Computational electromagnetics and electromagnetic inverse imaging

这个为期五年的NSERC发现资助计划是关于生物医学应用的高性能计算电磁学（CEM）和EM逆成像（EMII）算法（例如，乳腺癌成像）和民用基础设施的结构健康监测（例如，检测桥面中的钢筋腐蚀）。通过先前的研究，我们现在有一个有限体积时域（FVTD）的代码，解决了EM问题的任意平面体积非结构化网格，执行用户指定的任意顺序的精度。一种新的积分方程网格截断方案允许我们终止网格非常接近的几何结构被建模。这个FVTD算法，以及其他算法，我们将调查作为本提案的一部分，将用于（1）合成复杂的EM散射数据，我们的EMII研究，（2）作为前向散射的一部分，我们将开发新的EMII算法。这将需要我们并行化我们的CEM算法，并在我们目前可用的网格计算机上实现它们。我们已经研究了几个EMII算法的散射数据与矢量网络分析仪为基础的探地雷达系统，我们已经建成。这需要对电磁反问题进行根本性的研究，我们最近发表了一种新的非线性正则化技术，它基于扭曲玻恩迭代技术。对于拟议的研究，高分辨率的技术，最近开发的反方法社区，将进行调查。这些方法包括（1）对比源反演方法，以及（2）基于残差的L曲线和归一化累积周期图的正则化方法。这些将被应用到使用我们现有的GPR系统收集的数据，以及我们正在开发的一个新的系统，用于成像人体幻影。这两个系统将扩大收集瞬态脉冲散射数据，我们将设计所需的瞬态脉冲天线。我们还将研究直接在时域中实现EMII技术的方法。

This five year NSERC Discovery Grant proposal is on high-performance computational electromagnetics (CEM) and EM inverse imaging (EMII) algorithms for biomedical applications (e.g., breast cancer imaging) and the structural-health monitoring of civil infrastructure (e.g., detection of rebar corrosion in bridge decks). Through prior research, we now have a finite-volume time-domain (FVTD) code that solves EM problems on arbitrary flat-faceted volumetric unstructured meshes which executes with a user-specifiable arbitrary order of accuracy. A new integral equation mesh truncation scheme allows us to terminate the mesh very close to the geometrical structures being modeled. This FVTD algorithm, as well as other algorithms we'll investigate as part of this proposal, will be used to (1) synthesize complex EM scattering data for our EMII research, and (2) as the forward-scattering part of the new EMII algorithms we will develop. This will require that we parallelize our CEM algorithms and implement them on the grid-computers that we currently have available. We've already investigated several EMII algorithms on scattering data collected with a vector network analyzer based ground penetrating radar system we've constructed. This has required fundamental investigations into the EM inverse problem and we've recently published a new nonlinear regularization technique based on both the distorted Born iterative technique. For the proposed research, high-resolution techniques, recently developed in the inverse-methods community, will be investigated. These include (1) the Contrast Source Inversion method, and (2) regularization methods based on the L-curve and the Normalized Cumulative Periodogram of the residual. These will be applied to the data collected using our existing GPR system as well as a new system we are developing for imaging human phantoms. Both systems will be expanded to collect transient-pulse scattering data and we will design the required transient-pulse antennas. We will also research ways of implementing the EMII techniques directly in the time-domain.