  The most common technique for generating B-mode ultrasound (US) images is
delay and sum (DAS) beamforming, where the signals received at the transducer
array are sampled before an appropriate delay is applied. This necessitates
sampling rates exceeding the Nyquist rate and the use of a large number of
antenna elements to ensure sufficient image quality. Recently we proposed
methods to reduce the sampling rate and the array size relying on image
recovery using iterative algorithms, based on compressed sensing (CS) and the
finite rate of innovation (FRI) frameworks. Iterative algorithms typically
require a large number of iterations, making them difficult to use in
real-time. Here, we propose a reconstruction method from sub-Nyquist samples in
the time and spatial domain, that is based on unfolding the ISTA algorithm,
resulting in an efficient and interpretable deep network. The inputs to our
network are the subsampled beamformed signals after summation and delay in the
frequency domain, requiring only a subset of the US signal to be stored for
recovery. Our method allows reducing the number of array elements, sampling
rate, and computational time while ensuring high quality imaging performance.
Using \emph{in vivo} data we demonstrate that the proposed method yields
high-quality images while reducing the data volume traditionally used up to 36
times. In terms of image resolution and contrast, our technique outperforms
previously suggested methods as well as DAS and minimum-variance (MV)
beamforming, paving the way to real-time applicable recovery methods.
