Non-Linear Regularized Attenuation Compensation for Microwave Breast Imaging

We develop non-linear optimization algorithms for attenuation compensation of rapidly time-varying microwave signals in the context of breast imaging. The breast tissues attenuate the energy of the scattered wavefield as it travels within the medium. Compensating the attenuation effect is a challenging and typically unstable task. To address this issue, we develop inversion-based algorithms that take advantage of prior knowledge about the system. We formulate the attenuation compensation as a regularized non-linear cost function and introduce two efficient algorithms. The first algorithm assumes that the reflectivity series is smooth and follows a Gaussian distribution, i.e., <inline-formula><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> norm, and the second algorithm assumes that it can be cast as a sparse series, i.e., <inline-formula><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> norm. Also, both algorithms force the inverted quality factor to be close to an expected value based on previous evaluations of different models and datasets. Through testing of the algorithms on simulated and experimental datasets, we show that the proposed algorithms successfully compensate for attenuation. The images after attenuation compensation provide more accurate localization of the tumors and superior resolution when compared with conventional imaging practice.