Filtered Backprojection Algorithm For Circular Cone-beam CT

Computed tomography(CT)is a non-destructive detection technology that uses high-energy rays to obtain projected images of objects,and reconstructs tomographic images of the measured objects from the projection data.In 1972,British electrical engineer Hounsfield obtained the patent for the first CT scanner and won the Nobel Prize in Medicine in 1979 with Cormark for this revolutionary achievement.With the rapid development of semiconductor technology and modern computer graphics,CT scanners have completed five major technological innovations in the 1990s,which has greatly promoted the progress of modern medical diagnosis,and also provided extremely powerful detection method in many fields such as industrial precision measurement,security imaging,geophysics,and chemical identification.Circular orbit cone-beam CT is the most common structure in the medical and industrial fields.Meanwhile,the FDK algorithm has become the most commonly used reconstruction algorithm in circular orbit cone-beam CT due to its small amount of calculation and time-consuming characteristics.However,in practical applications,FDK algorithm does not meet the Tuy-Smith conditions for accurate reconstruction,problems such as geometric distortion and intensity degradation that are proportional to the angle of the cone angle will occur in the reconstruction domain away from its orbital plane.Only its small cone angle reconstruction domain(within ± 10°)has considerable quality.In recent years,the size and response speed of the detector has not been the main obstacle to the quality of CT reconstruction.While the circular orbit cone beam CT used in medical clinical and industrial gauging has detectors of sufficient size,how to ensure the reconstruction quality of the FDK algorithm under the increasing cone angle has become a major challenge faced by cone-beam CT.This paper takes the expansion of the cone-beam reconstructable domain as the research purpose,and makes some study on how to improve the reconstruction quality of the large cone angle area without changing the projection method.The main work of this paper is summarized as follows:(1)Both the two-dimensional and the three-dimensional analytical reconstruction method are deduced in detail,the structure and discrete expression of commonly used filters are studied,the geometric relationship in fan beam imaging is analyzed,the short scanning of the fan beam using conjugated light is discussed,furthermore,the fan beam rebinning algorithm is introduced.The physical meaning of the 3D Radon transform is abstractly described and the essential difference between the exact algorithm and the approximate algorithm is analyzed from the perspective of the 3D Radon support domain.The main discussion is the FDK algorithm and the properties of the FDK algorithm are proved.(2)Focus on the problem of imaging artifacts faced by the circular orbit cone beam FDK algorithm at large cone angles,an improved method of conjugate light in three-dimensional conditions is given,and then the rebinning algorithm for three-dimensional reconstruction is further introduced.Based on P-FDK and T-FDK,a new algorithm with variable filter path(v-FDK)is proposed.There are three main advantages of v-FDK:First,it simplifies the complex pre-weighted expressions of P-FDK and T-FDK since placing the pre-weighting step before the rebinning step.Second,the tuning factor of v-FDK makes the three rebinning algorithms unified in the form of reconstruction formula.Third,v-FDK can improve the reconstruction quality in the region of large cone angle without changing the projection data.(3)The reconstruction results were verified through simulation experiments.The influence of different projection data calculation methods on the reconstruction quality was analyzed through a comparative experiment,and the changing trends of the main parameters in the simulation process were discussed.The performance of v-FDK was tested,and the three-dimensional Shepp-Logan phantom was reconstructed under different cone angles.It was concluded that the tuning factor of v-FDK tended to be stable under different cone angles.And when the reconstruction cone angle is 30°,the imaging quality of v-FDK,FDK,P-FDK and T-FDK is compared,which verifies the practical feasibility of v-FDK,the artifacts of circular orbit cone beam reconstruction at large cone angles are better improved,finally the surface shape of v-FDK projection data is further discussed.