Title: Time-domain Compressive Beamforming for Medical Ultrasound Imaging
Description: Over the past 10 years, Compressive Sensing has gained a lot of visibility from the medical imaging research community. The most compelling feature for the use of Compressive Sensing is its ability to perform perfect reconstructions of under-sampled signals using l1-minimization. Of course, that counter-intuitive feature has a cost. The lacking information is compensated for by a priori knowledge of the signal under certain mathematical conditions. This technology is currently used in some commercial MRI scanners to increase the acquisition rate hence decreasing discomfort for the patient while increasing patient turnover. For echography, the applications could go from fast 3D echocardiography to simplified, cheaper echography systems. Real-time ultrasound imaging scanners have been available for nearly 50 years. During these 50 years of existence, much has changed in their architecture, electronics, and technologies. However one component remains present: the beamformer. From analog beamformers to software beamformers, the technology has evolved and brought much diversity to the world of beam formation.

Currently, most commercial scanners use several focalized ultrasonic pulses to probe tissue. The time between two consecutive focalized pulses is not compressible, limiting the frame rate. Indeed, one must wait for a pulse to propagate back and forth from the probe to the deepest point imaged before firing a new pulse. In this work, we propose to outline the development of a novel software beamforming technique that uses Compressive Sensing. Time-domain Compressive Beamforming (t-CBF) uses computational models and regularization to reconstruct de-cluttered ultrasound images. One of the main features of t-CBF is its use of only one transmit wave to insonify the tissue. Single-wave imaging brings high frame rates to the modality, for example allowing a physician to see precisely the movements of the heart walls or valves during a heart cycle. t-CBF takes into account the geometry of the probe as well as its physical parameters to improve resolution and attenuate artifacts commonly seen in single-wave imaging such as side lobes.

In this thesis, we define a mathematical framework for the beamforming of ultrasonic data compatible with Compressive Sensing. Then, we investigate its capabilities on simple simulations in terms of resolution and super-resolution. Finally, we adapt t-CBF to real-life ultrasonic data. In particular, we reconstruct 2D cardiac images at a frame rate 100-fold higher than typical values.