A novel mathematical method for solving inverse scattering problems in microwave imaging using a virtual Veselago lens
| dc.contributor.author | Eini Keleshteri, Marzieh | |
| dc.contributor.examiningcommittee | Jeffrey, Ian (Electrical and Computer Engineering) | |
| dc.contributor.examiningcommittee | Lui, Shaun (Mathematics) | |
| dc.contributor.examiningcommittee | Eleftheriades, George V (University of Toronto) | |
| dc.contributor.supervisor | LoVetri, Joe | |
| dc.contributor.supervisor | Okhmatovski, Vladimir | |
| dc.date.accessioned | 2023-08-24T20:56:43Z | |
| dc.date.available | 2023-08-24T20:56:43Z | |
| dc.date.issued | 2023-08-17 | |
| dc.date.submitted | 2023-08-21T19:33:16Z | en_US |
| dc.degree.discipline | Electrical and Computer Engineering | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | |
| dc.description.abstract | This study presents a promising method for microwave imaging using the mathematical characteristics of the Veselago lens. The Veselago lens is a perfect lens that exhibits unique focusing phenomena. The research aims to achieve several key objectives: 1) to investigate the impact of the Veselago lens in regularizing the ill-posedness of the inverse scattering problem; 2) to formulate a simpler solution to the inverse problem by deriving a regularizing Green's operator that improves matrix conditionality, facilitating inversion; 3) to develop a new mathematical foundation for faster, non-expensive, and non-iterative algorithms; and 4) to enhance the accuracy and spatial resolution of reconstructed images, surpassing the diffraction limit and allowing for sub-wavelength resolution. To accomplish these objectives, a comprehensive study was conducted to understand the implications of incorporating the Veselago lens in the inverse scattering problem associated with microwave imaging. A new Helmholtz equation was derived, and explicit analytic expressions for the corresponding Green's function were obtained. The lens was applied in an imaging scenario with an actual lens, and a novel data equation employing the Veselago lens Green's function was used to solve the inverse problem. Numerical analysis of synthetic data confirmed the efficacy of the new operator, demonstrating superior quality reconstructed images even for small features. The study also introduced novel filtering techniques to address noise in reconstructed images caused by the Veselago lens inverse operator. These techniques utilized truncated Singular Value Decomposition of the operators. Although the physical implementation of a Veselago lens may pose challenges, the research explored the possibility of using a virtual Veselago lens in microwave imaging. A mathematical formulation demonstrated the feasibility of virtualizing the lens utilization, allowing for high-quality imaging without the physical presence of a lens. The proposed method for microwave imaging using the virtual Veselago lens has shown potential in regularizing the inverse scattering problem and improving the precision and spatial resolution of reconstructed images. The derivation of the Veselago lens Green's function facilitated a simpler solution to the inverse problem and the development of faster and cost-effective algorithms. These advancements have implications for medical imaging and non-destructive testing, among other applications. | |
| dc.description.note | October 2023 | |
| dc.identifier.uri | http://hdl.handle.net/1993/37491 | |
| dc.language.iso | eng | |
| dc.rights | open access | en_US |
| dc.subject | Microwave | |
| dc.subject | Imaging | |
| dc.subject | Veselago Lens | |
| dc.subject | Perfect lens | |
| dc.subject | Focusing | |
| dc.subject | Double negative | |
| dc.subject | Inverse scattering problems | |
| dc.subject | Boundary value problems | |
| dc.subject | Partial differential equations | |
| dc.title | A novel mathematical method for solving inverse scattering problems in microwave imaging using a virtual Veselago lens | |
| dc.type | doctoral thesis | en_US |
| local.subject.manitoba | no | |
| oaire.awardTitle | Price Graduate Scholarships for Women in Engineering 2019 | |
| project.funder.identifier | NSERC |