  The interest of compressive sampling in ultrasound imaging has been recently
extensively evaluated by several research teams. Following the different
application setups, it has been shown that the RF data may be reconstructed
from a small number of measurements and/or using a reduced number of ultrasound
pulse emissions. Nevertheless, RF image spatial resolution, contrast and signal
to noise ratio are affected by the limited bandwidth of the imaging transducer
and the physical phenomenon related to US wave propagation. To overcome these
limitations, several deconvolution-based image processing techniques have been
proposed to enhance the ultrasound images. In this paper, we propose a novel
framework, named compressive deconvolution, that reconstructs enhanced RF
images from compressed measurements. Exploiting an unified formulation of the
direct acquisition model, combining random projections and 2D convolution with
a spatially invariant point spread function, the benefit of our approach is the
joint data volume reduction and image quality improvement. The proposed
optimization method, based on the Alternating Direction Method of Multipliers,
is evaluated on both simulated and in vivo data.
