University of Oulu

Z. Purisha et al., "An Automatic Regularization Method: An Application for 3-D X-Ray Micro-CT Reconstruction Using Sparse Data," in IEEE Transactions on Medical Imaging, vol. 38, no. 2, pp. 417-425, Feb. 2019. doi: 10.1109/TMI.2018.2865646

An automatic regularization method : an application for 3-D X-ray micro-CT reconstruction using sparse data

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Author: Purisha, Zenith1,2; Karhula, Sakari S.3,4; Ketola, Juuso H.4;
Organizations: 1Department of Mathematics and Statistics, University of Helsinki, Finland
2Department of Mathematics, Universitas Gadjah Mada, Indonesia
3Infotech Oulu, University of Oulu, Oulu, Finland
4Research Unit of Medical Imaging, Physics and Technology, University of Oulu, Oulu Finland
5Medical Research Center, University of Oulu and Oulu University Hospital, Oulu, Finland
6Department of Diagnostic Radiology, Oulu University Hospital, Oulu, Finland
7Department of Orthopaedics, Traumatology and Hand Surgery, Kuopio University Hospital, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 1.5 MB)
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Language: English
Published: Institute of Electrical and Electronics Engineers, 2019
Publish Date: 2019-05-24


X-ray tomography is a reliable tool for determining the inner structure of 3-D object with penetrating X-rays. However, traditional reconstruction methods, such as Feldkamp-Davis-Kress (FDK), require dense angular sampling in the data acquisition phase leading to long measurement times, especially in X-ray micro-tomography to obtain high-resolution scans. Acquiring less data using greater angular steps is an obvious way for speeding up the process and avoiding the need to save huge data sets. However, computing 3-D reconstruction from such a sparsely sampled data set is difficult because the measurement data are usually contaminated by errors, and linear measurement models do not contain sufficient information to solve the problem in practice. An automatic regularization method is proposed for robust reconstruction, based on enforcing sparsity in the 3-D shearlet-transform domain. The inputs of the algorithm are the projection data and a priori known expected degree of sparsity, denoted as 0 <; C pr ≤ 1. The number Cpr can be calibrated from a few dense-angle reconstructions and fixed. Human subchondral bone samples were tested, and morphometric parameters of the bone reconstructions were then analyzed using standard metrics. The proposed method is shown to outperform the baseline algorithm (FDK) in the case of sparsely collected data. The number of X-ray projections can be reduced up to 10% of the total amount 300 projections over 180° with uniform angular step while retaining the quality of the reconstruction images and of the morphometric parameters.

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Series: IEEE transactions on medical imaging
ISSN: 0278-0062
ISSN-E: 1558-254X
ISSN-L: 0278-0062
Volume: 38
Issue: 2
Pages: 417 - 425
DOI: 10.1109/TMI.2018.2865646
Type of Publication: A1 Journal article – refereed
Field of Science: 3126 Surgery, anesthesiology, intensive care, radiology
Funding: This work was supported in part by the Academy of Finland (Finnish Centre of Excellence in Inverse Problems Research 2012–2017) under Grant 268378 and Grant 303786 and in part by the European Research Council through the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC under Grant 336267.
EU Grant Number: (336267) 3D-OA-HISTO - Development of 3D Histopathological Grading of Osteoarthritis
Academy of Finland Grant Number: 268378
Detailed Information: 268378 (Academy of Finland Funding decision)
303786 (Academy of Finland Funding decision)
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