Abstract-The microwave imaging system currently being developed at the Technical University of Denmark is described and its performance tested on simulated data. The system uses an iterative Newton-based imaging algorithm for reconstructing the images in conjunction with an efficient method-of-moments solution of the associated forward scattering problem. A cylindrical multistatic antenna setup with 32 horizontally oriented antennas is used for collecting the data. It has been found that formulating the imaging algorithm in terms of the logarithm of the amplitude and the unwrapped phase of the measured signals improves its performance when compared to the more commonly used complex phasor formulation. This improvement is illustrated by imaging a simulated hemispherical breast model using both formulations. In addition to this, the importance of using the correct position and orientation of the antennas in the measurement system is shown by imaging the same breast model using a measurement setup in which the antennas are vertically oriented.Index Terms-Biomedical imaging, cancer, electromagnetic scattering inverse problems, microwave imaging, nonlinear equations.

Microwave tomographic imaging falls under a broad category of nonlinear parameter estimation methods when a Gauss-Newton iterative reconstruction technique is used. A fundamental requirement in using these approaches is evaluating the appropriateness of the regression model. While there have been numerous investigations of regularization techniques to improve overall image quality, few, if any, studies have explored the underlying statistical properties of the model itself. The ordinary least squares (OLS) approach is used most often, but there are other options such as the weighted least squares (WLS), maximum likelihood (ML), and maximum a posteriori (MAP) that may be more appropriate. In addition, a number of variance stabilizing transformations can be applied to make the inversion intrinsically more linear. In this paper, a statistical analysis is performed of the properties of the residual errors from the reconstructed images utilizing actual measured data and it is demonstrated that the OLS algorithm with a log transformation (OLSlog) is clearly advantageous relative to the more commonly used OLS approach by itself. In addition, several high contrast imaging experiments are performed, which demonstrate that different subsets of data are emphasized in each method and may contribute to the overall image quality differences.

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The contrast source inversion (CSI) algorithm was introduced for microwave imaging in 1997 and has since proven to be one of the most successful algorithms for nonlinear microwave tomography. In the CSI algorithm, the nonlinear integral equation, which must be solved to extract the constitutive electromagnetic parameters of the object under test from the microwave measurements, is represented by two linear equations, known as the data and the object equations. In this paper, the data equation in the CSI algorithm is reformulated using the so-called log-phase formulation. In this formulation, the measured data is represented by the change in the logarithm of the amplitude and the change in the unwrapped phase. This formulation has previously been applied for nonlinear tomography within the framework of a Gauss-Newton based algorithm for detection of breast cancer. Here, significant improvements have been observed compared to the more commonly used real-imaginary formulation. The modified CSI algorithm is tested on both simulated data and on a measurement of a breast. It is shown that for imaging setups with large differences in the measured signals, the new formulation of the data equation significantly improves the performance of the CSI algorithm

Purpose: The aim of this paper is to evaluate the performance of an EEG source localization method that combines a finite element method (FEM) and the reciprocity theorem. Methods: The reciprocity method is applied to solve the forward problem in a four-layer spherical head model for a large number of test dipoles. To benchmark the proposed method, the results are compared with an analytical solution and two state-of-the-art methods from the literature. Moreover, the dipole localization error resulting from utilizing the method in the inverse procedure for a realistic head model is investigated with respect to EEG signal noise and electrode misplacement. Results: The results show approximately 3% relative error between numerically calculated potentials done by the reciprocity theorem and the analytical solutions. When adding EEG noise with SNR between 5 and 10, the mean localization error is approximately 4.3 mm. For the case with 10 mm electrode misplacement the locali zation error is 4.8 mm. The reciprocity EEG source localization speeds up the solution of the inverse problem with more than three orders of magnitude compared to the state-of-the-art methods. Conclusions: The reciprocity method has high accuracy for modeling the dipole in EEG source localization, is robust with respect to noise, and faster than alternative methods