Meng Ling-Jian, Li Nan
Nuclear, Plasma, and Radiological Sciences, University of Illinois, Urbana-Champaign, Urbana, IL 61801 USA.
IEEE Trans Nucl Sci. 2009 Feb 1;56(1):81-90. doi: 10.1109/TNS.2008.2006609. Epub 2009 Feb 10.
In this paper, we present the use of modified uniform Cramer-Rao type bounds (MUCRB) for the design of single photon emission tomography (SPECT) systems. The MUCRB is the lowest attainable total variance using any estimator of an unknown vector parameter, whose mean gradient matrix satisfies a given constraint. Since the mean gradient is closely related to local impulse function, the MUCRB approach can be used to evaluate the fundamental tradeoffs between spatial resolution and variance that are achievable with a given SPECT system design. As a possible application, this approach allows one to compare different SPECT system designs based on the optimum average resolution-variance tradeoffs that can be achieved across multiple control-points inside a region-of-interest. The formulation of the MUCRB allows detailed modelling of physical aspects of practical SPECT systems and requests only a modest computation load. It can be used as an analytical performance index for comparing different SPECT system or aperture designs.
在本文中，我们展示了改进的均匀克拉美 - 罗型界（MUCRB）在单光子发射断层扫描（SPECT）系统设计中的应用。MUCRB是使用未知向量参数的任何估计器所能达到的最低总方差，其平均梯度矩阵满足给定约束。由于平均梯度与局部脉冲函数密切相关，MUCRB方法可用于评估给定SPECT系统设计所能实现的空间分辨率和方差之间的基本权衡。作为一种可能的应用，这种方法允许基于在感兴趣区域内多个控制点可实现的最佳平均分辨率 - 方差权衡来比较不同的SPECT系统设计。MUCRB的公式允许对实际SPECT系统的物理方面进行详细建模，并且只需要适度的计算量。它可以用作比较不同SPECT系统或孔径设计的分析性能指标。
