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

Multiple-Target Tracking in Complex Scenarios

In this dissertation, we develop computationally efficient algorithms for multiple-target tracking: MTT) in complex scenarios. For each of these scenarios, we develop measurement and state-space models, and then exploit the structure in these models to propose efficient tracking algorithms. In addition, we address design issues such as sensor selection and resource allocation. First, we consider MTT when the targets themselves are moving in a time-varying multipath environment. We develop a sparse-measurement model that allows us to exploit the inherent joint delay-Doppler diversity offered by the environment. We then reformulate the problem of MTT as a block-support recovery problem using the sparse measurement model. We exploit the structure of the dictionary matrix to develop a computationally efficient block support recovery algorithm: and thereby a multiple-target tracking algorithm) under the assumption that the channel state describing the time-varying multipath environment is known. Further, we also derive an upper bound on the overall error probability of wrongly identifying the support of the sparse signal. We then relax the assumption that the channel state is known. We develop a new particle filter called the Multiple Rao-Blackwellized Particle Filter: MRBPF) to jointly estimate both the target and the channel states. We also compute the posterior Cramér-Rao bound: PCRB) on the estimates of the target and the channel states and use the PCRB to find a suitable subset of antennas to be used for transmission in each tracking interval, as well as the power transmitted by these antennas. Second, we consider the problem of tracking an unknown number and types of targets using a multi-modal sensor network. In a multi-modal sensor network, different quantities associated with the same state are measured using sensors of different kinds. Hence, an efficient method that can suitably combine the diverse information measured by each sensor is required. We first develop a Hierarchical Particle Filter: HPF) to estimate the unknown state from the multi-modal measurements for a special class of problems which can be modeled hierarchically. We then model our problem of tracking using a hierarchical model and then use the proposed HPF for joint initiation, termination and tracking of multiple targets. The multi-modal data consists of the measurements collected from a radar, an infrared camera and a human scout. We also propose a unified framework for multi-modal sensor management that comprises sensor selection: SS), resource allocation: RA) and data fusion: DF). Our approach is inspired by the trading behavior of economic agents in commercial markets. We model the sensors and the sensor manager as economic agents, and the interaction among them as a double sided market with both consumers and producers. We propose an iterative double auction mechanism for computing the equilibrium of such a market. We relate the equilibrium point to the solutions of SS, RA and DF. Third, we address MTT problem in the presence of data association ambiguity that arises due to clutter. Data association corresponds to the problem of assigning a measurement to each target. We treat the data association and state estimation as separate subproblems. We develop a game-theoretic framework to solve the data association, in which we model each tracker as a player and the set of measurements as strategies. We develop utility functions for each player, and then use a regret-based learning algorithm to find the correlated equilibrium of this game. The game-theoretic approach allows us to associate measurements to all the targets simultaneously. We then use particle filtering on the reduced dimensional state of each target, independently

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