Computational electromagnetics and electromagnetic inverse imaging

这项为期五年的NSERC发现拨款提案是关于高性能计算电磁学（CEM）和电磁逆成像（EMII）算法，用于生物医学应用（例如，乳腺癌成像）和民用基础设施的结构健康监测（例如，检测桥面钢筋腐蚀）。通过之前的研究，我们现在有了一个有限体积时域（FVTD）代码，它可以解决任意平面体积非结构化网格上的电磁问题，并以用户指定的任意精度顺序执行。一个新的积分方程网格截断方案允许我们终止网格非常接近被建模的几何结构。该FVTD算法以及我们将作为本提案的一部分研究的其他算法将用于(1)为我们的EMII研究合成复杂的EM散射数据，以及(2)作为我们将开发的新EMII算法的前向散射部分。这将要求我们并行化CEM算法，并在我们现有的网格计算机上实现它们。我们已经研究了几种EMII算法对我们构建的基于矢量网络分析仪的探地雷达系统收集的散射数据的处理。这需要对EM逆问题进行基础研究，我们最近发表了一种新的非线性正则化技术，该技术基于畸变玻恩迭代技术。对于提议的研究，将调查最近在反方法社区开发的高分辨率技术。这些方法包括(1)对比源反演方法和(2)基于l曲线和残差归一化累积周期图的正则化方法。这些将应用于我们现有的探地雷达系统以及我们正在开发的用于成像人类幽灵的新系统收集的数据。这两个系统将扩展到收集瞬态脉冲散射数据，我们将设计所需的瞬态脉冲天线。我们还将研究在时域中直接实现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.