混合高斯参数估计的两种EM算法比较

混合高斯模型是一种典型的非高斯概率密度模型,获得广泛应用。其参数的优效估计可以通过最大似然方法获得,但最大似然估计往往因其非线性而难以实现,故期望最大化（Expectation-Maximization,EM）迭代算法成为一种常用的替代方法。常规EM算法性能受迭代初值设置影响大,且不能对模型阶数做出估计。一种名为贪婪EM的改进算法可以克服这两个缺点,获得更为准确的模型参数估计,但其运算量一般会远大于前者。本文对这两种EM算法进行综合研究,深入挖掘两者之间的关系,并基于相同的数值仿真实例,直观地演示比较两者的性能差异。  

ANFIS‐EM approach for PET brain image reconstruction

In this article, for the reconstruction of the positron emission tomography (PET) images, an iterative MAP algorithm was instigated with its adaptive neurofuzzy inference system based image segmentation techniques which we call adaptive neurofuzzy inference system based expectation maximization algorithm (ANFIS‐EM). This expectation maximization (EM) algorithm provides better image quality when compared with other traditional methodologies. The efficient result can be obtained using ANFIS‐EM algorithm. Unlike any usual EM algorithm, the predicted method that we call ANFIS‐EM minimizes the EM objective function using maximum a posteriori (MAP) method. In proposed method, the ANFIS‐EM algorithm was instigated by neural network based segmentation process in the image reconstruction. By the image quality parameter of PSNR value, the adaptive neurofuzzy based MAP algorithm and de‐noising algorithm compared and the PET input image is reconstructed and simulated in MATLAB/simulink package. Thus ANFIS‐EM algorithm provides 40% better peak signal to noise ratio (PSNR) when compared with MAP algorithm. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 1–6, 2015  

Robust estimation of mean and variance using environmental data sets with below detection limit observations

Scientists, especially environmental scientists, often encounter trace level concentrations that are typically reported as less than a certain limit of detection, L. Type I left-censored data arises when certain low values lying below L are ignored or unknown as they cannot be measured accurately. In many environmental quality assurance and quality control (QA/QC), and groundwater monitoring applications of the United States Environmental Protection Agency (USEPA), values smaller than L are not required to be reported. However, practitioners still need to obtain reliable estimates of the population mean μ, and the standard deviation (S.D.) σ. The problem gets complex when a small number of high concentrations are observed with a substantial number of concentrations below the detection limit. The high-outlying values contaminate the underlying censored sample, leading to distorted estimates of μ and σ. The USEPA, through the National Exposure Research Laboratory-Las Vegas (NERL-LV), under the Office of Research and Development (ORD), has research interests in developing statistically rigorous robust estimation procedures for contaminated left-censored data sets. Robust estimation procedures based upon a proposed (PROP) influence function are shown to result in reliable estimates of population parameters of mean and S.D. using contaminated left-censored samples. It is also observed that the robust estimates thus obtained with or without the outliers are in close agreement with the corresponding classical estimates after the removal of outliers. Several classical and robust methods for the estimation of μ and σ using left-censored (truncated) data sets with potential outliers have been reviewed and evaluated.