Fourier-based Methods for Image Reconstruction in PET

该项目的长期目标是改进断层成像在诊断放射学和核医学中的应用，特别是正电子发射断层成像(PET)。该项目涉及根据PET扫描仪的原始探测器测量结果生成图像的计算机方法(即根据投影数据重建图像的算法)。傅里叶变换是非迭代重建方法理论中的一种重要数学工具，但其提高实际计算量的潜力在这些方法中还没有得到充分的发挥，对于迭代重建方法也没有得到充分的研究。该项目旨在开发和评估基于傅里叶变换的方法在3DPET中用于非迭代和迭代重建的有用性。所提出的方法旨在减少在处理由扫描仪的探测器系统测量的发射数据和传输数据的过程中进行的近似次数，同时所需的扫描和处理时间比目前临床PET中使用的简化方法更少。对于发射数据，具体目标是测试和评估用于全3D PET几何的直接傅立叶方法的仔细研究和优化实施，并利用重建模型中的衰减、散射和随机信息开发、实施、测试和评估基于傅立叶的3D迭代技术。对于传输数据，具体目的是根据该数据开发和评估全3D迭代重建，随后是衰减图的基于傅立叶的快速重投影，用于校正全3D发射数据，或者用于根据发射数据的全3D迭代重建内的衰减效应的建模。使用正电子发射计算机断层扫描进行癌症成像，特别是全身扫描，受到发射和传输数据集可获得的计数数量较少以及散布和随机事件的较大比例的限制。提高PET临床实用数据采集和处理的定量准确性、信噪比性能和病变检测能力，将有助于改善癌症的检测、诊断和治疗计划。

The long-term aim of this project is the improvement of tomographic imaging in diagnostic radiology and nuclear medicine, especially positron emission tomography (PET). The project involves computer methods for generating images from the raw detector measurements of the PET scanner (i.e., algorithms for image reconstruction from projection data). The Fourier transform is an important mathematical tool in the theory of non- iterative reconstruction methods, but its potential for improving practical computation has not been fully exploited for these methods, and has not been investigated at all for iterative reconstruction methods. The project aims to develop and evaluate the usefulness of Fourier-based approaches for non-iterative and iterative reconstruction in 3D PET. The proposed approaches aim to decrease the number of approximations that are made during the processing of the emission data and transmission data measured by the detector system of the scanner, while requiring less scanning and processing time than the simplified approaches currently used in clinical PET. For the emission data, the specific aim is to test and evaluate a carefully studied and optimized implementation of the direct Fourier method for the geometry of fully-3D PET, and to develop, implement, test, and evaluate Fourier-based 3D iterative techniques utilizing information on attenuation, scatter and randoms within the reconstruction model. For the transmission data, the specific aim is to develop and evaluate fully-3D iterative reconstruction from this data, followed by fast Fourier-based reprojection of the attenuation map, to be used either for correction of the fully-3D emission data, or for modeling of attenuation effects within the fully-3D iterative reconstruction from the emission data. Cancer imaging with PET, especially whole-body scanning, is limited by the low numbers of counts obtainable in the emission and transmission data sets and by the large fractions of scatter and random events. Improving the quantitative accuracy, signal- to-noise performance and lesion detectability of clinically practical data acquisition and processing in PET would lead to improved detection, diagnosis, and treatment planning of cancer.