.pet / Spect / Tat Image Reconstruction Algorithms And Numerical Systems Development,

PET and SPECT are two modern imaging techniques of broad medical application.In nowadays,TAT is a research central point in the medical imaging equipment,with good prospects for development.This paper aims to study the imaging mathematical model of PET,SPECT TAT and projective transforms and the formulae of reconstruction,then eventually realizes the image reconstruction.In the first chapter,we introduce the imaging mathematical principles and the mathematical problems of the PET,SPECT and TAT. Give a preliminary introduction of the formulae and algorithms of the image reconstruction.Then we summarize the imaging mathematical principle of these medical imaging equipments into Radon-type transform and inverse Radon-type transform.In Chapter two,we study the application of the KL transform in the PET imaging.The KL transform operates on the image data of Radon transform,and then we gain all levels of the principle components.At last the inverse Radon transform operates on the principal components of all levels to achieve the image reconstruction.In Chapter three,we achieve some numerical experiments SPECT projective transformation - attenuation Radon transform and give a brief introduction about the inverse attenuation Radon transform formula-Novikov formula.In Chapter four,firstly we survey the imaging mathematical principle and state its projective transform - the Spherical Mean Radon transform of TAT.Secondly we introduce the imaging reconstruction formula of three-dimensional;Thirdly we apply the Fourier Transform and the special function integral to transform the two-dimensional reconstruction formula deduced by L.A.Kuyansky,including oscillatory integrals into a simple formula,which including Hilbert transform.Then we use Matlab to develop a simulation system of the TAT imaging reconstruction of the two-dimensional formulae,based on the D.Finch's four reconstruction formulae and the formula which is derived in this chapter.The numerical experiments are successful.Therefore we gain a comparison.Last but not the least,we point out the text of the yet to be perfected and further research in chapter five.