A Multithreshold Iterative DBIM-Based Algorithm for the Imaging of Heterogeneous Breast Tissues

Objective: This paper proposes a novel microwave imaging (MWI) multifrequency technique, which combines compressive sensing (CS) with the well-known distorted Born iterative method. CS strategies are emerging as a promising tool in MWI applications, which can improve reconstruction quality and/or reduce the number of data samples. Methods: The proposed approach is based on iterative shrinkage thresholding algorithm (ISTA), which has been modified to include an automatic and adaptive selection of multithreshold values. Results: This adaptive multithreshold ISTA implementation is applied in reconstruction of two-dimensional (2-D) numerical heterogeneous breast phantoms, where it outperforms the standard thresholding implementation. We show that our approach is also successful in 3-D simulations of a realistic imaging experiment, despite the mismatch between the data and our algorithm's forward model. Conclusion: These results suggest that the proposed algorithm is a promising tool for medical MWI applications. Significance: Important novelties of this approach are the use of multiple thresholds to recover the different unknowns in the Debye model as well as the adaptive selection of these thresholds. Moreover, we have shown that employing modified hard constraints inside the linear step of the inversion procedure can enhance reconstruction quality.