  High resolution ultrasound image reconstruction from a reduced number of
measurements is of great interest in ultrasound imaging, since it could enhance
both the frame rate and image resolution. Compressive deconvolution, combining
compressed sensing and image deconvolution, represents an interesting
possibility to consider this challenging task. The model of compressive
deconvolution includes, in addition to the compressive sampling matrix, a 2D
convolution operator carrying the information on the system point spread
function. Through this model, the resolution of reconstructed ultrasound images
from compressed measurements mainly depends on three aspects: the acquisition
setup, i.e. the incoherence of the sampling matrix, the image regularization,
i.e. the sparsity prior, and the optimization technique. In this paper, we
mainly focused on the last two aspects. We proposed a novel simultaneous
direction method of multipliers-based optimization scheme to invert the linear
model, including two regularization terms expressing the sparsity of the RF
images in a given basis and the generalized Gaussian statistical assumption on
tissue reflectivity functions. The performance of the method is evaluated on
both simulated and in vivo data.
