Parameter Scaling in Non-Linear Microwave Tomography

Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions. In this paper, a method for obtaining a more uniform sensitivity throughout the breast is investigated. The method for obtaining uniform sensitivity throughout the imaging domain is a scaling of the parameters to be reconstructed. This scaling, based on the norms of the columns of the Jacobian, is also introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data.