Numerical optimization for large-scale experimental design of ill-posed inverse problems

不适定反问题大规模实验设计的数值优化

基本信息

批准号：
0915121
负责人：
James Nagy
金额：
$ 32.68万
依托单位：
Emory University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2009
资助国家：
美国
起止时间：
2009-09-01 至 2011-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915121&HistoricalAwards=false
关键词：
Numerical optimization large scale experimental

项目摘要

Inverse problems play a key role in a variety of fields such as computer vision, geophysics and medical imaging. The proposed work focuses on experimental design of ill-posed inverse problems; a field that has not received sufficient attention in the inverse problems community where the focus is usually on the analysis of the inverse problem given the data. Obviously, this already imposes restrictions on the quality of the possible solutions. On the other hand, the objective of the funded work is the study of an important pre-data acquisition question: How should the experiment be conducted to obtain optimal data given the physical constraints and available resources? Solutions to this question require techniques from numerical optimization, statistics and inverse problem theory. In particular, the problem of experimental design can be cast as a bilevel optimization problem that consists of two nested optimization problems. The proposed work is a study of design criteria and new numerical algorithms for the solution of the bilevel optimization problems that arise from them.This work will address the fundamental question of experimental design of ill-posed inverse problems. Such problems arise in the design of any practical experiment or instrumentation from geophysical and medical imaging to the production of better vision systems. This work will develop new criteria for the design and development of new algorithms that will enable its numerical implementation. The results of the research will be applied to electromagnetic imaging, a field that is routinely used in geophysics and medical physics. It will lead to better experiments that yield better images and as such, will assist in the decision making of geoscientists and and physicians.

反问题在计算机视觉、地球物理学和医学成像等多个领域发挥着关键作用。拟议的工作重点是不适定反问题的实验设计；在反问题社区中尚未受到足够关注的领域，其重点通常是对给定数据的反问题进行分析。显然，这已经对可能的解决方案的质量施加了限制。另一方面，资助工作的目标是研究一个重要的数据采集前问题：在考虑到物理限制和可用资源的情况下，应该如何进行实验以获得最佳数据？解决这个问题需要数值优化、统计学和反问题理论的技术。特别是，实验设计问题可以转化为由两个嵌套优化问题组成的双层优化问题。所提出的工作是研究设计标准和新的数值算法，以解决由此产生的双层优化问题。这项工作将解决不适定反问题的实验设计的基本问题。从地球物理和医学成像到更好的视觉系统的生产，任何实际实验或仪器的设计都会出现此类问题。这项工作将为新算法的设计和开发制定新标准，从而实现其数值实现。研究结果将应用于电磁成像，这是地球物理学和医学物理学中常用的领域。它将带来更好的实验，产生更好的图像，因此将有助于地球科学家和医生的决策。