  Biomedical imaging is unequivocally dependent on the ability to reconstruct
interpretable and high-quality images from acquired sensor data. This
reconstruction process is pivotal across many applications, spanning from
magnetic resonance imaging to ultrasound imaging. While advanced data-adaptive
reconstruction methods can recover much higher image quality than traditional
approaches, their implementation often poses a high computational burden. In
ultrasound imaging, this burden is significant, especially when striving for
low-cost systems, and has motivated the development of high-resolution and
high-contrast adaptive beamforming methods. Here we show that deep neural
networks that adopt the algorithmic structure and constraints of adaptive
signal processing techniques can efficiently learn to perform fast high-quality
ultrasound beamforming using very little training data. We apply our technique
to two distinct ultrasound acquisition strategies (plane wave, and synthetic
aperture), and demonstrate that high image quality can be maintained when
measuring at low data-rates, using undersampled array designs. Beyond
biomedical imaging, we expect that the proposed deep~learning based adaptive
processing framework can benefit a variety of array and signal processing
applications, in particular when data-efficiency and robustness are of
importance.
