Systems and methods for medical imaging, specifically ultrasound imaging capable of achieving spatial resolutions that can resolve point objects smaller than 100 μm irrespective of them to be well-resolved, using the principles of compressive sensing and sparse recovery are described. Ultrasound system uses the transmit transducers sequentially to sonicate the medium and the data is acquired over the receive transducers. The acquired signals are then sampled by the low-dimensional acquisition system. The signals are recovered using an optimization method before a frequency domain beamforming technique is applied. The time reversal focused frequency matrix is formed to focus the energy of different frequency bands into a single frequency. Next, a super-resolution synthetic time reversal Phase Coherent MUltiple SIgnal Classification (PC-MUSIC) method is applied to focus spatially on the target locations considering the frequency dependent phase response of the transducers and the green's function of the ROI at the focused frequency.
