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Title
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Reconstruction of a uniform star object from interior x-ray data: uniqueness, stability and algorithm
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Author
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Abstract
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| In this paper we consider the problem of reconstructing a two-dimensional star-shaped object of uniform density from truncated projections of the object. In particular, we prove that such an object is uniquely determined by its parallel projections sampled over a full ð angular range with a detector that only covers an interior field-of-view, even if the density of the object is not known a priori. We analyze the stability of this reconstruction problem and propose a reconstruction algorithm. Simulation experiments demonstrate that the algorithm is capable of reconstructing a star-shaped object from interior data, even if the interior region is much smaller than the size of the object. In addition, we present results for a heuristic reconstruction algorithm called DART, that was recently proposed. The heuristic method is shown to yield accurate reconstructions if the density is known in advance, and to have a very good stability in the presence of noisy projection data. Finally, the performance of the DBP and DART algorithms is illustrated for the reconstruction of real micro-CT data of a diamond. |
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Language
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English
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Source (journal)
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Inverse problems. - Bristol
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Publication
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Bristol
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2009
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ISSN
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0266-5611
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DOI
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10.1088/0266-5611/25/6/065010
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Volume/pages
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25
:6
(2009)
, p. 065010,1-065010,19
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ISI
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000266066100011
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Full text (Publisher's DOI)
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