Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this survey paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family generative regularisers. The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results. Finally, we discuss future directions and open problems in the field.
Original languageEnglish
JournalJournal of Mathematical Imaging and Vision
Early online date9 Oct 2023
Publication statusPublished - 9 Oct 2023

Bibliographical note

Funding Information:
Margaret Duff is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/L015684/1. Matthias Ehrhardt acknowledges support from the EPSRC (EP/S026045/1, EP/T026693/1), the Faraday Institution (EP/T007745/1) and the Leverhulme Trust (ECF-2019-478). Neill Campbell acknowledges support from the EPSRC CAMERA Research Centre (EP/M023281/1 and EP/T022523/1) and the Royal Society.

Publisher Copyright:
© 2023, The Author(s).


  • Generative models
  • Imaging
  • Inverse problems
  • Machine learning

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Applied Mathematics
  • Geometry and Topology
  • Computer Vision and Pattern Recognition
  • Statistics and Probability
  • Modelling and Simulation


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