论文标题
PCA降低了高斯混合模型，并在上分辨率中应用
PCA Reduced Gaussian Mixture Models with Applications in Superresolution
论文作者
论文摘要
尽管计算硬件的发展迅速，但对大和高维数据集的处理仍然是一个具有挑战性的问题。本文为该主题提供了双重贡献。首先，我们通过主成分分析（称为pca-gmm）提出了一个高斯混合模型与模型每个组件中数据的维度的降低。要了解混合模型的（低维）参数，我们提出了一种EM算法，其M-Step需要解决约束优化问题的解决方案。幸运的是，这些受约束的问题不取决于通常大量的样本，并且可以通过（惯性）近端交替线性化最小化算法有效地解决。其次，我们将PCA-GMM应用于基于Sandeep和Jacob的方法的2D和3D材料图像的超级分析。数值结果证实了降低性降低对总体分辨率结果的中等影响。
Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture Model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, called PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.
