Exploiting wavelet decomposition to enhance sparse recovery in microwave imaging

Over the last years, various new non-invasive methodologies have been proposed for medical imaging. Among them, microwave imaging (MWI) seems to be a promising technique for applications such as stroke detection and breast cancer imaging (BCI). This diagnostic modality is based on measurements of the scattered field outside an imaging domain, in which the object of interest is located. This inverse problem requires strategies such as regularization to increase the stability of the reconstructions. This work presents a method to increase stability based on exploiting the wavelet transform (WT) as a regularization strategy combined with a sparsity-based approach. The proposed technique is based on the theory of compressed sensing (CS) to treat the strong ill-posedness of the non-linear electromagnetic inverse scattering (EIS) problem.