We propose here a real time approach for aberration correction and Speed Of Sound quantification in the context of ultrafast ultrasound imaging. Theoretical works demonstrate the physical meaning of Singular Value Decomposition of the Ultrafast Compound Matrix. In heterogeneous media, we show that the first spatial and angular singular vectors retrieve respectively the non-aberrated image, and the aberration law. In vitro and in vivo experiments probe the efficiency of our method for angular coherence optimization through severe aberrations. Besides correcting the image, it provides knowledge of phase and amplitude aberration, allowing also a local Speed Of Sound estimation.
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