mlsanityData to 14 Oct 2026

Deep Microlocal Reconstruction for Limited-Angle Tomography

arXiv 2108.05732 ↗First posted 12 Aug 2021cs.LG cs.CV cs.NAcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 19 of its 109 references that are in the map. First posted on arXiv 12 Aug 2021.

Builds on

19 of 109 references.

References · 19

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2017Learned Primal-dual Reconstructioncited by 251
  4. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  5. 2019EdgeConnect: Generative Image Inpainting with Adversarial Edge Learningcited by 163
  6. 2018Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomographycited by 29
  7. 2019On the well-posedness of Bayesian inverse problemscited by 20
  8. 2018BCR-Net: a neural network based on the nonstandard wavelet formcited by 18
  9. 2019Meta-learning Pseudo-differential Operators with Deep Neural Networkscited by 17
  10. 2018Task adapted reconstruction for inverse problemscited by 16
  11. 2020Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomographycited by 15
  12. 2020Limited-angle CT reconstruction via the L1/L2 minimizationcited by 12
7 more
  1. 2021Fourier Image Transformercited by 12
  2. 2020Learning the geometry of wave-based imagingcited by 7
  3. 2018Unsupervised Learnable Sinogram Inpainting Network (SIN) for Limited Angle CT reconstructioncited by 6
  4. 2020Limited Angle Tomography for Transmission X-Ray Microscopy Using Deep Learningcited by 6
  5. 2018Directional Sinogram Inpainting for Limited Angle Tomographycited by 4
  6. 2019Extraction of digital wavefront sets using applied harmonic analysis and deep neural networkscited by 4
  7. 2020Deep learning reconstruction of digital breast tomosynthesis images for accurate breast density and patient-specific radiation dose estimationcited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 0; 2024: 0; 2025: 1; 2026: 1.

4 papers.

  1. 2022On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detectorcited by 2
  2. 2022The Mathematics of Artificial Intelligencecited by 0
  3. 2025The method of the approximate inverse for limited-angle CTcited by 0
  4. 2026MiNO: Cotangent-bundle propagator learning for PDEscited by 0