A Variational Reconstruction Method for Undersampled Dynamic X-ray Tomography based on Physical Motion Models

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http://hdl.handle.net/10138/312412

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Burger , M , Dirks , H , Frerking , L , Hauptmann , A , Helin , T & Siltanen , S 2017 , ' A Variational Reconstruction Method for Undersampled Dynamic X-ray Tomography based on Physical Motion Models ' , Inverse Problems , vol. 33 , no. 12 , 124008 . https://doi.org/10.1088/1361-6420/aa99cf

Title: A Variational Reconstruction Method for Undersampled Dynamic X-ray Tomography based on Physical Motion Models
Author: Burger, Martin; Dirks, Hendrik; Frerking, Lena; Hauptmann, Andreas; Helin, Tapio; Siltanen, Samuli
Contributor: University of Helsinki, Universtity College London
University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2017-12
Language: eng
Number of pages: 24
Belongs to series: Inverse Problems
ISSN: 0266-5611
URI: http://hdl.handle.net/10138/312412
Abstract: In this paper we study the reconstruction of moving object densities from undersampled dynamic x-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications, i.e. we do not assume to have a full Radon transform in each time step, but only projections in few angular directions. This restriction enforces a space-time reconstruction, which we perform by incorporating physical motion models and regularization of motion vectors in a variational framework. The methodology of optical flow, which is one of the most common methods to estimate motion between two images, is utilized to formulate a joint variational model for reconstruction and motion estimation. We provide a basic mathematical analysis of the forward model and the variational model for the image reconstruction. Moreover, we discuss the efficient numerical minimization based on alternating minimizations between images and motion vectors. A variety of results are presented for simulated and real measurement data with different sampling strategy. A key observation is that random sampling combined with our model allows reconstructions of similar amount of measurements and quality as a single static reconstruction.
Subject: 111 Mathematics
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