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Journal of Electronic Imaging

Reconstruction of three-dimensional localized objects from limited angle x-ray projections: an approach based on sparsity and multigrid image representation
Author(s): Charles Soussen; Jerome Idier
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Paper Abstract

We report on three-dimensional image reconstruction from a limited set of computed tomography projections. We focus on configurations with very limited angle of view and on applications in which the image to be reconstructed is composed of one or several localized objects laying in a known background. We propose an original method based on the detection of the localized object voxels and on a sparse modeling of the image. Reconstruction is done by computing the maximum a posteriori estimator of the image parameters. To implement image reconstruction, we adopt a multigrid strategy in which coarse-to-fine resoluted images are successively reconstructed. This strategy provides detection of localized object voxels as well as accurate initial solutions at each resolution level. Each optimization stage is carried out by using an iterative deterministic descent algorithm. We propose a convergent single-site update algorithm that consists of successive constrained optimizations with respect to one voxel at a time. We show the performance of the multigrid method on simulated data corresponding to a set of limited angle cone-beam projections of a synthetic image. The results are accurate, while both memory storage and numerical time of computation are dramatically reduced compared to the monogrid reconstruction method.

Paper Details

Date Published: 1 July 2008
PDF: 19 pages
J. Electron. Imag. 17(3) 033011 doi: 10.1117/1.2954960
Published in: Journal of Electronic Imaging Volume 17, Issue 3
Show Author Affiliations
Charles Soussen, Ctr. de Recherche en Automatique de Nancy (France)
Jerome Idier, Institute of Research in Communications and Cybernetics of Nantes (France)

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