Deep Microlocal Reconstruction for Limited-Angle Tomography

Héctor Andrade-Loarca; Gitta Kutyniok; Ozan Öktem; Philipp Petersen

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arXiv · 2108.05732

Deep Microlocal Reconstruction for Limited-Angle Tomography

Héctor Andrade-Loarca·Gitta Kutyniok·Ozan Öktem·Philipp Petersen

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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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Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen. 2021-08-12. Deep Microlocal Reconstruction for Limited-Angle Tomography. https://arxiv.org/abs/2108.05732

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