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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
Keyword [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: 2017-12-07Bibliographically approved

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Öktem, Ozan

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  • apa
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  • de-DE
  • en-GB
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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