  Deep learning has been successfully demonstrated in MRI reconstruction of
accelerated acquisitions. However, its dependence on representative training
data limits the application across different contrasts, anatomies, or image
sizes. To address this limitation, we propose an unsupervised, auto-calibrated
k-space completion method, based on a uniquely designed neural network that
reconstructs the full k-space from an undersampled k-space, exploiting the
redundancy among the multiple channels in the receive coil in a parallel
imaging acquisition. To achieve this, contrary to common convolutional network
approaches, the proposed network has a decreasing number of feature maps of
constant size. In contrast to conventional parallel imaging methods such as
GRAPPA that estimate the prediction kernel from the fully sampled
autocalibration signals in a linear way, our method is able to learn nonlinear
relations between sampled and unsampled positions in k-space. The proposed
method was compared to the start-of-the-art ESPIRiT and RAKI methods in terms
of noise amplification and visual image quality in both phantom and in-vivo
experiments. The experiments indicate that APIR-Net provides a promising
alternative to the conventional parallel imaging methods, and results in
improved image quality especially for low SNR acquisitions.
