Functional Analysis and Computational Methods in Imaging, Materials, and Atmospheric Sciences

成像、材料和大气科学中的函数分析和计算方法

• 批准号: 1217239
• 负责人: Luminita Vese
• 金额: $ 24万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1217239&HistoricalAwards=false
• 关键词: Functional; Analysis; Computational; Methods; Imaging

The investigators, their students and collaborators study mathematical formulations and efficient computational techniques for applications arising in image analysis, materials science, and atmospheric and climate modeling. This multidisciplinary research combines areas of computational mathematics, inverse problems, image analysis, interfaces and free boundaries, and atmospheric sciences. They study image restoration using cartoon and texture decompositions, restoration of images in the presence of a stochastic point spread function, implicit open curve evolution and applications to free boundary problems in materials sciences, and variational data fusion of atmospheric records acquired by multiple instruments. The research team develops novel variational approaches, iterative and numerical analysis techniques for solving these inverse problems.The proposed activity provides the link between efficient mathematical formulations, imaging approaches, and applications in climate and materials sciences, where similar approaches have not yet been attempted. In particular, capability for merging data acquired by multiple sensors is a key part to our understanding of the Earth's climate system, and therefore, is of importance when making projections about climate change and climate impacts. Current atmospheric data fusion methods are largely ad hoc and establishing a firm mathematical foundation and computational methods for combining important records enhances their scientific credibility and further a wide range of scientific analyses. The investigators promote multidisciplinary teaching, training and learning. Mathematics students are exposed to a broad range of topics and techniques: (i) in applied and computational mathematics, image processing and analysis; and (ii) topics outside mathematics, including materials and atmospheric sciences.

研究人员，他们的学生和合作者研究数学公式和有效的计算技术，用于图像分析，材料科学以及大气和气候建模中的应用。这种多学科的研究结合了计算数学，反问题，图像分析，界面和自由边界，以及大气科学领域。他们研究图像恢复使用卡通和纹理分解，恢复图像中存在的随机点扩散函数，隐式开放曲线演化和应用程序的自由边界问题，在材料科学，和变分数据融合的大气记录获得多个仪器。该研究团队开发了新的变分方法，迭代和数值分析技术来解决这些逆问题。拟议的活动提供了高效的数学公式，成像方法和气候和材料科学应用之间的联系，其中类似的方法尚未尝试。特别是，合并多个传感器获得的数据的能力是我们了解地球气候系统的关键部分，因此，在预测气候变化和气候影响时非常重要。目前的大气数据融合方法在很大程度上是临时性的，建立一个坚实的数学基础和计算方法来合并重要的记录，可以提高其科学可信度，并促进广泛的科学分析。调查人员促进多学科教学、培训和学习。数学专业的学生接触到广泛的主题和技术：（一）在应用和计算数学，图像处理和分析;（二）数学以外的主题，包括材料和大气科学。