  Wireless ultrasound (US) systems that produce high-quality images can improve
current clinical diagnosis capabilities by making the imaging process much more
efficient, affordable, and accessible to users. The most common technique for
generating B-mode US images is delay and sum (DAS) beamforming, where an
appropriate delay is introduced to signals sampled and processed at each
transducer element. However, sampling rates that are much higher than the
Nyquist rate of the signal are required for high resolution DAS beamforming,
leading to large amounts of data, making transmission of channel data over WIFI
impractical. Moreover, the production of US images that exhibit high resolution
and good image contrast requires a large set of transducers which further
increases the data size. Previous works suggest methods for reduction in
sampling rate and in array size. In this work, we introduce compressed Fourier
domain convolutional beamforming, combining Fourier domain beamforming, sparse
convolutional beamforming, and compressed sensing methods. This allows reducing
both the number of array elements and the sampling rate in each element, while
achieving high resolution images. Using in vivo data we demonstrate that the
proposed method can generate B-mode images using 142 times less data than DAS.
Our results pave the way towards wireless US and demonstrate that high
resolution US images can be produced using sub-Nyquist sampling and a small
number of receiving channels.
