Machine Learning in Inverse Problems - Learning Regularisation Functionals and Operator Corrections
View / Open Files
Authors
Lunz, Sebastian
Advisors
Schönlieb, Carola-Bibiane
Date
2021-01-21Awarding Institution
University of Cambridge
Qualification
Doctor of Philosophy (PhD)
Type
Thesis
Metadata
Show full item recordCitation
Lunz, S. (2021). Machine Learning in Inverse Problems - Learning Regularisation Functionals and Operator Corrections (Doctoral thesis). https://doi.org/10.17863/CAM.84210
Abstract
In this thesis, we investigate properties of deep neural networks and their application to inverse problems.
A successful classical approach to inverse problems is variational regularisation, combining knowledge and modelling of the imaging modality at hand with a regularisation functional that incorporates prior knowledge about solutions to the inverse problem. With the success of deep neural networks in many imaging tasks such as image classification or semantic segmentation, recently algorithms that leverage the power of neural networks have been explored to solve inverse problems.
In this thesis, we discuss various approaches to incorporate deep learning into reconstruction algorithms for inverse problems and in particular into variational approaches. We propose and discuss an algorithm to train a neural network as regularisation functional. This is achieved by training the network to tell apart an unregularised pseudo-inverse from ground truth images. The resulting regulariser decreases the Wasserstein distance between reconstructions and ground truth images at an optimal rate. We present computational results for computed tomography (CT) and magnetic resonance imaging (MRI) reconstruction and investigate generalisation properties of the learned regularisation functional.
In another line of research, we turn our attention to making use of neural networks to correct for errors in the forward operator. While an approximate model of the forward operator is available in many applications, this model can exhibit artefacts compared to the true behaviour of the imaging modality. We train a neural network to learn how to correct for these shortcomings by learning a correction from data. The aim is to obtain a corrected operator that can be employed within a variational framework for reconstruction. We investigate key challenges of this approach and propose a recursive forward-adjoint algorithm to efficiently train an operator correction for photo-acoustic tomography reconstruction.
Keywords
Machine Learning, Inverse Problems, Neural Networks
Sponsorship
EPSRC (1804164)
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.84210
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.
Recommended or similar items
The current recommendation prototype on the Apollo Repository will be turned off on 03 February 2023. Although the pilot has been fruitful for both parties, the service provider IKVA is focusing on horizon scanning products and so the recommender service can no longer be supported. We recognise the importance of recommender services in supporting research discovery and are evaluating offerings from other service providers. If you would like to offer feedback on this decision please contact us on: support@repository.cam.ac.uk