Beamforming through regularized inverse problems in ultrasound medical imaging

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.