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.

X射线计算机断层摄影术已经在各个领域进行了研究。已经集中了相当多的精力来从刚性样本中重建投影图像集。然而，从显示弹性运动的物体投影的图像的重建受到最小的关注。在本文中，提出了一种数学方法来重建从具有特定弹性运动（周期性，规则性和椭圆形扩展或收缩的标本）的对象获得的投影图像集。为了从膨胀或收缩的样本中重建投影图像集，提出了检测样本的运动模式，像素值的数学重新缩放以及公共层的投影角度转换的方法。