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

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.