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Deep Bayesian Inversion
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Elekta.ORCID iD: 0000-0001-9928-3407
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1118-6483
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most realistic imaging applications in the clinic. We introduce two novel deep learning based methods for solving large-scale inverse problems using Bayesian inversion: a sampling based method using a WGAN with a novel mini-discriminator and a direct approach that trains a neural network using a novel loss function. The performance of both methods is demonstrated on image reconstruction in ultra low dose 3D helical CT. We compute the posterior mean and standard deviation of the 3D images followed by a hypothesis test to assess whether a "dark spot" in the liver of a cancer stricken patient is present. Both methods are computationally efficient and our evaluation shows very promising performance that clearly supports the claim that Bayesian inversion is usable for 3D imaging in time critical applications.

National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics, Numerical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-262726OAI: oai:DiVA.org:kth-262726DiVA, id: diva2:1362344
Note

QC 20191021

Available from: 2019-10-18 Created: 2019-10-18 Last updated: 2019-10-21Bibliographically approved
In thesis
1. Data-driven Methods in Inverse Problems
Open this publication in new window or tab >>Data-driven Methods in Inverse Problems
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis on data-driven methods in inverse problems we introduce several new methods to solve inverse problems using recent advancements in machine learning and specifically deep learning. The main goal has been to develop practically applicable methods, scalable to medical applications and with the ability to handle all the complexities associated with them.

In total, the thesis contains six papers. Some of them are focused on more theoretical questions such as characterizing the optimal solutions of reconstruction schemes or extending current methods to new domains, while others have focused on practical applicability. A significant portion of the papers also aim to bringing knowledge from the machine learning community into the imaging community, with considerable effort spent on translating many of the concepts. The papers have been published in a range of venues: machine learning, medical imaging and inverse problems.

The first two papers contribute to a class of methods now called learned iterative reconstruction where we introduce two ways of combining classical model driven reconstruction methods with deep neural networks. The next two papers look forward, aiming to address the question of "what do we want?" by proposing two very different but novel loss functions for training neural networks in inverse problems. The final papers dwelve into the statistical side, one gives a generalization of a class of deep generative models to Banach spaces while the next introduces two ways in which such methods can be used to perform Bayesian inversion at scale.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2019. p. 196
Series
TRITA-SCI-FOU ; 2019;49
Keywords
Inverse Problems, Machine Learning, Tomography
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-262727 (URN)978-91-7873-334-7 (ISBN)
Public defence
2019-10-31, F3, Lindstedtsvägen26, KTH, Stockholm, 14:00 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research
Available from: 2019-10-21 Created: 2019-10-18 Last updated: 2019-10-21Bibliographically approved

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