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

Time Reversal Compressive Sensing MIMO Radar Systems

Active radar systems transmit a probing signal and use the return backscatters received from the channel to determine properties of the channel. After detecting the presence of targets, the localization of targets is achieved by estimating relevant target parameters, including the range, Doppler's frequency, and azimuth associated with the targets. A major source of error in parameter estimation is the presence of clutter (undesired targets) that also reflects the probing signal back to the radar. To eliminate the fading effect introduced by backscatters originating from the clutter, the multiple input multiple output (MIMO) radar transmits a set of simultaneous uncorrelated probing signals from the transmit elements comprising the transmit array. A major problem with MIMO radars is the large amount of data generated when the recorded backscatters are discretized at the Nyquist sampling rate. This in turn necessitates the need of expensive, high speed analog-to-digital converter circuits. Compressive sensing (CS) has emerged as a new sampling paradigm for reconstructing sparse signals with relatively few observations and at a lower computational cost compared to other sparsity promoting approaching. Although compressive beamforming has the potential of high resolution estimates, the approach has several limitations arising mainly due to the difficulty in achieving complete incoherency and sparsity in the CS dictionary. This PhD thesis will apply the principle of time reversal (TR) to MIMO radars to improve the incoherency and sparsity of the compressive beamforming dictionary. The resulting CS TR MIMO radar is analytically studied and assessed for performance gains as compared to the conventional MIMO systems