An Angular Framework for Ultrasound Imaging

Ultrasound imaging is one of the most widely used medical imaging modalities, with numerous applications in various fields of medicine. Today, its democratization is in full swing, with the increasing availability of quantitative parameters that simplify its interpretability and the mass adoption of ultraportable devices that bring ultrasound to the point of care. These evolutions have led to a deep transformation of ultrasound imaging, replacing heavy hardware architectures by advanced software algorithms and reducing power and emissions.

Throughout its history, various approaches have sustained the constant development of ultrasound imaging. With the revolution of ultrafast ultrasound imaging and the use of unfocused waves, a new perspective has emerged which considers ultrasound imaging as a tomographic image reconstruction problem. In this approach, time-of-flight computations replace focal properties, and the acquired raw data is described as a set of integrals along specific curves, designated as isochronous curves. Although this formulation has paved the way to plenty of new techniques, the complexity of the shape of isochronous curves (e.g. parabolic or ellipsoidal) hinders the complete fulfillment of the tomographic approach.

In this thesis, we investigate a new framework, coined as the angular framework, in which plane waves are considered both in emission and reception. This change of paradigm drastically simplifies the tomographic model as isochronous curves become straight lines. In this revised model, strong structural properties arise that bring new insights to ultrasound imaging. This leads to precise and robust methods that estimate ultrasound propagation properties with a reduced number of ultrasound emissions, therefore compatible with ultraportable imaging.

The simplicity of the new tomographic model can be harnessed to devise efficient solutions to complex ultrasound problems. First, we focus on B-Mode imaging and leverage the simplified tomographic model to devise efficient image formation techniques, for instance reducing the dimensionality of inverse problems by a factor equal to the number of emissions. Next, we revisit aberration correction and formulate a path-based model of aberration that is both physically accurate and computationally simple. We propose an aberration correction technique based on this path-based approach and demonstrate that it outperforms a state-of-the-art technique. In the third chapter, we introduce a novel local speed of sound estimation algorithm that relies on a direct analytical link between signal correlations and local speed of sound. This algorithm enables a real-time estimation of the speed of sound with a low number of transmits, which is crucial for applications such as liver steatosis screening, one of the fastest-growing fields in medical ultrasound imaging. Finally, we take advantage of the angular framework perspective and the far-field conditions it provides to quantify multiple