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Beamforming in ultrasound imaging has significant impact on the quality ofthe final image, controlling its resolution and contrast. Despite its lowspatial resolution and contrast, delay-and-sum is still extensively usednowadays in clinical applications, due to its real-time capabilities. The mostcommon alternatives are minimum variance method and its variants, whichovercome the drawbacks of delay-and-sum, at the cost of higher computationalcomplexity that limits its utilization in real-time applications.  In this paper, we propose to perform beamforming in ultrasound imagingthrough a regularized inverse problem based on a linear model relating thereflected echoes to the signal to be recovered. Our approach presents two majoradvantages: i) its flexibility in the choice of statistical assumptions on thesignal to be beamformed (Laplacian and Gaussian statistics are tested herein)and ii) its robustness to a reduced number of pulse emissions. The proposedframework is flexible and allows for choosing the right trade-off between noisesuppression and sharpness of the resulted image. We illustrate the performanceof our approach on both simulated and experimental data, with \textit{in vivo}examples of carotid and thyroid. Compared to delay-and-sum, minimimum varianceand two other recently published beamforming techniques, our method offersbetter spatial resolution, respectively contrast, when using Laplacian andGaussian priors.

Beamforming through regularized inverse problems in ultrasound medical imaging