Deep Microlocal Reconstruction for Limited-Angle Tomography

TL;DR

This paper introduces a deep learning method that enhances limited-angle tomography by jointly reconstructing images and extracting wavefront sets, leveraging microlocal analysis and neural networks for improved accuracy.

Contribution

It develops a novel deep learning framework that combines wavefront set extraction with image reconstruction, grounded in microlocal analysis and neural network theory.

Findings

Numerical experiments show improved reconstruction quality.

The method accurately extracts wavefront sets from limited-angle data.

Theoretical identification of microlocal relations for neural networks.

Abstract

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.