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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.

APIR-Net: Autocalibrated Parallel Imaging Reconstruction Using a Neural Network