Efficient inverse scattering algorithms based on conjugate gradient approaches for microwave imaging

• Autor(a) principal: Jose Olger Vargas Garay
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/46930; http://orcid.org/0000-0002-5431-6823
• topic: Integral equations; Microwave imaging; Conjugate gradient methods; Inverse scattering problems; Image reconstruction; Engenharia elétrica; Equações integrais; Microondas; Ondas eletromagnéticas - Espalhamento

The electromagnetic inverse scattering problem in microwave imaging aims to recover the dielectric properties, location, size, and shape of scatterers inside an inaccessible domain. This is an important field of electromagnetic wave applications, such as biomedical imaging, buried object detection, oil-gas exploration, and nondestructive evaluation. The imaging is performed by analyzing the scattered field measurements, which are usually cast into an optimization problem. In this context, an iterative inversion method is often required to minimize a cost function constructed by the mismatch of the measured scattered field and the computed one. In this thesis, different efficient algorithms based on the conjugate gradient method (CGM) to solve two- and three-dimensional inverse scattering problems are presented. The inversion CGM requires the solution of the forward scattering problem and the calculation of the gradient direction of the cost function at each iteration step. Depending on the gradient approximation, the CGM can be classified into two main approaches, linearized and nonlinearized methods. Each computation of the forward problem can be very time consuming. To avoid the computational burden, the forward solvers are efficiently implemented by using iterative methods to solve systems of simultaneous equations combined with FFT (fast Fourier transform) algorithms. The inversion methods proposed in this thesis are based on conjugate gradient approaches. Firstly, an efficient implementation of the nonlinearized CGM is proposed, which does not require calculating the inverse matrix. Such an approach reduces the computational cost and storage requirement of the reconstruction algorithm compared to the original one. Secondly, a subspace-based CGM (S-CGM) is also proposed, which is based on the linearized CGM and the concept of subspaces. Lastly, we propose a fast CGM to solve inverse scattering problems with a low degree of nonlinearity. Several numerical simulations have been carried out to validate the proposed inversion algorithms. In the 2D case, the methods are tested against both synthetic and experimental data. The reconstruction results show effectiveness in estimating the location, object shape, and permittivity values of the scatterers. In addition, numerical simulations using synthetic data show effectiveness for image reconstruction in three-dimensional problems.