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Parallel MRI techniques in the k-space, like GRAPPA are widely used in accelerated MRI. Recently neural-network based non-linear approaches have shown improved performance over linear methods like GRAPPA. But present day neural networks are largely tailored to process real data, hence the complex-valued k-space data is processed as two-dimensional real data in these. In this work, we study the performance of an end-to-end complex-valued architecture trained using complex-valued optimization, for interpolating missing values in the k-space for parallel MR which we call the Complex rRAKI. We propose a generalized version of the ReLU activation function on the complex plane called the PlaneReLU. The performance of the Complex rRAKI is evaluated on two publicly-available k-space MRI datasets, the fastmri multicoil brain dataset and the fastmri multicoil knee dataset. Com- parison of obtained results with those on the baseline rRAKI are also presented. The proposed Complex rRAKI achieves improved performance over the baseline with respect to standard metrics SSIM and NRMSE with 50% fewer parameters.
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