The Study Of The Inverse Problem Of The Generalized Radon Transform In SPECT

For the generalized Radon transform, an explicit formula has a very important significanceto the development of the reconstruction algorithm and the local dependence of the solution ofprojection data, the methods of inversion also has immeasurable value to the study of processingproblems of other images. Single-Photon Emission Computed Tomography (SPECT) has beenthe indispensable tool of organ imaging such as heart, brain imaging, cerebral blood flow andfunctional imaging, and has been more and more widely applied in medical image and so on theother scientific field. The image reconstruction is a process obtaining the internal tomographicimaging of the object by the projection data (i.e.the Radon transform and the generalized Radontransform et al), so the problems of the image reconstruction can ultimately be attributed to theinversion of the Radon transform and the generalized Radon transform and so on. Thus, thereis a very important theoretical and practical value for the study of the inversion problems of thegeneralized Radon transform in SPECT. In this paper, the inversion problems of the generalizedRadon transform in SPECT and the methods of the improvements are explored by the wayof the mathematical methods and numerical solution such as Fourier transform, Fourier seriesand some techniques of integral transformation, otherwise, the inversion equations are derived.In order to ensure the efect of the method, numerical simulations of computer simulation areconducted.This thesis is composed of four chapters as follows:In Chapter1, we systematically introduce the background and significance on studyingthe inverse problems of Radon transform in SPECT, discuss the status of the study anddevelopment trends in future.In Chapter2, we introduce and develop some related contents of the generalized Radontransform and Fourier transform.In Chapter3, we discuss the π-scheme short-scan SPECT for the uniformly attenuatedproject data which is obtained in the π-scheme short-scan SPECT; we study the results ofimage reconstruction by Fourier approximation reconstruction algorithm.In Chapter4, we analyze the related results of image Reconstruction by decomposing the Novikov’s inversion operator for the non-uniform attenuated project data which is obtainedin the π-scheme short-scan SPECT.