单光子发射断层成像图像重建的定量优化分析研究

本项目研究单光子发射断层成像的定量优化重建。SPECT是一种核医学成像技术。它能重建器官的功能图像，有广泛的应用。若要得到定量的图像，需要在图像重建中对各种影响因素进行补偿。采用调和技术、迭代法、Monte Carlo方法研究在均匀、非均匀衰减情形下，对非平行束探测模式的解析反演公式，为解决此类衰减Radon变换的数值解法和应用奠定理论基础。以Kunyansky及Natterer的研究工作为基础,针对平行、扇束探测模式, 拟建立有效的可对噪声、散射、衰减同时进行补偿的解析重建算法,用于获取SPECT定量快速成像并作仿真实验。采用衰减Radon变换的一致性条件和仅发射型数据的方法估计衰减系数图像，在考虑衰减和散射背景下，研究SPECT图像的定量优化重建；尝试探讨 ML-EM法，OSEM算法的加速收敛、精确实现, 给出计算机仿真结果，评价重建框架的可行性。

This project focuses on quantitative and optimal analysis research in SPECT image reconstruction. SPECT is one of the nuclear medicine imaging techniques．It can reconstruct the functional image of the organs，so it is widely applied．However, most of SPECT protocols for clinical use support only qualitative reconstruction．Its lack of quantitative capability affects the accurate evaluation of diseases．To get quantitative image, you simultaneously need to compensate in image reconstruction for various influencing factors. The variety of the existing SPECT algorithm can be divided into a family of analytical methods and a wide class of iterative techniques．By means of harmonic analysis, iterative reconstruction algorithm, Monte Carlo methods, Deriving explicit analytical inversion formulae for nonparallel beam collimation geometries and for uniform or non-uniform attenuation will be studied as theoretical basis of numerical evaluation and application about attenuated Radon transform-type. Based on Kunyansky's and Natterer's work, an efficient, analytical solution to the reconstruction problem of SPECT for parallel-beam and fan-beam geometries will be developed and that allows simultaneous compensation for non-uniform attenuation, and scatter, as well as suppression of signal-dependent Poisson noise. The numerical experiment and Monte Carlo simulation are to be created. Quantitative and optimal SPECT image reconstruction can be well achieved if photon attenuation, scatter are taken into account in the reconstruction process. Using a transmission scan is a common approach. A dramatic simplification could be made if the attenuation map could be obtained from the emission data. We try to develop a new method to estimate the attenuation map using the data consistency under the conditions of the attenuated Radon transform. An accelerated ML-EM, OSEM algorithm with bigger step size and theirs convergence will be studied and presented. Computer simulation results will be used to show that our reconstruction framework is feasible．