This paper refers to quantitative reconstruction of the dielectric and conductive property distributions of biological objects by means of active microwave imaging. An iterative reconstruction algorithm based on the Levenberg-Marquardt method is tested with synthetic data. The influence of the receiver geometry is investigated and two methods for choosing the regularization parameter, an empirical method and generalized cross validation (GCV) method, are examined.

Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method

Stochastic methods are now very common in electromagnetics. Among the various applications, they have been recently proposed for solving inverse problems arising in radio-frequency and microwave imaging. Some of the recently proposed stochastic inversion procedures are critically discussed (e.g., genetic algorithms, differential evolution methods, memetic algorithms, particle swarm optimizations, hybrid techniques, etc.) and the way they have been applied in this area. The use of the ant colony optimization method, which is a relatively new method in electromagnetics, is also proposed. Various imaging modalities are considered (tomography, buried object detection, and borehole sensing). Finally, the main features making these approaches useful for imaging purposes are discussed and the currently considered strategies to reduce the computational load associated with stochastic optimization procedures delineated

Stochastic Optimization Methods Applied to Microwave Imaging: A Review

A reconstruction algorithm is detailed for three-dimensional full-vectorial microwave imaging based on Newton-type optimization. The goal is to reconstruct the three-dimensional complex permittivity of a scatterer in a homogeneous background from a number of time-harmonic scattered field measurements. The algorithm combines a modified Gauss-Newton optimization method with a computationally efficient forward solver, based on the fast Fourier transform method and the marching-on-in-source-position extrapolation procedure. A regularized cost function is proposed by applying a multiplicative-additive regularization to the least squares datafit. This approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non-linearity of the optimization problem. It is furthermore shown that the modified Gauss-Newton method converges much faster than the Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method. Promising quantitative reconstructions from both simulated and experimental data are presented. The latter data are bi-static polarimetric free-space measurements provided by Institut Fresnel, Marseille, France.

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Full-Wave Three-Dimensional Microwave Imaging With a Regularized Gauss–Newton Method— Theory and Experiment

It is shown how to generate oblique slices from a set of parallel slices. An algorithm that can produce planes or contours through the volume without any loss of the volume resolution of the original data set is presented. The algorithm uses the Fourier-shift theorem and is efficient for calculating large numbers of slices. Although the algorithm is general, it is particularly well suited for three-dimensional magnetic resonance images, as demonstrated with examples. >

A general algorithm for oblique image reconstruction

A nonlinear estimation approach to solving the inverse scattering problem, and reconstructing the space-varying complex permittivity of unknown objects is considered. The bilinear operator equations governing the scattering are approximated into finite dimensional spaces on the basis of the finite degrees of freedom of data, and on the simple concept that one cannot expect to reconstruct an arbitrary function from a finite number of independent equations. As a consequence, a discrete model, well suited to numerical inversion, is developed. The particular bilinear nature of the equations, and a suitable choice of contrast and field unknowns allows the functional adopted in the estimation to be minimized in an accurate and numerically efficient manner. Numerical experiments show how the method is capable, when a proper number of searched unknowns is adopted, to manage the possible convergence to local minima (which is a typical question in nonlinear inverse problems), and validate the effectiveness of the proposed approach.

A nonlinear estimation method in tomographic imaging

A preliminary study of the application of simulated annealing (SA) to complex permittivity reconstruction in microwave tomography is presented. Reconstructions of a simplified model of a human arm obtained with simulated noise-free data are presented for three different methods: SA, quenching, and a Newton-Kantorovich method. These results show that SA can converge to an accurate solution in cases where the two deterministic methods fail. For this reason SA can be used to get closer to the final solution before applying a faster deterministic method. >

Microwave imaging-complex permittivity reconstruction-by simulated annealing

An iterative algorithm based on simulated annealing, for the reconstruction of the permittivity and conductivity distributions of a section of a strongly inhomogeneous cylindrical object, is presented. It has been tested, using simulated noise-free data, for some small objects. The effect of simulated annealing is compared to a conventional iterative method.

L. Garnero

Papers

Microwave imaging-complex permittivity reconstruction-by simulated annealing

Application of the Simulated Annealing Technique to Microwave Tomography: Preliminary Results