Zeng Gengsheng L
Utah Center for Advanced Imaging Research (UCAIR), Department of Radiology, University of Utah, Salt Lake City, UT 84108.
Int J Imaging Syst Technol. 2012 Jun;22(2):114-120. doi: 10.1002/ima.22011. Epub 2012 May 12.
The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm.
迭代最大似然期望最大化（ML-EM）算法是一种出色的图像重建算法，通常能提供比滤波反投影（FBP）算法更好的图像。然而，当使用与真实图像的最小二乘差（即最小二乘误差，LSE）作为比较标准时，加窗FBP算法在某些情况下可能优于ML-EM算法。对这两种算法进行了计算机模拟。对于给定的数据集，首先从每种算法中获得与真实图像相比的最佳重建结果，然后比较这两种重建结果。确定了ML-EM算法的停止迭代次数和加窗FBP算法的参数，以使它们生成最接近真实图像的图像。然而，要使用LSE标准来比较算法，必须知道真实图像。当真实图像未知时如何选择最优参数是一个实际的开放性问题。对于有噪声的泊松投影，计算机模拟结果表明ML-EM算法生成的图像优于常规FBP算法生成的图像，而加窗FBP算法生成的图像优于ML-EM算法生成的图像。对于无噪声投影，FBP算法优于ML-EM算法。计算机模拟表明，加窗FBP算法能提供比ML-EM算法更接近真实图像的重建结果。
