Multiple-Frequency DBIM-TwIST Algorithm for Microwave Breast Imaging

A novel distorted Born iterative method (DBIM) algorithm is proposed for microwave breast imaging based on the two-step iterative shrinkage/thresholding method. We show that this implementation is more flexible and robust than using traditional Krylov subspace methods such as the CGLS as solvers of the ill-posed linear problem. This paper presents several strategies to increase the algorithm’s robustness: a hybrid multifrequency approach to achieve an optimal tradeoff between imaging accuracy and reconstruction stability; a new approach to estimate the average breast tissues properties, based on sampling along their range of possible values and running a few DBIM iterations to find the minimum error; and finally, a new regularization strategy for the DBIM method based on the $L^{1}$ norm and the Pareto curve. We present reconstruction examples which illustrate the benefits of these optimization strategies, which have resulted in a DBIM algorithm that outperforms our previous implementations for microwave breast imaging.

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