CHS: Small: Novel Data-adaptive Analytics for Manifold Informatics: Theory, Algorithms, and Applications

CHS：小型：流形信息学的新型数据自适应分析：理论、算法和应用

• 批准号: 1812606
• 负责人: Hong Qin
• 金额: $ 50万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-03-01 至 2025-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812606&HistoricalAwards=false
• 关键词: CHS; Small; Novel; Data; adaptive

This research will make significant contributions towards completely data-adaptive space-frequency analytics. Project outcomes will also impact information processing and analytics of data types/domains such as scalar/vector/tensor fields in 3D volume, 4D time-varying medical data, higher-dimensional data with curved and regular structure, or graphs of irregular structure. This project's overarching objective is to trailblaze a data-adaptive theory for manifold information modeling and analysis, inspired by the Hilbert-Huang transform (HHT) on one-dimensional signals, and to apply the new theory to manifold geometry/texture/appearance analysis, synthesis, and visualization, with an emphasis on data-driven analytics and informatics. HHT has exhibited initial success in handling nonlinear and nonstationary time series in one-dimensional space. It comprises empirical mode decomposition (EMD) and Hilbert spectral analysis. Despite its growing popularity in many scientific and engineering fields (including geophysics, marine science, and climate studies), technical challenges and unsolved research issues still prevail when trying to bridge the large gap between HHT and data-adaptive space-frequency analytics for manifold data. Additionally, Hilbert spectral analysis (based on instantaneous frequencies, local amplitude, and local phase at each point) remains an open research problem for data processing and analysis on manifolds. This research will explore a new theory of data-adaptive space-frequency analysis on manifolds, and articulate a novel data-adaptive analytics framework enabling multi-scale space-frequency analysis/process, which has never been attempted before. Research activities will include: (1) definition of a new computational theory based on texture-geometry decomposition with adaptive scales, and discovery of the intrinsic connection between the EMD and compressed sensing theory on manifolds; (2) space-frequency analysis via Riesz transforms, to enable computation of local instantaneous frequency, amplitude, and phase for each IMF anywhere on a manifold so as to achieve more accurate feature description and quantitative feature analysis in a brand new, high-dimensional, intrinsic feature space; (3) creation of new, efficient algorithms to compute IMFs and Riesz transforms of (multi-channel) signals on manifolds as well as in high-dimensional datasets; and (4) conducing comprehensive experimental validation, including feature description, noise and feature decoupling, feature-aware shape completion and editing, structure-sensitive deformation, and saliency visualization.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这项研究将为完全数据自适应空频分析做出重大贡献。项目成果还将影响数据类型/域的信息处理和分析，例如 3D 体积中的标量/矢量/张量场、4D 时变医疗数据、具有弯曲和规则结构的高维数据或不规则结构的图形。该项目的总体目标是受一维信号希尔伯特-黄变换（HHT）的启发，为流形信息建模和分析开拓数据自适应理论，并将新理论应用于流形几何/纹理/外观分析，综合和可视化，重点是数据驱动的分析和信息学。 HHT 在处理一维空间中的非线性和非平稳时间序列方面取得了初步成功。它包括经验模态分解（EMD）和希尔伯特谱分析。尽管它在许多科学和工程领域（包括地球物理学、海洋科学和气候研究）越来越受欢迎，但在试图弥合 HHT 与流形数据的数据自适应空间频率分析之间的巨大差距时，技术挑战和未解决的研究问题仍然普遍存在。此外，希尔伯特谱分析（基于每个点的瞬时频率、局部幅度和局部相位）仍然是流形数据处理和分析的一个开放研究问题。 这项研究将探索流形上数据自适应空频分析的新理论，并阐明一种新颖的数据自适应分析框架，以实现多尺度空频分析/处理，这是以前从未尝试过的。研究活动将包括：（1）定义基于自适应尺度纹理几何分解的新计算理论，并发现EMD与流形压缩感知理论之间的内在联系； (2)通过Riesz变换进行空频分析，可以计算流形上任意位置的每个IMF的局部瞬时频率、幅度和相位，从而以全新的高维方式实现更准确的特征描述和定量特征分析，内在特征空间； (3) 创建新的、高效的算法来计算流形以及高维数据集中的（多通道）信号的 IMF 和 Riesz 变换； （4）进行全面的实验验证，包括特征描述、噪声和特征解耦、特征感知形状补全和编辑、结构敏感变形和显着性可视化。该奖项体现了NSF的法定使命，经评估认为值得支持利用基金会的智力优势和更广泛的影响审查标准。