A Shape-Based Inversion Algorithm Applied to Microwave Imaging of Breast Tumors

We propose a new shape-based inversion algorithm to identify an anomaly embedded in an inhomogeneous layered geometry. We apply our approach to microwave breast imaging where the geometry consists of several inhomogeneous layers and the potential tumor is embedded in the innermost layer. In addition to the tumor identification, we estimate the irregular transition layer between the breast inner layers. Our inversion algorithm is based on a low-dimensional parametric form of the relevant geometries, and uses multiple-frequency multi-source data to estimate the unknowns. Several numerical examples are provided to evaluate the effectiveness of our approach and demonstrate its robustness both to the initial choice of parameter values and uncertainty in the complex dielectric properties of the media even with the complex geometry and the simplified inverse model.