Deep Microlocal Reconstruction for Limited-Angle Tomography
This work addresses image reconstruction challenges in tomographic imaging, particularly for limited-angle scenarios, representing an incremental improvement by integrating wavefront set extraction with deep learning.
The authors tackled the problem of limited-angle tomography by developing a deep learning algorithm that jointly reconstructs images and extracts wavefront sets, using digital microlocal relations to improve accuracy, with strong numerical evidence supporting its effectiveness.
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.