Optimization and High-Order Fast Algorithms Applied to Microwave Imaging

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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.