# Deep Microlocal Reconstruction for Limited-Angle Tomography

arXiv: https://arxiv.org/abs/2108.05732 · HTML: https://mlsanity.com/paper/2108.05732/

## 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 (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [EdgeConnect: Generative Image Inpainting with Adversarial Edge Learning](https://mlsanity.com/paper/1901.00212/) (2019)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [On the well-posedness of Bayesian inverse problems](https://mlsanity.com/paper/1902.10257/) (2019)
- [BCR-Net: a neural network based on the nonstandard wavelet form](https://mlsanity.com/paper/1810.08754/) (2018)
- [Meta-learning Pseudo-differential Operators with Deep Neural Networks](https://mlsanity.com/paper/1906.06782/) (2019)
- [Task adapted reconstruction for inverse problems](https://mlsanity.com/paper/1809.00948/) (2018)
- [Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography](https://mlsanity.com/paper/2006.01620/) (2020)
- [Limited-angle CT reconstruction via the L1/L2 minimization](https://mlsanity.com/paper/2006.00601/) (2020)
- [Fourier Image Transformer](https://mlsanity.com/paper/2104.02555/) (2021)
- [Learning the geometry of wave-based imaging](https://mlsanity.com/paper/2006.05854/) (2020)
- [Unsupervised Learnable Sinogram Inpainting Network (SIN) for Limited Angle CT reconstruction](https://mlsanity.com/paper/1811.03911/) (2018)
- [Limited Angle Tomography for Transmission X-Ray Microscopy Using Deep Learning](https://mlsanity.com/paper/2001.02469/) (2020)
- [Directional Sinogram Inpainting for Limited Angle Tomography](https://mlsanity.com/paper/1804.09991/) (2018)
- [Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks](https://mlsanity.com/paper/1901.01388/) (2019)
- [Deep learning reconstruction of digital breast tomosynthesis images for accurate breast density and patient-specific radiation dose estimation](https://mlsanity.com/paper/2006.06508/) (2020)

## Built on by (most cited first, 4 of 4)

- [On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector](https://mlsanity.com/paper/2204.10001/) (2022)
- [The Mathematics of Artificial Intelligence](https://mlsanity.com/paper/2203.08890/) (2022)
- [The method of the approximate inverse for limited-angle CT](https://mlsanity.com/paper/2510.04369/) (2025)
- [MiNO: Cotangent-bundle propagator learning for PDEs](https://mlsanity.com/paper/2608.15187/) (2026)

## 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.