Collaborative Research: Trust-Search Methods for Inverse Problems in Imaging

合作研究：成像反问题的信任搜索方法

• 批准号: 1333326
• 负责人: Roummel Marcia
• 金额: $ 15万
• 依托单位: University of California - Merced
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1333326&HistoricalAwards=false
• 关键词: Collaborative; Research; Trust; Search; Methods

The research objective of this award is to develop and implement first-order trust-search methods for use in large-scale data-generated optimization problems. Data-generated problems arise in applications such as signal and image processing. These problems are especially difficult to solve since the data are often high dimensional and are noisy, incomplete, and/or inexact. This research will develop first-order quasi-Newton trust-search methods for solving large data-generated problems. The methods to be used are trust-search methods, which are hybridizations of the most fundamental types of methods for unconstrained optimization: trust-region methods and line-search methods. Trust-search methods seek to implement line-search strategies in combination with trust-region theoretics to obtain more robust methods.If successful, the results of this research will help scientists and engineers solve optimization problems involving large volumes of corrupted data. In today's world, scientific data are more abundant than ever before; moreover, projects are already underway to produce even more data at a faster rate. To keep pace, the emerging field of "big data" requires sophisticated, fast, robust, and large-scale numerical algorithms. This research will use linear algebra and optimization theory to develop software for processing and analyzing very large data sets. In particular, the results of this research will help solve important problems in image processing applications such as medical imaging, low-light video surveillance, and nocturnal ecological activity monitoring, where the generated data are not only very large but are very noisy. The algorithms will be disseminated publically for use within and outside the scientific community. Graduate students will be trained in scientific research and programming through this research, and the participation of students from under-represented backgrounds will be highly encouraged.

该奖项的研究目标是开发和实现用于大规模数据生成优化问题的一阶信任搜索方法。在信号和图像处理等应用中会出现数据生成问题。这些问题尤其难以解决，因为数据通常是高维的，并且有噪声、不完整和/或不准确。这项研究将开发一阶拟牛顿信任搜索方法来解决大数据生成问题。要使用的方法是信任搜索方法，它是无约束优化的最基本类型的方法的混合：信赖域方法和线搜索方法。信任搜索方法试图将线搜索策略与信赖域理论相结合，以获得更健壮的方法，如果成功，该研究结果将帮助科学家和工程师解决涉及大量损坏数据的优化问题。在当今世界，科学数据比以往任何时候都更加丰富；此外，已经在进行以更快的速度产生更多数据的项目。为了跟上步伐，新兴的大数据领域需要复杂、快速、健壮和大规模的数值算法。这项研究将使用线性代数和最优化理论来开发处理和分析超大数据集的软件。特别是，本研究的成果将有助于解决医学成像、微光视频监控、夜间生态活动监测等图像处理应用中的重要问题，这些应用产生的数据量不仅非常大，而且非常噪声。这些算法将被公开传播，供科学界内外使用。通过这项研究，研究生将接受科学研究和编程方面的培训，并将高度鼓励来自代表性不足背景的学生参与。