Stayman J Webster, Fessler Jeffrey A
Department of Electrical Engineering and Computer Science (4415 EECS), University of Michigan, Ann Arbor, MI 48109-2122, USA.
IEEE Trans Med Imaging. 2004 Mar;23(3):269-84. doi: 10.1109/TMI.2003.823063.
Imaging systems that form estimates using a statistical approach generally yield images with nonuniform resolution properties. That is, the reconstructed images possess resolution properties marked by space-variant and/or anisotropic responses. We have previously developed a space-variant penalty for penalized-likelihood (PL) reconstruction that yields nearly uniform resolution properties. We demonstrated how to calculate this penalty efficiently and apply it to an idealized positron emission tomography (PET) system whose geometric response is space-invariant. In this paper, we demonstrate the efficient calculation and application of this penalty to space-variant systems. (The method is most appropriate when the system matrix has been precalculated.) We apply the penalty to a large field of view PET system where crystal penetration effects make the geometric response space-variant, and to a two-dimensional single photon emission computed tomography system whose detector responses are modeled by a depth-dependent Gaussian with linearly varying full-width at half-maximum. We perform a simulation study comparing reconstructions using our proposed PL approach with other reconstruction methods and demonstrate the relative resolution uniformity, and discuss tradeoffs among estimators that yield nearly uniform resolution. We observe similar noise performance for the PL and post-smoothed maximum-likelihood (ML) approaches with carefully matched resolution, so choosing one estimator over another should be made on other factors like computational complexity and convergence rates of the iterative reconstruction. Additionally, because the postsmoothed ML and the proposed PL approach can outperform one another in terms of resolution uniformity depending on the desired reconstruction resolution, we present and discuss a hybrid approach adopting both a penalty and post-smoothing.
使用统计方法进行估计的成像系统通常会生成具有非均匀分辨率特性的图像。也就是说，重建图像具有以空间变化和/或各向异性响应为特征的分辨率特性。我们之前已经为惩罚似然（PL）重建开发了一种空间变化惩罚项，它能产生几乎均匀的分辨率特性。我们展示了如何高效地计算这个惩罚项，并将其应用于几何响应是空间不变的理想化正电子发射断层扫描（PET）系统。在本文中，我们展示了这个惩罚项在空间变化系统中的高效计算和应用。（当系统矩阵已经预先计算时，该方法最为适用。）我们将这个惩罚项应用于一个大视野PET系统，其中晶体穿透效应使几何响应具有空间变化性，以及一个二维单光子发射计算机断层扫描系统，其探测器响应由一个半高宽线性变化的深度相关高斯函数建模。我们进行了一项模拟研究，将使用我们提出的PL方法的重建结果与其他重建方法进行比较，展示了相对分辨率均匀性，并讨论了产生几乎均匀分辨率的估计器之间的权衡。我们观察到，在分辨率仔细匹配的情况下，PL方法和后平滑最大似然（ML）方法具有相似的噪声性能，因此在选择估计器时应基于其他因素，如计算复杂度和迭代重建的收敛速度。此外，由于后平滑ML方法和我们提出的PL方法在分辨率均匀性方面可能会根据所需的重建分辨率而相互优于对方，我们提出并讨论了一种同时采用惩罚项和后平滑的混合方法。
