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A shift of paradigm is currently underway in biomedical ultrasound thanks toplane and diverging waves for ultrafast imaging. One remaining challengeconsists in the correction of phase and amplitude aberrations induced duringpropagation through complex layers. Unlike conventional line-per-line imaging,ultrafast ultrasound provides for each transmission, backscattering informationfrom the whole imaged area. Here, we take benefit from this feature and proposean efficient approach to perform fast aberration correction based on theSingular Value Decomposition of an ultrafast compound matrix built frombackscattered data for several plane wave transmissions. First, we explain thephysical signification of SVD and associated singular vectors within theultrafast matrix formalism. We theoretically demonstrate that the spatial andangular variables separation, rendered by SVD on ultrafast data, provides anelegant and straightforward way to optimize angular coherence of backscattereddata. In heterogeneous media with an aberrating phase screen approximation, wedemonstrate that the first spatial and angular singular vectors retrieve on oneside the non-aberrated image, and on the other, the phase and amplitude of theaberration law. In vitro results prove the efficiency of the image correction,but also the accuracy of the aberrator determination. Based on spatial andangular coherence, we introduce a complete methodology for adaptive beamformingof ultrafast data, performed on successive isoplanatism patches undergoing SVDbeamforming. The simplicity of this method paves the way to real-time adaptiveultrafast ultrasound imaging and provides a theoretical framework for futurequantitative ultrasound applications.

The SVD Beamformer: Physical Principles and Application to Ultrafast Adaptive Ultrasound