  Magnetic resonance (MR) image acquisition is an inherently prolonged process,
whose acceleration by obtaining multiple undersampled images simultaneously
through parallel imaging has always been the subject of research. In this
paper, we propose the Dual-Octave Convolution (Dual-OctConv), which is capable
of learning multi-scale spatial-frequency features from both real and imaginary
components, for fast parallel MR image reconstruction. By reformulating the
complex operations using octave convolutions, our model shows a strong ability
to capture richer representations of MR images, while at the same time greatly
reducing the spatial redundancy. More specifically, the input feature maps and
convolutional kernels are first split into two components (i.e., real and
imaginary), which are then divided into four groups according to their spatial
frequencies. Then, our Dual-OctConv conducts intra-group information updating
and inter-group information exchange to aggregate the contextual information
across different groups. Our framework provides two appealing benefits: (i) it
encourages interactions between real and imaginary components at various
spatial frequencies to achieve richer representational capacity, and (ii) it
enlarges the receptive field by learning multiple spatial-frequency features of
both the real and imaginary components. We evaluate the performance of the
proposed model on the acceleration of multi-coil MR image reconstruction.
Extensive experiments are conducted on an {in vivo} knee dataset under
different undersampling patterns and acceleration factors. The experimental
results demonstrate the superiority of our model in accelerated parallel MR
image reconstruction. Our code is available at:
github.com/chunmeifeng/Dual-OctConv.
