Optimization and High-Order Fast Algorithms Applied to Microwave Imaging

本文提出的研究计划旨在开发一套高性能计算工具，可用于优化微波成像（MWI）系统的设计，并使用这些工具来发现和设计用于生物医学和农业应用的最先进的下一代MWI系统。这项研究的动机是基于最近的研究表明，适当的系统设计和建模将提高MWI分辨率，使MWI更适合成像应用。所提出的计算方法将降低执行MWI所需的计算能力和系统的复杂性，从而降低工业安装的成本。MWI一直是生物医学成像、安全措施和无损质量保证领域的重要研究课题。我们最近将其应用扩展到监测储存谷物作物质量的领域，在这个领域需要一种对储存容器的整个内容物敏感的工具。MWI很有吸引力，因为它既安全（非电离）又便宜。MWI的目标是通过对目标外部电磁场的采样，非侵入性地重建被照射目标的电学特性模型。对目标特性的了解具有实际用途，例如生物医学应用中的肿瘤检测，以及谷物储存期间腐烂情况的早期检测。尽管除了测量数据中的信噪比之外没有已知的分辨率限制，以及与生成图像相关的计算成本，但从标准MWI系统获得的分辨率相对较低，阻碍了MWI在许多应用中的应用。历史上，对MWI的研究主要集中在反演算法上。最近，人们尝试将数据中包含的可检索目标信息的数量作为噪声的函数进行量化。为了补充这项工作，将致力于提高前向求解器的精度和调整可控系统参数（发射器/接收器位置/类型，外部介质的轮廓/边界），以提高和/或优化MWI分辨率能力，并最大限度地减少建模误差。为了实现这些目标，我们将开发一种新型的并行、高阶、频域软件包，用于求解麦克斯韦方程组，然后将该数值工具应用于优化程序，以确定最佳的发射器/接收器配置和外部电磁特性配置，从而平衡系统实现的成本与产生的图像的准确性。我将使用软件工具设计、实施和测试用于乳腺癌检测和粮食储存监测的创新MWI系统。由此产生的MWI系统将以更低的成本提供更高的分辨率和更快的图像生成时间。这些工具还将使加拿大研究小组能够提高其自身用于乳腺癌检测的MWI系统的成像准确性，其目标是开发一种强大的、负担得起的大规模筛查工具，以便对加拿大妇女过早死亡的主要原因之一进行早期诊断。粮食储存MWI系统是创新的，新颖的，对加拿大确保我们的粮食储存用于国内消费和出口都很重要。这项工作将在马尼托巴大学进行，该大学在电磁成像实验室的MWI和粮食储存研究中心的粮食储存监测方面都有既定的研究记录。拟议的研究成果将加强加拿大在开发新兴技术方面的作用，这将使加拿大人和全球人口受益。

The research program proposed herein aims to develop a set of high-performance computational tools that can be applied to optimize the design of microwave imaging (MWI) systems and to use these tools to discover and design state-of-the-art next-generation MWI systems for biomedical and agricultural applications. The motivation for this research is based on recent work that suggests proper system design and modelling will improve MWI resolution, making MWI more amenable to imaging applications. The proposed computational methods will reduce both the computing power necessary to perform MWI and the complexity of the systems, resulting in lower costs for industrial installations. MWI has been the subject of significant research in the areas of biomedical imaging, security measures and non-destructive quality assurance. We have recently extended its application to the area of monitoring the quality of stored grain crops where there is a need for a tool that is sensitive to the entire contents of a storage container. MWI is attractive because it is both safe (non-ionizing) and inexpensive. The goal of MWI is to non-invasively reconstruct a model of the electrical properties of an irradiated target from a sampling of the electromagnetic fields external to the target. Knowledge of the target properties has practical uses such as tumour detection in biomedical applications, and early detection of rot conditions during grain storage. The adoption of MWI for many applications has been hindered by the relatively low resolution obtained from standard MWI systems, despite the fact that there is no known resolution limit except the signal-to-noise ratio in the measured data, and by the computational cost associated with generating images. Historically, research on MWI has been focused on inversion algorithms. More recently, attempts have been made to quantify the amount of retrievable target information contained in the data as a function of noise. To complement this work, effort will be devoted to improving forward solver accuracy and adjusting controllable system parameters (transmitter/receiver position/type, profile/boundaries of the external medium) in an attempt to improve and/or optimize MWI resolution capabilities and minimize modelling error. To accomplish these goals we will develop a novel parallel, high-order, frequency-domain, software package for solving Maxwell’s equations and then apply this numerical tool to optimization procedures for determining the best transmitter/receiver configurations and external electromagnetic property profiles that balance the cost of system implementation with the accuracy of the images that are produced. I will use the software tools to design, implement and test innovative MWI systems for breast cancer detection and grain storage monitoring. The resulting MWI systems will provide enhanced resolution and faster image generation times at a lower cost. These tools will also enable Canadian research groups to improve the imaging accuracy of their own MWI systems for breast cancer detection, with the goal of a robust, affordable, mass-screening tool to permit early diagnosis of one of the leading causes of premature death amongst Canadian women. Grain-storage MWI systems are innovative, novel, and important to Canada for securing our grain stores for both domestic consumption and export. This work will be undertaken at the University of Manitoba, an institution with an established record for research in both MWI, at the Electromagnetic Imaging Lab, and grain storage monitoring, at the Centre for Grain Storage Research. The outcomes of the proposed research will strengthen Canada’s role in developing emerging technologies that will benefit both Canadians and the global population.