BIGDATA: F: IA: Robust Convolutional Modeling for Massive-Scale Electron Microscopy Data

显微镜学是现代科学的支柱，它使我们能够理解、观察和改进自然。虽然现代显微镜技术在过去几十年里取得了突飞猛进的发展，但显微镜学家用来分析数据的方法仍然很原始。常见的新的和新兴的显微镜模式是产生大量的，多维的数据集。该项目开发基本分析工具，从这些数据集中提取基本图案；特别是，从扫描隧道显微镜产生的数据。这些分析工具将通过提高材料原子尺度观察的质量和统计意义来改变显微镜成像。将解决的关键分析目标包括保证算法产生的模型准确地反映感兴趣的材料的物理特性，以及算法在可能包含噪声和错误的实际数据上可靠地执行。主要实验目标包括从多种显微镜模式生成大规模数据集，这些数据集将用于测试和扩展分析工具。该项目利用高维非凸优化的最新进展来解决卷积数据建模中的基本挑战，即将数据建模为翻译基元的叠加问题。由于目标是产生关于尚未了解其特性的新材料的准确信息，因此研究人员寻求表现出(i)保证性能，（ii）对严重错误的鲁棒性以及（iii）对大规模高维数据集的可扩展性的算法。基于词典学习的最新进展，研究者研究了具有一个或多个基序的模型的有效恢复方法的性质。他们使用黎曼优化和活动集方法，寻求高度可扩展的算法来解决这些问题。他们研究了对常见的严重错误（包括像素和扫描线损坏以及对比度变化）具有鲁棒性的变体。该算法用于研究以前的分析方法无法研究的材料，包括具有多种缺陷的材料，准粒子干涉和高温超导体。对于每一种材料，高分辨率扫描隧道显微镜和光谱成像将被执行，以产生大规模的多维数据集。充分研究材料的数据集将用于测试和验证分析算法，将这些算法应用于新材料的数据集将用于改变我们对复杂材料电子结构的理解。还将获得其他显微镜模式的数据集，以将分析工具推广到空间，时间和能量的多个尺度。

Microscopy is a pillar of modern science, which enables us to understand, inspect and improve on nature. While the technology of modern microscopes has progressed by leaps and bounds in the past decades, the methods used by microscopists to analyze data remain primitive. Common to new and emerging modalities of microscopy is the generation of massive, multi-dimensional data sets. This project develops fundamental analysis tools to extract basic motifs from these datasets; in particular, from data produced by scanning tunneling microscopes. These analysis tools will transform microscopy imaging by improving the quality and statistical significance of atomic-scale observations of materials. Key analysis goals that will be addressed include guarantees that algorithms produce models which accurately reflect the physics of the material of interest, and that algorithms perform reliably on practical data which may contain noise and errors. Key experimental goals include the generation of large scale data sets from multiple microscopy modalities which will be used to test and extend the analysis tools.The project leverages recent advances in high-dimensional nonconvex optimization to address fundamental challenges in convolutional data modeling, the problem of modeling data as superpositions of translated motifs. Because the goal is to produce accurate information about novel materials whose properties are not yet understood, the investigators seek algorithms which exhibit (i) guaranteed performance,(ii) robustness to gross errors and (iii) scalability to massive, high-dimensional datasets. Building on recent progress in dictionary learning, the investigators study the properties of efficient methods for recovering models with one or more motifs. They seek highly scalable algorithms for these problems, using Riemannian optimization and active set methods. They study variants which are robust to commonly occurring gross errors, including pixel and scanline corruption, and contrast variations. The algorithms are applied to study materials for which previous analysis methodologies fail, including materials with multiple types of defects, quasiparticle interference, and high temperature superconductors. For each of these materials, high resolution scanning tunneling microscopy and spectroscopic imaging will be performed to produce large-scale, multidimensional data sets. Data sets on well-studied materials will be used to test and verify analysis algorithms, and the application of these algorithms to data sets on novel materials will be used to transform our understanding of the electronic structure of complex materials. Data sets on other microscopy modalities will also be obtained to generalize analysis tools to multiple scales in space, time and energy.