Pre-scaled two-parameter Gauss–Newton image reconstruction to reduce property recovery imbalance

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Abstract
Gauss–Newton image reconstruction in microwave imaging can be formulated in terms of a single complex quantity, the wave number squared (k2), with the understanding that the relative permittivity and conductivity images can be extracted afterwards through a simple constitutive relationship. However, this approach ignores the fact that the magnitude of the average real and imaginary components can be considerably out of balance depending on the operating frequency and tissue characteristics which can inadvertently imbalance the process in favour of one parameter over the other. In an effort to achieve property recovery which is balanced, we introduce a pre-scaling procedure at the property update stage of the reconstruction. Utilization of this concept in conjunction with our two-step regularization process for both simulation and phantom experiments demonstrates that the penalty term weighting parameters for the optimal mean-squared property errors for the two recovered distributions (relative permittivity and conductivity) together with that yielding the lowest least-squared electric field error coincide only when the scaling is applied. The scheme provides a means for simultaneous optimization of the two permittivity and conductivity images.

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