  Beamforming in ultrasound imaging has significant impact on the quality of
the final image, controlling its resolution and contrast. Despite its low
spatial resolution and contrast, delay-and-sum is still extensively used
nowadays in clinical applications, due to its real-time capabilities. The most
common alternatives are minimum variance method and its variants, which
overcome the drawbacks of delay-and-sum, at the cost of higher computational
complexity that limits its utilization in real-time applications.
  In this paper, we propose to perform beamforming in ultrasound imaging
through a regularized inverse problem based on a linear model relating the
reflected echoes to the signal to be recovered. Our approach presents two major
advantages: i) its flexibility in the choice of statistical assumptions on the
signal to be beamformed (Laplacian and Gaussian statistics are tested herein)
and ii) its robustness to a reduced number of pulse emissions. The proposed
framework is flexible and allows for choosing the right trade-off between noise
suppression and sharpness of the resulted image. We illustrate the performance
of our approach on both simulated and experimental data, with \textit{in vivo}
examples of carotid and thyroid. Compared to delay-and-sum, minimimum variance
and two other recently published beamforming techniques, our method offers
better spatial resolution, respectively contrast, when using Laplacian and
Gaussian priors.
