A shift of paradigm is currently underway in biomedical ultrasound thanks to plane or diverging waves coherent compounding for faster imaging. One remaining challenge consists in handling phase and amplitude aberrations induced during the ultrasonic propagation through complex layers. Unlike conventional line-per-line imaging, ultrafast ultrasound provides backscattering information from the whole imaged area for each transmission. Here, we take benefit from this feature and propose an efficient approach to perform fast aberration correction. Our method is based on the Singular Value Decomposition (SVD) of an ultrafast compound matrix containing backscattered data for several plane wave transmissions. First, we explain the physical signification of SVD and associated singular vectors within the ultrafast matrix formalism. We theoretically demonstrate that the separation of spatial and angular variables, rendered by SVD on ultrafast data, provides an elegant and straightforward way to optimize the angular coherence of backscattered data. In heterogeneous media, we demonstrate that the first spatial and angular singular vectors retrieve respectively the non-aberrated image of a region of interest, and the phase and amplitude of its aberration law. Numerical, in vitro and in vivo results prove the efficiency of the image correction, but also the accuracy of the aberrator determination. Based on spatial and angular coherence, we introduce a complete methodology for adaptive beamforming of ultrafast data, performed on successive isoplanatism patches undergoing SVD beamforming. The simplicity of this method paves the way to real-time adaptive ultrafast ultrasound imaging and provides a theoretical framework for future quantitative ultrasound applications.

The non-invasive quantification of human tissue fat fraction using easily scalable and accessible imaging technologies is crucial for the diagnosis of many diseases including liver steatosis. Here, we propose a non-invasive quantification of fat content using a highly accessible ultrasonic imaging technology. Ultrasonic echoes backscattered from human liver tissues are recombined to synthetize echoes of a virtual point-like reflector within the organs. This virtual point-like reflector is an ultrasonic analogue of artificial stars generated by laser beams in the field of astronomy, which are used to estimate the aberrations induced in the propagation medium. Here, the ultrasonic echoes from the point-like reflector provide an estimate of the Green’s function relating the ultrasonic array and the reflector location and consequently represent a measurement of the aberrations induced along the ultrasonic beam travel path. Maximizing the spatial coherence of echoes backscattered from this targeted region provides an estimate of the acoustic sound speed while iteratively making the reflector more echogenic. The acoustic sound speed is dependent of the organ fat content, and we derive and cross-validate a theoretical equation relating acoustic sound speed and fat content both in phantom experiments and humans. An ultrasound-based fat fraction was found to be highly correlated with the oil paraffin concentration (R2  =  0.985) in phantoms and well correlated with the gold standard magnetic resonance imaging proton density fat fraction measurements (R2  =  0.73) in patients.