MSPA-MCS: High-Dimensional, Nonparametric Density Estimation for the Analysis of Images and Shapes

MSPA-MCS：用于图像和形状分析的高维非参数密度估计

• 批准号: 0732227
• 负责人: Ross Whitaker
• 金额: $ 47.4万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0732227&HistoricalAwards=false
• 关键词: MSPA; MCS; Dimensional; Nonparametric; Density

A proliferation of technical instruments, computational resources, and digital media are opening up new opportunities in security, entertainment, science and medicine. We are automatically acquiring large databases of measurements that span physical scales from the molecule, to the cell, tissue, organism, ecosystem, and beyond to stars and galaxies. However, the rate of acquisition of these data exceeds our ability to analyze them, and many applications are stymied not by the lack of data but by the daunting task of understanding it all. This project addresses the problem of constructing statistical models of such data sets using examples from the data itself. The researchers will study the technical problems associated with constructing statistical modeling in high-dimensional spaces from mathematical and computational points of view. This research will focus on applications of these methods to problems in multidimensional image analysis, including denoising, segmentation, and image synthesis. This project will develop new algorithms for analyzing large sets of data. These algorithms make very weak assumptions about the statistical structure of data, and instead learn the statistics through large sets of examples, using raw measurements from very high dimensional spaces. The project combines a small team of researchers from probability theory, applied mathematics, and computer science to simultaneously address several important, fundamental questions pertaining to estimates of high-dimensional probability density functions, the computational challenges associated with these estimations, and the applications of these ideas to ongoing problems in science and medicine. The work in probability theory addresses basic questions about probability density functions in very high dimensional spaces. The applied mathematics work is developing methods for approximating these densities through lower-dimensional or sparse representations. The computer science research is examining implementation issues and the application of these methods to a wide range of ongoing problems that demand better algorithms for data analysis.

技术工具、计算资源和数字媒体的激增正在安全、娱乐、科学和医学领域开辟新的机会。我们正在自动获取庞大的测量数据库，涵盖了从分子到细胞、组织、有机体、生态系统，再到恒星和星系的物理尺度。然而，获取这些数据的速度超过了我们分析它们的能力，许多应用程序受到阻碍，不是因为缺乏数据，而是因为理解所有数据的艰巨任务。该项目解决了使用数据本身的示例构建此类数据集的统计模型的问题。研究人员将从数学和计算的角度研究与在高维空间中构建统计模型相关的技术问题。本研究将集中于这些方法在多维图像分析中的应用，包括去噪、分割和图像合成。该项目将开发用于分析大型数据集的新算法。这些算法对数据的统计结构做了非常弱的假设，而是通过大量的示例集来学习统计数据，使用来自非常高维空间的原始测量。该项目将概率论、应用数学和计算机科学的研究人员组成一个小团队，同时解决与高维概率密度函数估计有关的几个重要的基本问题，与这些估计相关的计算挑战，以及这些想法在科学和医学中持续问题的应用。概率论的工作是解决关于高维空间中概率密度函数的基本问题。应用数学工作正在开发通过低维或稀疏表示近似这些密度的方法。计算机科学研究正在研究实现问题，并将这些方法应用于广泛的持续问题，这些问题需要更好的数据分析算法。