Modified Newton Kantorovich Methods for Solving Microwave Inverse Scattering Problems

The Modified Newton-Kantorovich method (MNK) was formulated due to the limitation of The Newton-Kantorovich method (NK) in reconstructing the imitation of bone muscle and fat object. It was sensitive to contrast and cell size. In this research MNK and NK methods were applied to reconstruct the dielectric properties distribution of homogeneous and inhomogeneous objects from simulated scattered field dataset to know how the results of image reconstruction using both methods were. The results revealed that the MNK method was more flexible than the NK one.

Convergence and stability assessment of Newton-Kantorovich reconstrutin algorithms for microwve tomography

For newly developed iterative Newton-Kantorovitch reconstruction techniques, the quality of the final image depends on both experimental and model noise. Experimental noise is inherent to any experimental acquisition scheme, while model noise refers to the accuracy of the numerical model, used in the reconstruction process, to reproduce the experimental setup. This paper provides a systematic assessment of the major sources of experimental and model noise on the quality of the final image. This assessment is conducted from experimental data obtained with a microwave circular scanner operating at 2.33 GHz. Targets to be imaged include realistic biological structures, such as a human forearm, as well as calibrated samples for the sake of accuracy evaluation. The results provide a quantitative estimation of the effect of experimental factors, such as temperature of the immersion medium, frequency, signal-to-noise ratio, and various numerical parameters.Peer Reviewe

3D microwave tomography with huber regularization applied to realistic numerical breast phantoms

Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration

Microwave Tomography Using Stochastic Optimization And High Performance Computing

This thesis discusses the application of parallel computing in microwave tomography for detection and imaging of dielectric objects. The main focus is on microwave tomography with the use of a parallelized Finite Difference Time Domain (FDTD) forward solver in conjunction with non-linear stochastic optimization based inverse solvers. Because such solvers require very heavy computation, their investigation has been limited in favour of deterministic inverse solvers that make use of assumptions and approximations of the imaging target. Without the use of linearization assumptions, a non-linear stochastic microwave tomography system is able to resolve targets of arbitrary permittivity contrast profiles while avoiding convergence to local minima of the microwave tomography optimization space. This work is focused on ameliorating this computational load with the use of heavy parallelization. The presented microwave tomography system is capable of modelling complex, heterogeneous, and dispersive media using the Debye model. A detailed explanation of the dispersive FDTD is presented herein. The system uses scattered field data due to multiple excitation angles, frequencies, and observation angles in order to improve target resolution, reduce the ill-posedness of the microwave tomography inverse problem, and improve the accuracy of the complex permittivity profile of the imaging target. The FDTD forward solver is parallelized with the use of the Common Unified Device Architecture (CUDA) programming model developed by NVIDIA corporation. In the forward solver, the time stepping of the fields are computed on a Graphics Processing Unit (GPU). In addition the inverse solver makes use of the Message Passing Interface (MPI) system to distribute computation across multiple work stations. The FDTD method was chosen due to its ease of parallelization using GPU computing, in addition to its ability to simulate wideband excitation signals during a single forward simulation. We investigated the use of distributed Particle Swarm Optimization (PSO) and Differential Evolution (DE) methods in the inverse solver for this microwave tomography system. In these optimization algorithms, candidate solutions are farmed out to separate workstations to be evaluated. As fitness evaluations are returned asynchronously, the optimization algorithm updates the population of candidate solutions and gives new candidate solutions to be evaluated to open workstations. In this manner, we used a total of eight graphics processing units during optimization with minimal downtime. Presented in this thesis is a microwave tomography algorithm that does not rely on linearization assumptions, capable of imaging a target in a reasonable amount of time for clinical applications. The proposed algorithm was tested using numerical phantoms that with material parameters similar to what one would find in normal or malignant human tissue

Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography

International audienc

Near-Field Scattering Tomography System for Object Imaging and Material Characterization

Electromagnetic inverse scattering based permittivity profile estimation is one of the most promising techniques for object imaging and material characterization. Electromagnetic scattering tomography at the microwaves and THz frequency range can be used for medical imaging since all parts of the human body are naturally non-magnetic and dielectric, and millimeter and submillimeter waves can penetrate inside dielectrics. However, because electromagnetic inverse scattering problems are ill-conditioned and ill-posed, electromagnetic inverse scattering has not yet been successfully implemented in many potential application areas, particularly in clinical imaging. This dissertation presents a new formulation, a novel concept, and an effective implementation procedure to alleviate these problems and hopefully shorten the gap between the current state-of-the-art and real applications and to improve the electromagnetic inverse scattering technique in general. The major contribution of this dissertation is a new formulation of the electromagnetic inverse scattering problem based on a discrete modal analysis. To do so, the scattered electric field and the volume equivalent current source (VECS) are projected into a subspace spanned by the singular vectors obtained from the spatial Green’s function of the near-field scattering tomography system representation. Differentiating between the significant singular values and the less significant one is an important step. The scattered electric field coefficients are bounded and stable, while the VECS coefficients are not stable in the new subspaces since the singular values of the Green’s function modal representation start decaying very rapidly beyond a certain threshold. Minimizing the mean square error of the estimated scattered electric field or the estimated permittivity profile is used to find the threshold. The singular vectors below the threshold are considered as the radiating singular vectors, so the VECS projected into the radiating singular vectors are called the radiating VECS, and the contrast factor calculated by the radiating VECS are called the radiating contrast factor. The expected radiating contrast factor is constructed by repeating the measurements at different angles and/or frequencies. Then, the radiating permittivity profile and radiating conductivity profile of the object under-test (OUT) are obtained. In fact, the radiating permittivity profile carries important information about the OUT. The experimental results show that the OUT boundary information is embedded into the radiating permittivity profile, and the boundary of the OUT is effectively determined by using the radiating permittivity profile of region of interest. The second and foremost contribution of this dissertation is proposing a novel approach for solving the electromagnetic inverse scattering problem to make the solution unique by introducing the non-radiating contrast factor and the non-radiating objective function. Decomposing the permittivity into two complementary parts, the radiating permittivity profile and the non-radiating permittivity profile, improves the ill-posedness nature of the electromagnetic inverse scattering problem. Since the radiating permittivity profile is visible, and the non-radiating permittivity profile is invisible from the view point of the outside observer, in the first step, the boundary of the OUT is determined by using the aforementioned radiating permittivity profile obtained from the measurement outside the OUT. Then, the electromagnetic properties of the OUT are estimated – with sufficient accuracy – by minimizing the non-radiating objective function. The electromagnetic properties of the low-contrast and high-contrast OUTs are successfully estimated by the proposed approach, and the approach performance is also verified in a noisy environment through extensive simulations. The third major contribution of this dissertation is the introduction of a new planar near-field scattering tomography (PNFST) system. The PNFST system calibration and operational procedures are discussed. The proposed PNFST system is the first scattering tomography system implemented at the W-band frequency range in free space. Eliminating the multipath effects in the system enable us to make the incident field measurement process fast and quite effective since the field is measured in the absence of the scatterer only once. The PNFST system reconstructs the radiating permittivity profile of the region of interest, determines the boundary of the OUT, characterizes the material, and provides the electromagnetic properties of the low-contrast and high-contrast OUT. The experimental results validate the performance of the implemented PNFST system.1 yea