Title
Reconstruction of a uniform star object from interior x-ray data: uniqueness, stability and algorithm Reconstruction of a uniform star object from interior x-ray data: uniqueness, stability and algorithm
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Bristol ,
Subject
Physics
Source (journal)
Inverse problems. - Bristol
Volume/pages
25(2009) :6 , p. 065010,1-065010,19
ISSN
0266-5611
ISI
000266066100011
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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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