# Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks

arXiv: https://arxiv.org/abs/1901.01388 · HTML: https://mlsanity.com/paper/1901.01388/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2019.

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

- [Explaining Image Classifiers with Multiscale Directional Image Representation](https://mlsanity.com/paper/2211.12857/) (2022)
- [Deep Microlocal Reconstruction for Limited-Angle Tomography](https://mlsanity.com/paper/2108.05732/) (2021)
- [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)

## Abstract (arXiv)

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.