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

合作研究：复杂介质中多波成像的改进算法：理论与计算

• 批准号: 1712639
• 负责人: Jesse Chan
• 金额: $ 20万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-15 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712639&HistoricalAwards=false
• 关键词: Collaborative; Research; Improved; Algorithms; Multiwave

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.

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心脏搭桥手术;然而，大约50%的儿童在围手术期发生脑损伤，导致先天性心脏病幸存者的损害性并发症。需要改进的脑成像技术来评估外科手术对脑灌注的影响。用于脑成像的最有前途的技术之一是多波成像方法，例如光声和热声层析成像，其联合收割机结合不同波的性质以获得传统模态无法达到的高对比度和分辨率。 本研究的目的是探讨多波成像技术在婴幼儿脑血流灌注监测中的应用。它旨在将头部（大脑，血管，血液，脑脊液，头骨，皮肤）中介质属性的复杂性纳入这些成像技术中，同时使这些技术对噪声和不确定性更加鲁棒。这个项目的目标是理论和计算。首先是确定一般假设下，光声测量呈现的内部源和波的速度的同时恢复。这将通过扩展有关声源和介质特性的同时恢复的数学理论来实现，这是关于光、热和磁声成像的主要未决问题之一。在初步工作的基础上，调查人员放宽了可能同时恢复的先验条件。下一步是确定哪些条件是必要的，哪些条件可以删除。第二个目标是计算性的，并且使用光声效应的固有特性，其产生高对比度压力分布。目的是设计新的不连续Galerkin方法，用于精确，低色散模拟高对比度压力波，用于新的成像算法。这些方法旨在在真实媒体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偏微分方程约束优化算法中，该算法除了近似介质的未知波速外，还将提供对噪声和信息缺乏的鲁棒性。

项目成果

Skew-Symmetric Entropy Stable Modal Discontinuous Galerkin Formulations

斜对称熵稳定模态不连续伽辽金公式

• DOI: 10.1007/s10915-019-01026-w
• 发表时间: 2019
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Chan, Jesse

Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit time-stepping and efficient mass matrix inversion

• DOI: 10.1016/j.cma.2018.01.022
• 发表时间: 2017-08
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Jesse Chan;John A. Evans

Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media: Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media

权重调整间断伽辽金方法：异质介质中的矩阵定值权重和弹性波传播：权重调整间断伽辽金方法：异质介质中的矩阵定值权重和弹性波传播

• DOI: 10.1002/nme.5720
• 发表时间: 2018
• 期刊: International Journal for Numerical Methods in Engineering
• 影响因子: 2.9
• 作者: Chan, Jesse

EFFICIENT ENTROPY STABLE GAUSS COLLOCATION METHODS

• DOI: 10.1137/18m1209234
• 发表时间: 2019-01-01
• 期刊: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• 影响因子: 3.1
• 作者: Chan, Jesse;Fernandez, David C. Del Rey;Carpenter, Mark H.
• 通讯作者: Carpenter, Mark H.

On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes

• DOI: 10.1016/j.jcp.2018.11.010
• 发表时间: 2019-02-01
• 期刊: JOURNAL OF COMPUTATIONAL PHYSICS
• 影响因子: 4.1
• 作者: Chan, Jesse;Wilcox, Lucas C.
• 通讯作者: Wilcox, Lucas C.