  Ultrafast ultrasound imaging remains an active area of interest in the
ultrasound community due to its ultra-high frame rates. Recently, a wide
variety of studies based on deep learning have sought to improve ultrafast
ultrasound imaging. Most of these approaches have been performed on radio
frequency (RF) signals. However, inphase/quadrature (I/Q) digital beamformers
are now widely used as low-cost strategies. In this work, we used complex
convolutional neural networks for reconstruction of ultrasound images from I/Q
signals. We recently described a convolutional neural network architecture
called ID-Net, which exploited an inception layer designed for reconstruction
of RF diverging-wave ultrasound images. In the present study, we derive the
complex equivalent of this network; i.e., the Complex-valued Inception for
Diverging-wave Network (CID-Net) that operates on I/Q data. We provide
experimental evidence that CID-Net provides the same image quality as that
obtained from RF-trained convolutional neural networks; i.e., using only three
I/Q images, the CID-Net produces high-quality images that can compete with
those obtained by coherently compounding 31 RF images. Moreover, we show that
CID-Net outperforms the straightforward architecture that consists of
processing the real and imaginary parts of the I/Q signal separately, which
thereby indicates the importance of consistently processing the I/Q signals
using a network that exploits the complex nature of such signals.
