Title: Two-stage dimension reduction for noisy high-dimensional images and application to Cryogenic Electron Microscopy Show Chinese title

Title: 针对噪声高维图像的两阶段降维及其在冷冻电子显微镜中的应用

Abstract: 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. Show Chinese abstract

Abstract: 主成分分析（PCA）可能是用于向量型数据的最广泛使用的降维方法。 当应用于图像样本时，PCA需要对图像数据进行向量化，这进而需要求解样本协方差矩阵的特征值问题。 本文提出了一种两阶段降维（2SDR）方法，用于从高维噪声图像数据中进行图像重建。 第一阶段将图像视为一个矩阵，即一个二阶张量，并使用多线性主成分分析（MPCA）进行矩阵秩降低和图像去噪。 第二阶段对降秩矩阵进行向量化，从而实现进一步的维度和噪声降低。 模拟研究展示了2SDR的优异性能，我们还开发了一种渐近理论，建立了其秩选择的一致性。 还提供了应用于冷冻电子显微镜（cryo-EM）的案例，冷冻电子显微镜在过去十年中彻底改变了结构生物学、有机和医学化学、细胞和分子生理学。 也讨论了与其他同时期图像重建和高维统计推断发展的联系。