Compressive Sensing and Time Reversal Beamforming Approaches for Ultrasound Imaging

The objective of this thesis is to develop a novel beamforming technique for ultrasound machines that enables field reconstruction at sampling rates much lower than the Nyquist rate. In our simulations, we use Field II, a MATLAB based program for simulating transducer fields and models of biological tissues for imaging applications. Field II is capable of generating the emitted and pulse-echo fields for a large number of transducers configurations, including linear, circular, and rectangular arrays. Once the ultrasound field is determined, the proposed imaging technique is applied to the received signals to reconstruct the image for reference biological tissues. Applying different adaptive beamforming techniques, including the delay and sum (DAS) and Capon algorithms, the received signals from Field II simulation program are used to render the ultrasound images. A second goal of the thesis is to apply compressive sensing (CS) on received signals to reconstruct full-length signals from a reduced number of samples. A third goal is to couple the principal of time reversal (TR) with compressive sensing to extend the CAPON beamformer for reconstructing images of biological tissues at low sampling frequencies in rich multipath environments. The outputs of compressive sensing and CAPON-based algorithms, alone or in conjunction with each other, are severely degraded in such environments. Through numerical simulations, I illustrate an enhancement in reconstructed quality of images depicting biological tissues with my time-reversal based compressive sensing, CAPON approach.