Deep Microlocal Reconstruction for Limited-Angle Tomography

Understand

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.