A Contrast Source Inversion Algorithm Formulated Using the Log-Phase Formulation

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 algorith