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Solving ill-posed inverse problems using iterative deep neural networks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1118-6483
2017 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 33, no 12, article id 124007Article in journal (Refereed) Published
Abstract [en]

We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the 'gradient' component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 x 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2017. Vol. 33, no 12, article id 124007
Keywords [en]
tomography, deep learning, gradient descent, regularization
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-219496DOI: 10.1088/1361-6420/aa9581ISI: 000416015300001Scopus ID: 2-s2.0-85038424472OAI: oai:DiVA.org:kth-219496DiVA, id: diva2:1163554
Note

QC 20171207

Available from: 2017-12-07 Created: 2017-12-07 Last updated: 2019-10-18Bibliographically 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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Öktem, Ozan

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