Lipinski B, Herzog H, Rota Kops E, Oberschelp W, Müller-Gärtner H W
Institute of Medicine, Research Centre Jülich GmbH, Germany.
IEEE Trans Med Imaging. 1997 Apr;16(2):129-36. doi: 10.1109/42.563658.
Using statistical methods the reconstruction of positron emission tomography (PET) images can be improved by high-resolution anatomical information obtained from magnetic resonance (MR) images. We implemented two approaches that utilize MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the expectation maximization (EM)-type algorithm with a maximum a posteriori (MAP) estimator is derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighboring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. A basic assumption of these methods is that the radioactivity is homogeneously distributed inside anatomical regions. Simulated and phantom data are investigated under the following aspects: count density, object size, missing anatomical information, and misregistration of the anatomical information. Compared with the maximum likelihood-expectation maximization (ML-EM) algorithm the results of both algorithms show a large reduction of noise with a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction (up to 50%). Regarding incorrect a priori information the Gauss-EM algorithm is very sensitive, whereas the Markov-GEM algorithm proved to be stable with a small change of recovery coefficients between 0.5 and 3%.
使用统计方法，通过从磁共振（MR）图像中获取的高分辨率解剖信息，可以改善正电子发射断层扫描（PET）图像的重建。我们实现了两种利用MR数据进行PET重建的方法。解剖学MR信息被建模为PET图像的先验分布，并与测量的PET数据分布相结合，以生成后验函数，从中推导出带有最大后验（MAP）估计器的期望最大化（EM）型算法。一种算法（马尔可夫 - GEM）使用吉布斯函数对解剖区域内相邻像素之间的相互作用进行建模。另一种（高斯 - EM）对给定解剖区域内的所有像素应用具有相同均值的高斯函数。这些方法的一个基本假设是放射性在解剖区域内均匀分布。从以下几个方面对模拟数据和体模数据进行了研究：计数密度、物体大小、缺失的解剖信息以及解剖信息的配准错误。与最大似然期望最大化（ML - EM）算法相比，两种算法的结果都显示出噪声大幅降低，边界描绘得更好。在测试的两种算法中，高斯 - EM方法在降噪方面更优（高达50%）。对于不正确的先验信息，高斯 - EM算法非常敏感，而马尔可夫 - GEM算法被证明是稳定的，恢复系数在0.5%至3%之间有小的变化。
