Acoustic Inverse Problems with Single and Multiple Measurements

单次和多次测量的声学反演问题

• 批准号: 2006881
• 负责人: Yang Yang
• 金额: $ 23.72万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2006881&HistoricalAwards=false
• 关键词: Acoustic; Inverse; Problems; Single; Multiple

The project addresses fundamental scientific challenges in non-destructive testing techniques. These techniques are widely used in medical imaging for tumor detection, in seismic imaging for oil prospecting, and in military applications for weapon defect inspection. This project facilitates resolution of these challenges by developing innovative theory and algorithms for the underlying mathematical problems. The theory will promote the domain knowledge in mathematics and relevant scientific areas. The theoretically consolidated algorithms will open new avenues for scientific computing in non-destructive testing techniques, consequently leading to innovation in medical imaging, seismic imaging, and military application that will advance the societal welfare and national security. Implementation of the project will be integrated with the educational mission to involve undergraduate and graduate students majoring in mathematics and engineering, especially those from underrepresented groups. Students will receive rigorous scientific training in mathematical theory and programming to prepare them as the next generation of the STEM workforce that can continue to promote science and technology in future decades.The overall goal of the project is determination and reconstruction of multiple acoustic parameters from single or multiple boundary measurements. In the first major topic, the investigator will devise novel algorithms to reconstruct the wave speed and potential from multiple boundary measurements using the boundary control method. The algorithms give direct reconstruction to the nonlinear inverse problems as opposed to traditional iterative algorithms. In the second major topic, the investigator will study uniqueness and stability for joint determination of a source and a coefficient from single boundary measurements. Novel sufficient and necessary conditions will be derived from the viewpoint of microlocal analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目解决了非破坏性测试技术中的基本科学挑战。这些技术广泛应用于肿瘤检测的医学成像、石油勘探的地震成像以及武器缺陷检查的军事应用。该项目通过为基础数学问题开发创新理论和算法来促进这些挑战的解决。该理论将促进数学及相关科学领域领域知识的发展。理论上巩固的算法将为无损检测技术的科学计算开辟新的途径，从而导致医学成像，地震成像和军事应用的创新，这将促进社会福利和国家安全。该项目的实施将与教育使命相结合，以吸引数学和工程专业的本科生和研究生，特别是来自代表性不足群体的学生。学生将接受严格的数学理论和编程科学培训，为下一代STEM劳动力做好准备，在未来几十年继续推动科学和技术的发展。该项目的总体目标是从单个或多个边界测量中确定和重建多个声学参数。在第一个主要课题中，研究人员将设计新的算法，使用边界控制方法从多个边界测量中重建波速和势能。与传统的迭代算法不同，该算法直接重构非线性反问题。在第二个主要课题中，研究者将研究从单个边界测量联合确定源和系数的唯一性和稳定性。该奖项体现了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Ultrasound modulated bioluminescence tomography with a single optical measurement

• DOI: 10.1088/1361-6420/abc8aa
• 发表时间: 2020-08
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: Francis J. Chung;Tianyu Yang;Yang Yang-Yang

An Acousto-electric Inverse Source Problem

• DOI: 10.1137/21m1406568
• 发表时间: 2021-01
• 期刊: SIAM J. Imaging Sci.
• 作者: Wei Li;J. Schotland;Yang Yang-Yang;Yimin Zhong

Source Independent Velocity Recovery Using Imaginary FWI

• DOI: 10.3997/2214-4609.202112976
• 发表时间: 2021
• 期刊: 82nd EAGE Annual Conference & Exhibition
• 作者: S. Qin;Y. Yang;R. Wang

Reconstruction of the Collision Kernel in the Nonlinear Boltzmann Equation

非线性玻尔兹曼方程碰撞核的重构

• DOI: 10.1137/20m1329366
• 发表时间: 2021
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Lai, Ru-Yu;Uhlmann, Gunther;Yang, Yang
• 通讯作者: Yang, Yang

Photoacoustic imaging of near-bone soft tissue vasculature in an ex vivo phantom

离体模型中近骨软组织脉管系统的光声成像

• DOI: 10.1117/12.2653348
• 发表时间: 2023
• 期刊: and Functional Imaging
• 作者: Wang, Guessy;Hix, Jeremy;Tavelli, Lorenzo;Yang, Yang
• 通讯作者: Yang, Yang