Abstract-In this paper, the recently developed multiplicative regularized contrast source inversion method is applied to microwave biomedical applications. The inversion method is fully iterative and avoids solving any forward problem in each iterative step. In this way, the inverse scattering problem can efficiently be solved. Moreover, the recently developed multiplicative regularizer allows us to apply the method blindly to experimental data. We demonstrate inversion from experimental data collected by a 2.33-GHz circular microwave scanner using a two-dimensional (2-D) TM polarization measurement setup. Further some results of a feasibility study of the present inversion method to the 2-D TE polarization and the full-vectorial three-dimensional measurement will be presented as well.

Abstract-In this paper, we developed a general framework for the inversion of electromagnetic measurements in cases where parametrization of the unknown configuration is possible. Due to the ill-posed nature of this nonlinear inverse scattering problem, this parametrization approach is needed when the available measurement data are limited and measurements are only carried out from limited transmitter-receiver positions (limited data diversity). By carrying out this parametrization, the number of unknown model parameters that need to be inverted is manageable. Hence the Newton based approach can advantageously be used over gradient-based approaches. In order to guarantee an error reduction of the optimization process, the iterative step is adjusted using a line search algorithm. Further unlike the most available Newton-based approaches available in the literature, we enhanced the Newton based approaches presented in this paper by constraining the inverted model parameters with nonlinear transformation. This constrain forces the reconstruction of the unknown model parameters to lie within their physical bounds. In order to deal with cases where the measurements are redundant or lacking sensitivity to certain model parameters causing non-uniqueness of solution, the cost function to be minimized is regularized by adding a penalty term. One of the crucial aspects of this approach is how to determine the regularization parameter determining the relative importance of the misfit between the measured and predicted data and the penalty term. We reviewed different approaches to determine this parameter and proposed a robust and simple way of choosing this regularization parameter with aid of recently developed multiplicative regularization analysis. By combining all the techniques mentioned above we arrive at an effective and robust parametric algorithm. As numerical examples we present results of electromagnetic inversion at induction frequency in the deviated borehole configuration. 266Habashy and Abubakar

Abstract-We discuss the problem of the reconstruction of the profile of an inhomogeneous object from scattered field data. Our starting point is the contrast source inversion method, where the unknown contrast sources and the unknown contrast are updated by an iterative minimization of a cost functional. We discuss the possibility of the presence of local minima of the nonlinear cost functional and under which conditions they can exist. Inspired by the successful implementation of the minimization of total variation and other edgepreserving algorithms in image restoration and inverse scattering, we have explored the use of these image-enhancement techniques as an extra regularization. The drawback of adding a regularization term to the cost functional is the presence of an artificial weighting parameter in the cost functional, which can only be determined through considerable numerical experimentation. Therefore, we first discuss the regularization as a multiplicative constraint and show that the weighting parameter is now completely prescribed by the error norm of the data equation and the object equation. Secondly, inspired by the edge-preserving algorithms, we introduce a new type of regularization, based on a weighted L 2 total variation norm. The advantage is that the updating parameters in the contrast source inversion method can be determined explicitly, without the usual line minimization. In addition this new regularization shows excellent edge-preserving properties. Numerical experiments illustrate that the present multiplicative regularized inversion scheme is very robust, handling noisy as well as limited data very well, without the necessity of artificial regularization parameters. Van den Berg and Abubakar

We present 2.5D fast and rigorous forward and inversion algorithms for deep electromagnetic (EM) applications that include crosswell and controlled-source EM measurements. The forward algorithm is based on a finite-difference approach in which a multifrontal LU decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single-source experiment for each frequency of operation. When the size of the linear system of equations is large, the use of this noniterative solver is impractical. Hence, we use the optimal grid technique to limit the number of unknowns in the forward problem. The inversion algorithm employs a regularized Gauss-Newton minimization approach with a multiplicative cost function. By using this multiplicative cost function, we do not need a priori data to determine the so-called regularization parameter in the optimization process, making the algorithm fully automated. The algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image. To increase the robustness of the algorithm, we also constrain the minimization and use a line-search approach to guarantee the reduction of the cost function after each iteration. To demonstrate the pros and cons of the algorithm, we present synthetic and field data inversion results for crosswell and controlled-source EM measurements.