  Many real-world signal sources are complex-valued, having real and imaginary
components. However, the vast majority of existing deep learning platforms and
network architectures do not support the use of complex-valued data. MRI data
is inherently complex-valued, so existing approaches discard the richer
algebraic structure of the complex data. In this work, we investigate
end-to-end complex-valued convolutional neural networks - specifically, for
image reconstruction in lieu of two-channel real-valued networks. We apply this
to magnetic resonance imaging reconstruction for the purpose of accelerating
scan times and determine the performance of various promising complex-valued
activation functions. We find that complex-valued CNNs with complex-valued
convolutions provide superior reconstructions compared to real-valued
convolutions with the same number of trainable parameters, over a variety of
network architectures and datasets.
