  During the past few years, inverse problem formulations of ultrasound
beamforming have attracted a growing interest. They usually pose beamforming as
a minimization problem of a fidelity term resulting from the measurement model
plus a regularization term that enforces a certain class on the resulting
image. Herein, we take advantages of alternating direction method of
multipliers to propose a flexible framework in which each term is optimized
separately. Furthermore, the proposed beamforming formulation is extended to
replace the regularization term by a denoising algorithm, based on the recent
approaches called plug-and-play (PnP) and regularization by denoising (RED).
Such regularizations are shown in this work to better preserve speckle texture,
an important feature in ultrasound imaging, than sparsity-based approaches
previously proposed in the literature. The efficiency of proposed methods is
evaluated on simulations, real phantoms, and \textit{in vivo} data available
from a plane-wave imaging challenge in medical ultrasound. Furthermore, a
comprehensive comparison with existing ultrasound beamforming methods is also
provided. These results show that the RED algorithm gives the best image
quality in terms of contrast index while preserving the speckle statistics.
