Collaborative Research: Improved Algorithms for Multiwave Imaging in Complex Media: Theory and Computation

改进的成像技术对于指导和告知日益复杂的外科手术是必要的。例如，先天性心脏缺陷的婴儿需要进行心脏搭桥手术；然而，大约50%的儿童围手术期发生脑损伤，导致先天性心脏病幸存者出现破坏性并发症。需要改进的脑成像技术来评估外科手术对脑灌注的影响。脑成像最有前途的技术之一是多波成像方法，如光声和热声断层扫描，它们结合不同波的特性来获得传统模式无法实现的高对比度和分辨率。本项目的动机是多波成像可能应用于监测婴儿脑血流灌注。它旨在将头部（脑、脉管系统、血液、脑脊液、头骨、皮肤）介质特性的复杂性纳入这些成像技术，同时使这些技术对噪声和不确定性更具鲁棒性。这个项目的目标是理论和计算。首先是确定光声测量同时恢复内源和波速的一般假设。这将通过扩展有关声源和介质性质同时恢复的数学理论来完成，这是关于光、热和磁声成像的主要开放问题之一。在初步工作的基础上，调查人员放宽了同时回收的先验条件。下一步是确定哪些条件是必要的，哪些条件可以消除。第二个目标是计算性的，并利用光声效应的固有特性，产生高对比度的压力曲线。目的是设计新颖的间断伽辽金方法，用于高对比度压力波的精确，低色散模拟，用于新的成像算法。这些方法的目的是在真实介质和几何图形存在的情况下，在GPU架构上实现高性能。第三个目标是将这些新发展纳入pde约束优化算法，这些算法除了可以近似未知介质的波速外，还可以提供关于噪声和信息缺乏的鲁棒性。

Improved imaging techniques are necessary to guide and inform increasingly complex surgical procedures. For example, cardiac bypass surgeries are required for infants born with congenital heart defects; however, approximately 50% of children develop brain injury perioperatively, leading to the damaging complications for survivors of congenital heart disease. Improved cerebral imaging techniques are needed to evaluate the effects of surgical procedures on brain perfusion. One of the most promising techniques for cerebral imaging are multiwave imaging methods such as photo-acoustic and thermo-acoustic tomography, which combine properties of different waves to obtain high contrast and resolution unattainable by traditional modalities. This project is motivated by the possible application of multiwave imaging to monitor cerebral blood perfusion in infants. It aims to incorporate the complexity of media properties in the head (brain, vasculature, blood, cerebrospinal fluid, skull, skin) into these imaging techniques, while making these techniques more robust to noise and uncertainty. The goals of this project are both theoretical and computational. The first is to identify general assumptions under which the photo-acoustic measurements render the simultaneous recovery of the internal source and the wave speed. This will be accomplished by expanding the mathematical theory concerning the simultaneous recovery of acoustic sources and media properties, which is one of the main open questions regarding photo-, thermo- and magneto- acoustic imaging. Based on preliminary work, the investigators have relaxed a-priori conditions under which simultaneous recovery is possible. The next step is to determine which conditions are essential and which ones can be removed. The second goal is computational and uses the intrinsic property of the photo-acoustic effect, which produces high contrast pressure profiles. The aim is to design novel discontinuous Galerkin methods for accurate, low dispersion simulations of high contrast pressure waves for use in new imaging algorithms. These methods are designed to achieve high performance on GPU architectures in the presence of realistic media and geometries. The third goal is to incorporate these new developments into PDE-constrained optimization algorithms, which, in addition to approximating the unknown wave speed of the medium, will also provide robustness with respect to noise and lack of information.