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

## TL;DR

This paper presents a novel algorithm that combines shearlet transforms and deep neural networks to accurately extract wavefront sets from images, significantly improving edge and orientation detection in imaging sciences.

## Contribution

It introduces the first algorithmic approach integrating data-driven and model-based methods for wavefront set extraction using shearlet transforms and deep learning.

## Key findings

- Outperforms existing algorithms in edge-orientation detection
- Achieves superior ramp-orientation detection accuracy
- Effectively combines shearlet analysis with neural networks

## Abstract

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.