When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.
Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.
Ultrasound is the second most frequently used medical imaging modality that is inexpensive, non-invasive, portable, and fast. As a real-time imaging system, ultrasound can also be used for tracking motion patterns to complement anatomical images. Temporal tracking of tissue motion, a non-trivial task, plays a pivotal role in many diagnostic applications of ultrasound, such as elastography and super-resolution ultrasound. Elastography is a non-invasive medical imaging technique that estimates tissue elastic properties to detect abnormalities in an organ. Ultrasound radio-frequency (RF) data can be tracked to compute tissue strain (which is a surrogate for elasticity) using energy-based algorithms. A continuity constraint along with the data similarity is imposed to obtain a unique solution to the displacement estimation problem. Existing energy-based methods consider only amplitude similarity to formulate the data function, which makes the displacement estimation process sensitive to outliers. In addition, they exploit the L2-norm of the first-order spatial derivative of the displacement field to construct the regularizer. This regularization scheme is not entirely consistent with the mechanics of tissue deformation while perturbed by an external force. Moreover, the L2-norm often over-penalizes the displacement discontinuity. Consequently, state-of-the-art techniques estimate noisy strain images with low target-background contrast and blurry inclusion edges. Another well-known limitation of the existing displacement tracking techniques is their poor lateral estimation ability.
Ultrasound localization microscopy (ULM) is a promising medical imaging modality that systematically leverages the advantages of contrast-enhanced ultrasound (CEUS) to surpass the diffraction barrier and delineate the microvascular map. Localization and tracking of intravenously injected microbubble (MB) contrast agents, two significant steps of ULM, facilitate generating the vascular map and the velocity distribution, respectively. The existing MB tracking algorithms predominantly incorporate template-matching and bipartite graph-based cost table minimization, disregarding the immense potential of an energy-based analytic framework.
Herein, we propose six novel energy-based strain imaging techniques (Chapters 2 to 6) and one analytic optimization-based MB tracking algorithm (Chapter 7) to resolve the aforementioned issues of the existing techniques. In Chapter 2, we penalize an adaptively-weighted combination of amplitude and gradient fidelities to devise a robust data function. In Chapter 3, we propose a physics-driven strain imaging algorithm that formulates the regularizer, taking both first- and second-order derivatives of the displacement field into account. In Chapters 4 and 5, we resolve the edge-blurring issue by considering the L1-norms of displacement derivatives using total-variation (TV) distance and ADMM-based alternating minimization strategy, respectively. In Chapter 6, we introduce L2- and L1-norm-based techniques that impose an effective Poisson’s ratio (EPR)-driven mechanical constraint for improving the lateral strain estimates. Considering temporal pairing as a bubble-set registration problem, we propose an MB tracking technique in Chapter 7 that iteratively registers the bubble sets in two consecutive time instants by analytically optimizing a novel cost function. All seven algorithms developed herein exhibit promising performance in synthetic and real experiments.