The inverse source problem arising in Photoacoustic Tomography

该项目解决了声波方程的基本分析问题。这些问题出现在但不限于光声断层扫描（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高对比度，以及超声波的高分辨率。现有的基于时间反转参数的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，在实际应用中，探测器阵列的使用大大加快了数据采集的速度。该项目的主要目标之一是开发由探测器阵列形成的反射腔中的PAT的综合分析理论。所得到的数学结果在偏微分方程和反问题的控制理论领域具有超越PAT的应用。我们将探讨这些应用。特别是，这些结果使我们更好地理解了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、过程监测和无损检测。在这些应用方面，我们的重点是地震成像。

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.