Nonlinear 3-D microwave imaging for breast-cancer screening: Log, phase and log-phase formulation

The imaging algorithm used in the 3-D microwave imaging system for breast cancer screening, currently being developed at the Technical University of Denmark, is based on an iterative Newton-type algorithm. In this algorithm, the distribution of the electromagnetic constitutive parameters is updated in each iteration based on a comparison between the measured signals and the signals computed by a forward solver for the current parameter distribution. A key feature of the algorithm is the use of the log-phase formulation in which the measured complex signals are represented by the logarithm of their amplitudes and their unwrapped phases. In this paper, simplifications of the log-phase formulation are proposed, namely the log formulation, in which only the logarithm of the amplitudes are used, and the phase formulation, in which only the unwrapped phases are used. These formulations allow for the use of simpler tomographic systems in which only the amplitudes or the phases of the signals are measured. The performance of the algorithms using the two proposed formulations is investigated by reconstructing images of data collected with the above-mentioned imaging system, and the resulting images are compared with those obtained using the log-phase formulation.