The Analysis and Study about the Problems of Image Reconstruction 

Author  JiangJun 
Tutor  WangJinPing 
School  Ningbo University 
Course  Basic mathematics 
Keywords  Image reconstruction Radon transform Filtered back projection(FBP) algorithm Fourier inversion formula Hilbert transform Parallelbeam and Fanbeam ROI reconstruction 
CLC  TP391.41 
Type  Master's thesis 
Year  2013 
Downloads  2 
Quotes  0 
Image reconstruction is to reconstruct internal tomographic image of the body by the basisof projection data detected from the object, and its significance lies in that though obtaining theinternal image of the object, the body is not physically damaged. Because of the visual features ofthe image, so it is widely used in medicine, astronomy, geography, chemistry and other fields, itsapplication and theoretical background usually can be attributed to the mathematical transform,such as Radon transform, Hilbert transform, Fourier transform and their associated inversionformula research. Especially the Radon transform, which is the mathematical basis of the riseof computed tomography and reconstruction issues in recent years. On this basis, we have gotsome image reconstruction algorithms. In particular, the filtered back projection algorithm iswidely used in CT. In this paper we firstly introduced the properties and inversion formulasof the exponential Radon transform on the basis of Radon transform. And on the backgroundof parallelbeam FBP, using the Xray scanning way, by changing the integral and derivativeorder, we not only improves the computational speed, but also greatly reduce the efects ofnoise. At the same time, in order to lead to the fan beam image reconstruction algorithm ofROI, we make appropriately improvement on the basis of this parallel beam, thereby optimizingthe reconstruction algorithm.This thesis is composed of four chapters as follows:In Chapter1we systematically introduce research background and main research work.In Chapter2we study npiline application question in CT reconstruction algorithm.In Chapter3we study a general scanning trajectory question in ROI CT reconstructionalgorithm.In Chapter4on the base of Novikovâ€™s inversion formula, we develop attenuated Radontransform and exponential Radon transform in practical problemâ€™s application of CT reconstruction.