Deep microlocal reconstruction for limited-angle tomography

被引:4
|
作者
Andrade-Loarca, Hector [1 ]
Kutyniok, Gitta [1 ,2 ]
Oektem, Ozan [3 ,4 ]
Petersen, Philipp [5 ,6 ]
机构
[1] Ludwig Maximilians Univ Munchen, Dept Math, D-80333 Munich, Germany
[2] Univ Tromso, Dept Phys & Technol, N-9019 Tromso, Norway
[3] KTH Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden
[4] Uppsala Univ, Dept Informat Technol, Div Sci Comp, SE-75105 Uppsala, Sweden
[5] Univ Vienna, Fac Math, A-1090 Vienna, Austria
[6] Univ Vienna, Res Network Data Sci, A-1090 Vienna, Austria
基金
瑞典研究理事会;
关键词
Inverse problems; Deep learning; Tomography; Microlocal analysis; Wavefront set; LOCAL TOMOGRAPHY; BREAST TOMOSYNTHESIS; IMAGE-RECONSTRUCTION; CT RECONSTRUCTION; INVERSE PROBLEMS; BACK-PROJECTION; RADON-TRANSFORM; ART; REGULARIZATION; IMPLEMENTATION;
D O I
10.1016/j.acha.2021.12.007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.(c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
引用
收藏
页码:155 / 197
页数:43
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