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

• 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

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、地球物理和医学成像等领域发挥着关键作用。提出的工作重点是不适定逆问题的实验设计；在反问题社区中没有得到足够重视的一个领域，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获取前问题：在物理约束和可用资源的情况下，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。具体来说，实验设计问题可以看作是由两个嵌套优化问题组成的双层优化问题。提出的工作是研究设计准则和解决由此产生的双层优化问题的新数值算法。这项工作将解决不适定逆问题的实验设计的基本问题。这些问题出现在任何实际实验或仪器的设计中，从地球物理和医学成像到生产更好的视觉系统。这项工作将为新算法的设计和开发制定新的标准，使其能够实现数值实现。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经常使用的领域。它将导致更好的实验，产生更好的图像，因此，将有助于地球科学家和医生的决策。