  Most ultrasound imaging techniques necessitate the fundamental step of
converting temporal signals received from transducer elements into a spatial
echogenecity map. This beamforming (BF) step requires the knowledge of
speed-of-sound (SoS) value in the imaged medium. An incorrect assumption of BF
SoS leads to aberration artifacts, not only deteriorating the quality and
resolution of conventional brightness mode (B-mode) images, hence limiting
their clinical usability, but also impairing other ultrasound modalities such
as elastography and spatial SoS reconstructions, which rely on faithfully
beamformed images as their input. In this work, we propose an analytical method
for estimating BF SoS. We show that pixel-wise relative shifts between frames
beamformed with an assumed SoS is a function of geometric disparities of the
transmission paths and the error in such SoS assumption. Using this relation,
we devise an analytical model, the closed form solution of which yields the
difference between the assumed and the true SoS in the medium. Based on this,
we correct the BF SoS, which can also be applied iteratively. Both in
simulations and experiments, lateral B-mode resolution is shown to be improved
by $\approx$25% compared to that with an initial SoS assumption error of 3.3%
(50 m/s), while localization artifacts from beamforming are also corrected.
After 5 iterations, our method achieves BF SoS errors of under 0.6 m/s in
simulations and under 1 m/s in experimental phantom data. Residual time-delay
errors in beamforming 32 numerical phantoms are shown to reduce down to 0.07
$\mu$s, with average improvements of up to 21 folds compared to initial
inaccurate assumptions. We additionally show the utility of the proposed method
in imaging local SoS maps, where using our correction method reduces
reconstruction root-mean-square errors substantially, down to their lower-bound
with actual BF SoS.
