Novel Inverse-Scattering Methods in Banach Spaces

The scientific community is presently strongly interested in the research of new microwave imaging methods, in order to develop reliable, safe, portable, and cost-effective tools for the non-invasive/non-destructive diagnostic in many fields (such as medicine, civil and industrial engineering, \u2026). In this framework, microwave imaging techniques addressing the full three-dimensional nature of the inspected bodies are still very challenging, since they need to cope with significant computational complexity. Moreover, non-linearity and ill-posedness issues, which usually affects the related inverse scattering problems, need to be faced, too. Another promising topic is the development of phaseless methods, in which only the amplitude of the electric field is assumed to be measurable. This leads to a significant complexity reduction and lower cost for the experimental apparatuses, but the missing information on the phase of the electric field samples exacerbates the ill-posedness problems. In the present Thesis, a novel inexact-Newton inversion algorithm is proposed, in which the iteratively linearized problems are solved in a regularized sense by using a truncated Landweber or a conjugate gradient method developed in the framework of the l^p Banach spaces. This is an improvement that allows to generalize the classic framework of the l^2 Hilbert spaces in which the inexact-Newton approaches are usually defined. The applicability of the proposed imaging method in both the 3D full-vector and 2D phaseless scenarios at microwave frequencies is assessed in this Thesis, and an extensive validation of the proposed imaging method against both synthetic and experimental data is presented, highlighting the advantages over the inexact-Newton scheme developed in the classic framework of the l^2 Hilbert spaces

Microwave tomography with phaseless data on the calcaneus by means of artificial neural networks

The aim of this study is to use a multilayer perceptron (MLP) artificial neural network (ANN) for phaseless imaging the human heel (modeled as a bilayer dielectric media: bone and surrounding tissue) and the calcaneus cross-section size and location using a two-dimensional (2D) microwave tomographic array. Computer simulations were performed over 2D dielectric maps inspired by computed tomography (CT) images of human heels for training and testing the MLP. A morphometric analysis was performed to account for the scatterer shape influence on the results. A robustness analysis was also conducted in order to study the MLP performance in noisy conditions. The standard deviations of the relative percentage errors on estimating the dielectric properties of the calcaneus bone were relatively high. Regarding the calcaneus surrounding tissue, the dielectric parameters estimations are better, with relative percentage error standard deviations up to ≈ 15%. The location and size of the calcaneus are always properly estimated with absolute error standard deviations up to ≈ 3 mm.Fil: Fajardo Freites, Jesús Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Lotto, Federico Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Carlevaro, Carlos Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Universidad Tecnológica Nacional. Facultad Regional La Plata. Departamento de Ingeniería Mecánica; ArgentinaFil: Irastorza, Ramiro Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Electromagnetic inverse scattering problems

Ph.DDOCTOR OF PHILOSOPH

Optimization-Based Approaches to Low-Coherence Optical Diffraction Tomography

Quantitative optical phase imaging techniques, such as optical diffraction tomography (ODT), are useful tools for refractive-index profiling. Many of them, however, rely on the weak-scattering assumptions, thus cannot be applied to multiple-scattering objects, or turbid media. In this thesis, I report several approaches for expanding the efficacy of ODT techniques and adapting them to new applications by use of low-coherence broadband illumination. First, I developed a method for ODT reconstruction using regularized convex optimization with a new phase-based fidelity criterion. The new criterion is necessary because objects with very different refractive-index distributions may produce similar diffracted fields (magnitude and principal-phase) on the detection planes. This surjective, but non-injective relation, attributed to the cyclical nature of the phase, makes optimization algorithms using a field-based cost function prone to local minima, particularly for objects introducing large optical pathlength difference. I developed a phase-based optimization algorithm that avoids this and successfully tested it using simulations on phantoms and experimental data measured from samples of optical fibers. I have developed a method that applies total-variation regularization at each iteration of an iterative framework for ODT, which was developed with co-workers. I performed numerical and experimental tests using various highly scattering objects and demonstrated significant improvement in reconstruction SNR. I have also designed and constructed a new experimental setup for ODT measurement and expanded the new ODT algorithms from 2D to 3D. These algorithms have been numerically and experimentally validated using simulated data and data collected from the new experimental setup. Additionally, I have investigated the use of temporally incoherent illumination in ODT and showed that it enables time-gating of artifacts caused by multiple-scattering. I have further demonstrated that ODT combined with Fourier-transform spectroscopy can be used for spectral tomographic imaging of the wavelength-dependent complex-valued refractive index volumetric distributions

Utilizing higher-order basis functions for estimating the shape of metallic and dielectric objects

Представљена је квалитативна метода нумеричке електромагнетике за микроталасно формирање слике, која се ослања на решавање инверзног проблема расејања. У уводном делу дат је преглед литературе и укратко су дефинисане предности предложеног алгоритма у односу на већ постојеће методе. Након увода, дефинисани су основни постулати инверзних проблема и упоређени са добро познатом формулацијом директних електромагнетских проблема. Након тога, објашњене су потешкоће које настају при решавању инверзних проблема, односно показано је да су они у општем случају нелинеарни и некоректно постављени. Такође, детаљно је описана техника развоја по мултиполима као фундаментална алатка у аналитичкој електромагнетици, на којој се заснива приказана метода...An electromagnetic qualitative microwave imaging method, which relies on solving an inverse scattering problem, is presented. In the introductory part of this dissertation, the state-of-the-art is briefly summarized. Also, main advantages of the proposed method, compared to other known methods, are outlined. After the introduction, we define the basic idea of an inverse problem, compared to the well-known direct electromagnetic problem formulation. Then, we explain the main difficulties arising during an attempt to solve such an inverse problem, i.e., it is shown that these problems are generally non-linear and ill-posed. Also, the multipole expansion technique, as a fundamental tool in analytical electromagnetics, is described in detail..