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.
@article{arxiv.2004.01738,
title = {Analysis of Deep Complex-Valued Convolutional Neural Networks for MRI Reconstruction},
author = {Elizabeth K. Cole and Joseph Y. Cheng and John M. Pauly and Shreyas S. Vasanawala},
journal= {arXiv preprint arXiv:2004.01738},
year = {2020}
}