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Deep microlocal reconstruction for limited-angle tomography
Ludwig Maximilians Univ Munchen, Dept Math, D-80333 Munich, Germany..
Ludwig Maximilians Univ Munchen, Dept Math, D-80333 Munich, Germany.;Univ Tromso, Dept Phys & Technol, N-9019 Tromso, Norway..ORCID iD: 0000-0001-9738-2487
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Department of Information Technology, Division of Scientific Computing, Uppsala University, Uppsala, Sweden.ORCID iD: 0000-0002-1118-6483
Univ Vienna, Fac Math, A-1090 Vienna, Austria.;Univ Vienna, Res Network Data Sci, A-1090 Vienna, Austria..
2022 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 59, p. 155-197Article in journal (Refereed) Published
Abstract [en]

We present a deep-learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a recently developed digital wavefront set extractor as well as the well-known microlocal canonical relation for the Radon transform. We use the wavefront set information about x-ray data to improve the reconstruction by requiring that the underlying neural networks simultaneously extract the correct ground truth wavefront set and ground truth image. As a necessary theoretical step, we identify the digital microlocal canonical relations for deep convolutional residual neural networks. We find strong numerical evidence for the effectiveness of this approach.

Place, publisher, year, edition, pages
Elsevier BV , 2022. Vol. 59, p. 155-197
Keywords [en]
Inverse problems, Deep learning, Tomography, Microlocal analysis, Wavefront set
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-314234DOI: 10.1016/j.acha.2021.12.007ISI: 000798563300005Scopus ID: 2-s2.0-85122624648OAI: oai:DiVA.org:kth-314234DiVA, id: diva2:1671350
Note

QC 20220617

Available from: 2022-06-17 Created: 2022-06-17 Last updated: 2022-06-25Bibliographically approved

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Öktem, Ozan

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