Toward a Unified Approach to Diffuse Wave Inverse Problems

这项工作的目标是创建一种统一的方法来描述给定在边界收集的漫射波场数据的介质的内部结构。扩散反问题被发现在许多领域，包括(1)使用扩散光学层析成像(DOT)检测乳腺癌的医学成像；(2)钢铁和半导体行业中使用光热方法的无损评估(NDE)；以及(3)通过电阻成像(ERT)监测环境清理过程。尽管这些问题无处不在，但由于物理规模、考虑中的材料和传感系统的不同，研究人员通常以特定于应用的方式处理它们。在这里，通过利用每个问题在物理和处理目标上的潜在相似性来构建解决这类反问题的统一方法。研究人员集中在三个基本困难上。首先，他们设计了正则化技术来克服这些反问题的不适定性。具体地说，他们探索了对未知的自适应、几何、低阶模型的使用，并重建了这些模型中相对较少的描述性参数。其次，他们设计的反演方法与传统方法不同，不需要精确了解介质的背景结构。解决这些非线性逆问题是非常耗费计算的，部分原因是一个三维正问题必须解决数千次。因此，研究的第三个重点是通过利用正演问题之间的关系来开发计算高效的反演技术。所得到的理论和算法将使用第一段中描述的三个应用领域的真实传感器数据进行验证：DOT、光热无损检测和ERT。

Miller, EricNortheastern UThe objective of this work is the creation of a unified approach to characterizing the internal structure of a medium given diffuse wavefield data collected at the boundaries. Diffusive inverse problems are found in anumber of areas including (1) medical imaging for breast cancer detection using diffuse optical tomography (DOT); (2) non-destructive evaluation (NDE) in the steel and semi-conductor industries with photo-thermal methods; and (3) monitoring of environmental cleanup processes via electrical resistancetomography (ERT). Despite the ubiquity of these problems, researchers have typically treated them in application-specific ways due to differences in the physical scale, materials under consideration, and sensing systems. Here, a unified approach to solving this class of inverse problems is constructed by exploiting the underlying similarities in the physics and processing objectives of each of these problems.The investigators focus on three fundamental difficulties. First, they design regularization techniques to overcome the ill-posedness of these inverse problems. Specifically they explore the use of adaptive, geometric, low-order models for the unknown and reconstruct the relatively small number of descriptive parameters in these models. Second, they design inversion methods that, unlike traditional approaches, do not require precise knowledge of the background structure of the medium. Solving these nonlinear inverse problems is extremely computationally intensive, in part because a three-dimensional forward problem must be solved thousands of times. Therefore, a third focus of the research is the development ofcomputationally efficient inversion techniques by exploiting the relationships among the forward problems. The resulting theory and algorithms will be validated using real sensor data from the threeapplication areas described in the first paragraph: DOT, photo-thermal NDE, and ERT.