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Deep Bayesian Inversion
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta.ORCID-id: 0000-0001-9928-3407
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).ORCID-id: 0000-0002-1118-6483
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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.

Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
Tillämpad matematik och beräkningsmatematik, Numerisk analys
Identifikatorer
URN: urn:nbn:se:kth:diva-262726OAI: oai:DiVA.org:kth-262726DiVA, id: diva2:1362344
Anmärkning

QC 20191021

Tillgänglig från: 2019-10-18 Skapad: 2019-10-18 Senast uppdaterad: 2019-10-21Bibliografiskt granskad
Ingår i avhandling
1. Data-driven Methods in Inverse Problems
Öppna denna publikation i ny flik eller fönster >>Data-driven Methods in Inverse Problems
2019 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2019. s. 196
Serie
TRITA-SCI-FOU ; 2019;49
Nyckelord
Inverse Problems, Machine Learning, Tomography
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:kth:diva-262727 (URN)978-91-7873-334-7 (ISBN)
Disputation
2019-10-31, F3, Lindstedtsvägen26, KTH, Stockholm, 14:00 (Engelska)
Opponent
Handledare
Forskningsfinansiär
Stiftelsen för strategisk forskning (SSF)
Tillgänglig från: 2019-10-21 Skapad: 2019-10-18 Senast uppdaterad: 2019-10-21Bibliografiskt granskad

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