Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration has long been the subject of research. This is commonly achieved by obtaining multiple undersampled images, simultaneously, through parallel imaging. In this article, we propose the dual-octave network (DONet), which is capable of learning multiscale spatial-frequency features from both the real and imaginary components of MR data, for parallel fast MR image reconstruction. More specifically, our DONet consists of a series of dual-octave convolutions (Dual-OctConvs), which are connected in a dense manner for better reuse of features. In each Dual-OctConv, the input feature maps and convolutional kernels are first split into two components (i.e., real and imaginary) and then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intragroup information updating and intergroup information exchange to aggregate the contextual information across different groups. Our framework provides three appealing benefits: 1) it encourages information interaction and fusion between the real and imaginary components at various spatial frequencies to achieve richer representational capacity; 2) the dense connections between the real and imaginary groups in each Dual-OctConv make the propagation of features more efficient by feature reuse; and 3) DONet enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. Extensive experiments on two popular datasets (i.e., clinical knee and fastMRI), under different undersampling patterns and acceleration factors, demonstrate the superiority of our model in accelerated parallel MR image reconstruction.

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.