The inverse source problem arising in Photoacoustic Tomography

光声层析成像中出现的逆源问题

• 批准号: EP/L026473/1
• 负责人: Lauri Oksanen
• 金额: $ 14.31万
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2014
• 资助国家: 英国
• 起止时间: 2014 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FL026473%2F1
• 关键词: inverse; source; problem; arising; Photoacoustic

The project addresses fundamental analytical questions on the acoustic waveequation. The questions arise in, but are not limited to the context ofPhotoacoustic Tomography (PAT). PAT is a medical imaging technique that combines the high contrast inelectromagnetic absorption, say between healthy and cancerous tissue, with thehigh resolution of ultrasound. The existing PAT image reconstruction methodsbased on time-reversal arguments do not work when photoacoustic measurementsare obtained by using an array of detectors that reflects acoustic waves.However, the use of detector arrays significantly speeds up the dataacquisition in practice. One of the main objectives of the project is todevelop a comprehensive analytical theory for PAT in a reflecting cavityformed by detector arrays. The mathematical results to be obtained have applications beyond PAT in thefields of Control Theory for Partial Differential Equations and InverseProblems. These applications will be explored. In particular, the resultsallow us to understand better the stability properties of hyperbolic inverseboundary value problems. These problems occur in a large number ofapplications including medical ultrasound tomography, seismology, oceanology,process monitoring and non-destructive testing. In terms of theseapplications, our focus is on seismic imaging.

该项目涉及声波方程的基本分析问题。这些问题出现在但不限于光声层析成像（PAT）的背景下。PAT是一种医学成像技术，它结合了电磁吸收的高对比度，比如健康组织和癌组织之间的对比度，以及超声的高分辨率。现有的基于时间反演参数的PAT图像重建方法在使用反射声波的探测器阵列获得光声测量时不起作用，然而，探测器阵列的使用在实践中显著地加快了数据采集速度.本项目的主要目标之一是建立探测器阵列形成的反射腔中PAT的综合分析理论。所得到的数学结果在偏微分方程的控制理论和反问题领域中有着超越PAT的应用。这些应用将被探索。特别是，所得结果有助于我们更好地理解双曲型反边值问题的稳定性.这些问题出现在大量的应用中，包括医学超声断层扫描、地震学、海洋学、过程监控和无损检测。在这些应用方面，我们的重点是地震成像。

项目成果

Stability estimate for scalar image velocimetry

标量图像测速的稳定性估计

• DOI: 10.1515/jiip-2020-0107
• 发表时间: 2023
• 期刊: Journal of Inverse and Ill-posed Problems
• 影响因子: 1.1
• 作者: Burman E

Primal dual mixed finite element methods for the elliptic Cauchy problem

椭圆柯西问题的原始对偶混合有限元方法

• DOI: 10.48550/arxiv.1712.10172
• 发表时间: 2017
• 作者: Burman E

A Fully Discrete Numerical Control Method for the Wave Equation

• DOI: 10.1137/19m1249424
• 发表时间: 2019-03
• 期刊: SIAM J. Control. Optim.
• 作者: E. Burman;A. Feizmohammadi;L. Oksanen

Unique continuation for the Helmholtz equation using stabilized finite element methods

• DOI: 10.1016/j.matpur.2018.10.003
• 发表时间: 2017-10
• 期刊: Journal de Mathématiques Pures et Appliquées
• 作者: E. Burman;Mihai Nechita;L. Oksanen

Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem

• DOI: 10.1137/17m1163335
• 发表时间: 2017-12
• 期刊: SIAM J. Numer. Anal.
• 作者: E. Burman;M. Larson;L. Oksanen