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.

该项目解决了关于声波方程的基本分析问题。这些问题出现了，但不仅限于光声断层扫描（PAT）的背景。 PAT是一种医学成像技术，结合了高对比度的无电磁吸收，例如健康组织和癌组织之间，以及超声的分辨率。当使用反映声波的探测器获得的光声测量值时，现有的PAT图像重建方法在时间反转参数上行不通。该项目的主要目标之一是在反射探测器阵列形成的空腔中进行综合的分析理论。要获得的数学结果在控制理论领域超出了部分微分方程和逆处问题。这些应用程序将被探讨。特别是，结果使我们能够更好地理解双曲线逆向价值问题的稳定性。这些问题发生在许多应用中，包括医学超声断层扫描，地震学，海洋学，过程监测和无损性测试。就这些plication而言，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

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

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

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