Research Article: Alignment theory of parallel-beam computed tomography image reconstruction for elastic-type objects using virtual focusing method

Date Published: June 15, 2018

Publisher: Public Library of Science

Author(s): Kyungtaek Jun, Dongwook Kim, Yuanquan Wang.


X-ray computed tomography has been studied in various fields. Considerable effort has been focused on reconstructing the projection image set from a rigid-type specimen. However, reconstruction of images projected from an object showing elastic motion has received minimal attention. In this paper, a mathematical solution to reconstructing the projection image set obtained from an object with specific elastic motions—periodically, regularly, and elliptically expanded or contracted specimens—is proposed. To reconstruct the projection image set from expanded or contracted specimens, methods are presented for detection of the sample’s motion modes, mathematical rescaling of pixel values, and conversion of the projection angle for a common layer.

Partial Text

X-ray computed tomography (CT) is an imaging technique in which the three-dimensional (3D) structure of a sample is reconstructed on the basis of two-dimensional projections formed by the penetration of X-rays at different projection angles. CT has become an essential technique in various fields, such as biology, archaeology, geoscience, and materials science [1–6].

Through the sinogram adjustment, an expanded or contracted reconstruction image of an elastic-type object can be obtained. Objects that regularly change in size require modification of the length in the sinogram, while objects that elliptically change require transformation of the unit pixel length and the projection angle in the sinogram. When modifying the projection angle, the spacing of the projection angles may not be equal. This does not cause a significant problem because inverse Radon transformation is defined for projection angles of unequal spacing. However, if the image is considerably expanded in one direction and a projection set is obtained for a change in equally spaced projection angles, the projection angle becomes dense at a certain angle. In this case, the image may be slightly blurred by the filter function. Further research on the filter function is needed (S5 Fig).




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