann, Andreas2,3; Öktem, Ozan4;
Organizations: 1Department of Computer Science, University of Bath, Bath, U.K.
2Research Unit of Mathematical Sciences, University of Oulu, Oulu, Finland
3Department of Computer Science, University College London, London, U.K.
4Department of Information Technology, Uppsala University, Uppsala, Sweden
5Mathematical Sciences and the School of Mathematical and Computer Sciences, Heriot–Watt University, Edinburgh, Scotland
6University of Cambridge, Cambridge, U.K.
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 2.1 MB)
Persistent link:
Language: English
Published: Institute of Electrical and Electronics Engineers, 2023
Publish Date: 2023-05-05


In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalyzed an ongoing quest for the precise characterization of the correctness and reliability of data-driven methods in critical use cases, for instance, in medical imaging. Notwithstanding the excellent performance and efficacy of deep learning-based methods, concerns have been raised regarding the approaches’ stability, or lack thereof, with serious practical implications. Significant advances have been made in recent years to unravel the inner workings of data-driven image recovery methods, challenging their widely perceived black-box nature. In this article, we specify relevant notions of convergence for data-driven image reconstruction, which forms the basis of a survey of learned methods with mathematically rigorous reconstruction guarantees. An example that is highlighted is the role of input-convex neural networks (ICNNs), offering the possibility to combine the power of deep learning with classical convex regularization theory for devising methods that are provably convergent. This survey article is aimed at both methodological researchers seeking to advance the frontiers of our understanding of data-driven image reconstruction methods as well as practitioners by providing an accessible description of useful convergence concepts and by placing some of the existing empirical practices on a solid mathematical foundation.

see all

Series: IEEE signal processing magazine
ISSN: 1053-5888
ISSN-E: 1558-0792
ISSN-L: 1053-5888
Volume: 40
Issue: 1
Pages: 164 - 182
DOI: 10.1109/MSP.2022.3207451
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
113 Computer and information sciences
Copyright information: © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.