Dept. Diagnostic Radiol. & Electr. Eng., State Univ. of New York, Stony Brook, NY.
IEEE Trans Med Imaging. 1995;14(4):669-80. doi: 10.1109/42.476108.
While the ML-EM algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem. Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, the authors propose an extension to a piecewise linear model-the weak plate-which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for the authors' application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, the authors model the prior as a Gibbs distribution and use a GEM formulation for the optimization. They compare quantitative performance of the ML-EM algorithm, a GEM algorithm with a prior favoring piecewise constant regions, and a GEM algorithm with their weak plate prior. Pointwise and regional bias and variance of ensemble image reconstructions are used as indications of image quality. The authors' results show that the weak plate and membrane priors exhibit improved bias and variance relative to ML-EM techniques.
虽然 ML-EM 算法由于问题的不适定性而导致发射断层重建不稳定。贝叶斯重建方法通过引入先验信息来克服这种不稳定性，通常以空间平滑正则化器的形式。更精细的平滑约束形式可用于扩展先验的作用，使其超越稳定器的作用，以捕获关于物体的实际空间信息。以前提出的这种先验分布形式基于源分布分段常数的假设。在这里，作者提出了一种扩展到分段线性模型的方法——弱板模型，该模型比分段常数模型更具表现力。弱板先验不仅保留了边缘，而且允许在重建中存在分段斜坡区域。实际上，对于作者在 SPECT 中的应用，这种斜坡区域以灵长类动物放射性自显影的 rCBF 放射性核素的形式存在于源分布的真实值中。为了在 MAP 方法中包含弱板先验，作者将先验建模为 Gibbs 分布，并使用 GEM 公式进行优化。他们比较了 ML-EM 算法、优先考虑分段常数区域的 GEM 算法和具有弱板先验的 GEM 算法的定量性能。集图像重建的点和区域偏差和方差用作图像质量的指示。作者的结果表明，与 ML-EM 技术相比，弱板和膜先验显示出改进的偏差和方差。
