Keywords: Complex-valued neural network, Complex ReLU, Parallel MRI, GRAPPA
TL;DR: Complex-valued neural network with novel PlaneReLU activation function on the complex plane for interpolating missing values in the complex-valued k-space in parallel MRI
Abstract: Parallel MRI techniques in the k-space, like GRAPPA are widely used in accelerated MRI. Recently neural-network 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 for interpolating missing values in the k-space for parallel MRI which we call the Complex rRAKI. We propose a novel activation function, the PlaneReLU, which is a generalized version of the ReLU on the complex plane. The performance of the Complex rRAKI is evaluated on two publicly-available k-space MRI datasets, the fastMRI multicoil brain and knee datasets. Comparison 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.