(A) study on three-dimensional image reconstruction algorithm using cone-beam projections

Abstract

Image Reconstruction, which is sometimes known as image reconstruction from projection, is now a well known mathematical image processing algorithm mainly developed for the X-ray computerized tomography. Projection reconstruction technique, however, is now widely used in many scientific and medical disciplines other than the original X-ray CT, such as X-ray crystallography and nuclear emission tomography as well as muclear magnetic resonance imaging. In this thesis the mathematical preliminaries for image reconstruction from projections are given in Chapter2, and the conventional 2-D image reconstruction algorithms for the parallel-beam and the fan-beam mode and the 3-D case for the parallel-beam mode are also represented in the subsequent chapters. This thesis proposes True Three-Dimensional Come-Beam Reconstruction. (TTCR) algorithm which is applicable to generalized (or truncated) spherical (or cylindrical) detector geometry as well as the complete sphere in chapter 5. The TTCR algorithm is derived by using the coordinate transformation technique and is based on the filtered back-projection technique. The proposed cone-beam reconstruction algorithm uses generally the space-variant filter functions for the superposition integral with some weighting functions both before and after the filtering process. The simulation results show that the proposed TTCR algorithm proved to be superior to the conventional 3-D reconstruction(GTTR) algorithm for the parallel-beam mode in the point of the resolution as well as the image quality, and to be applicable to the truncated cylindrical (or spherical) detection system of an arbitrary truncation angle.