The Application And Research Of The Complex Analysis Method In SPECT Image Reconstruction

Single photon emission computed tomography (SPECT) is a new kind of nuclear medi-cal imaging technology of which the research is one of the hot direction of today’s computer image science, maths, biological engineering, earth physics, nuclear medicine etc. Due to the illumination coming from many researchers devoting themselves to looking for new ways to research SPECT image reconstruction, this paper mainly takes advantage of complex anal-ysis theory to study image reconstruction and application of SPECT. By means of complex analysis technology and integral transform theory, we study the analysis inversion of atten-uated Radon transform with nonuniform complex attenuation based on SPECT detection and imaging. Meanwhile, we apply the inversion formula and the fan-beam acquisition ge-ometry for the Region of Interest (ROI) to derive the local analysis reconstruction formula for SPECT with nonuniform imaginary absorption fan-beam data. Moreover, we research Riemann-Hilbert reconstruction problem to obtain inversion formula of exponential Radon transform with complex attenuation and attenuated Radon transform with real absorption by using taylor series expansion and relative complex analysis technology. Furthermore, we could solve the analysis inversion and related application of such attenuated Radon transform.This thesis is composed of five chapters as follows:· In Chapter 1, we systematically introduce the research background and significance of SPECT, the domestic and foreign present research situation and development trends as well.· In Chapter 2, we introduce related contents of two-dimensional generalized Radon trans-form and weighted Hilbert transform.· In Chapter 3, We study two-dimensional generalized Radon transform, and derive the inversion formula of attenuated Radon transform with nonuniform complex attenuation by utilizing complex analysis method and integral transform theory. Meanwhile, we obtain the local analysis reconstruction formula with nonuniform imaginary absorption fan-beam data based on a usual transformation between parallel-beam and fan-beam coordinates.· In Chapter 4, we research Riemann-Hilbert reconstruction problem to obtain inversion formula of exponential Radon transform with complex attenuation and attenuated Radon transform with real absorption by using taylor series expansion and relative complex analysis technology.In Chapter 5, we summarize the whole text and put forward the outlook.