Department of Electrical Engineering and Computer Science and Radiology, University of Michigan, Ann Arbor, MI 48109, USA.
IEEE Trans Med Imaging. 2013 Feb;32(2):141-52. doi: 10.1109/TMI.2012.2206604. Epub 2012 Jun 29.
Motion-compensated image reconstruction (MCIR) methods incorporate motion models to improve image quality in the presence of motion. MCIR methods differ in terms of how they use motion information and they have been well studied separately. However, there have been less theoretical comparisions of different MCIR methods. This paper compares the theoretical noise properties of three popular MCIR methods assuming known nonrigid motion. We show the relationship among three MCIR methods-motion-compensated temporal regularization (MTR), the parametric motion model (PMM), and post-reconstruction motion correction (PMC)-for penalized weighted least square cases. These analyses show that PMM and MTR are matrix-weighted sums of all registered image frames, while PMC is a scalar-weighted sum. We further investigate the noise properties of MCIR methods with Poisson models and quadratic regularizers by deriving accurate and fast variance prediction formulas using an "analytical approach." These theoretical noise analyses show that the variances of PMM and MTR are lower than or comparable to the variance of PMC due to the statistical weighting. These analyses also facilitate comparisons of the noise properties of different MCIR methods, including the effects of different quadratic regularizers, the influence of the motion through its Jacobian determinant, and the effect of assuming that total activity is preserved. Two-dimensional positron emission tomography simulations demonstrate the theoretical results.
运动补偿图像重建 (MCIR) 方法通过使用运动模型来提高存在运动时的图像质量。MCIR 方法在使用运动信息方面有所不同，并且已经进行了单独的深入研究。然而，对于不同的 MCIR 方法，理论比较较少。本文在假设已知非刚性运动的情况下，比较了三种流行的 MCIR 方法的理论噪声特性。我们展示了三种 MCIR 方法——运动补偿时间正则化 (MTR)、参数运动模型 (PMM) 和后重建运动校正 (PMC)——在惩罚加权最小二乘情况下的关系。这些分析表明，PMM 和 MTR 是所有注册图像帧的矩阵加权和，而 PMC 是标量加权和。我们通过使用“解析方法”推导出准确且快速的方差预测公式，进一步研究了具有泊松模型和二次正则化的 MCIR 方法的噪声特性。这些理论噪声分析表明，由于统计加权，PMM 和 MTR 的方差低于或可与 PMC 的方差相媲美。这些分析还方便了不同 MCIR 方法的噪声特性比较，包括不同二次正则化的影响、运动通过雅可比行列式的影响以及假设总活动得到保留的影响。二维正电子发射断层扫描模拟验证了理论结果。
