Toward a Unified Approach to Diffuse Wave Inverse Problems

米勒，EricNortheastern U这项工作的目的是建立一个统一的方法来表征介质的内部结构，给出了在边界处收集的漫射波场数据。 扩散逆问题在许多领域都有应用，包括：（1）利用扩散光学层析成像（DOT）进行乳腺癌检测的医学成像;（2）利用光热方法进行钢铁和半导体工业的无损评价（NDE）;（3）通过电阻层析成像（ERT）监测环境净化过程。尽管这些问题普遍存在，但由于物理尺度、所考虑的材料和传感系统的差异，研究人员通常以特定于应用的方式处理它们。 在这里，一个统一的方法来解决这类反问题的构造，利用这些问题的物理和处理目标的基本相似性。 首先，他们设计正则化技术来克服这些逆问题的不适定性。 具体来说，他们探索使用自适应，几何，低阶模型的未知和重建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。 求解这些非线性逆问题是非常计算密集型的，部分原因是三维正问题必须求解数千次。 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效率高的反演技术。 由此产生的理论和算法将使用真实的传感器数据进行验证，从第一段中描述的三个应用领域：DOT，光热NDE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.