This work proposes a novel microwave imaging (MWI) multi-frequency technique, which combines compressive sensing (CS) with the well-known distorted Born iterative method (DBIM) to enhance the accuracy in the imaging procedure. CS strategies are emerging as a promising tool in MWI applications, which can also reduce the number of data samples. The proposed approach is based on an iterative shrinkage thresholding algorithm (ISTA), which has been modified to include an automatic and adaptive selection of multi-threshold values. The proposed implementation is applied in reconstruction of two-dimensional numerical heterogeneous breast phantoms, where it outer-performs the standard thresholding implementation and proves to be an interesting tool for medical imaging applications.