Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed.
翻译:五氯苯甲醚在应用到图像样本时,需要将图像数据矢量化,这反过来需要解决样本共变矩阵中的半值问题。我们在此建议用高维噪音图像数据进行图像重建的两阶段性量减少(2SDR)方法。第一阶段将图像作为矩阵处理,这是第2级的微调,并使用多线性主要部分分析(MPCA)进行矩阵级降级和图像脱色。第二阶段是降级矩阵并实现进一步的维度和减少噪音。模拟研究显示了2SDR的出色性能,我们为此还开发了一种确定等级选择一致性的无源性理论。还讨论了对过去十年中结构生物学、有机和医学化学、蜂窝和分子物理学革命的低温微微镜的应用,并用基准低温数据集进行了演示。还讨论了与图像重建和高维度统计中其他同步发展的联系。