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Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1118-6483
2019 (English)In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 12, no 4, p. 1936-1966Article in journal (Refereed) Published
Abstract [en]

Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct extraction of those. In this paper, we introduce the first algorithmic approach to extract the wavefront set of images, which combines data-based and model-based methods. Based on a celebrated property of the shearlet transform to unravel information on the wavefront set, we extract the wavefront set of an image by first applying a discrete shearlet transform and then feeding local patches of this transform to a deep convolutional neural network trained on labeled data. The resulting algorithm outperforms all competing algorithms in edge-orientation and ramp-orientation detection.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2019. Vol. 12, no 4, p. 1936-1966
Keywords [en]
Convolutional neural networks, Deep learning, Shearlets, Wavefront set, Convolution, Data mining, Extraction, Image processing, Inverse problems, Neural networks, Wavefronts, Algorithmic approach, Competing algorithms, Convolutional neural network, Microlocal analysis, Model-based method, Orientation detections, Shearlet transforms, Deep neural networks
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-268578DOI: 10.1137/19M1237594Scopus ID: 2-s2.0-85077054159OAI: oai:DiVA.org:kth-268578DiVA, id: diva2:1428689
Note

QC 20200506

Available from: 2020-05-06 Created: 2020-05-06 Last updated: 2020-05-06Bibliographically 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
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Output format
  • html
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  • asciidoc
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