  X-ray tomography has been studied in various fields. Although a great deal of
effort has been directed at reconstructing the projection image set from a
rigid-type specimen, little attention has been addressed to the reconstruction
of projected images from an object showing elastic motion. Here, we present a
mathematical solution to reconstruct the projection image set obtained from an
object with specific elastic motions: periodically, regularly, and elliptically
expanded or contracted specimens. To reconstruct the projection image set from
expanded or contracted specimens, we introduce new methods; detection of
sample's motion modes, mathematical re-scaling pixel values and converting
projection angle for a common layer
