Deep Microlocal Reconstruction for Limited-Angle Tomography

• URL: http://arxiv.org/abs/2108.05732v1
• Date: Thu, 12 Aug 2021 13:16:38 GMT
• Title: Deep Microlocal Reconstruction for Limited-Angle Tomography
• Authors: H\'ector Andrade-Loarca, Gitta Kutyniok, Ozan \"Oktem, Philipp Petersen
• Abstract summary: 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.
• Score: 1.559929646151698
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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