Three‐dimensional tomographic image reconstruction from cone beam projections by single scanning method

Abstract

AbstractThe single‐scanning method has been proposed as a data acquisition method for reconstructing the three‐dimensional CT image, where a confronting pair of the cone beam X‐ray source and the planar detector are rotated on a circle surrounding the object. This paper discusses the problem of reconstructing the three‐dimensional image from the cone beam projection obtained by such a method. The traditional method of image reconstruction for this method is an approximation based on the two‐dimensional CT image reconstruction, and has a problem in that the quality of the reconstructed image is deteriorated when the circle on which the X‐ray source is moved has a small radius. First, a method is presented by which the problem of image reconstruction by the cone beam projection is reduced to the reconstruction problem by the three‐dimensional Radon transform. It is shown that the information required for the image reconstruction by the inverse three‐dimensional Radon transform cannot be obtained completely by the single‐scanning method. Then the image reconstruction by the two‐dimensional incomplete Radon transform is extended to the three‐dimensional case, and then applied to the image reconstruction by the cone beam projection. By this method, a mathematical strict image reconstruction can be achieved even by the single‐scanning method. The forementioned problem in the traditional method is now solved.