Deep learning has had success with MRI reconstruction, but previously published works use real-valued networks. The few works which have tried complexvalued networks have not fully assessed their impact on phase. Therefore, the purpose of this work is to fully investigate end-to-end complex-valued convolutional neural networks (CNNs) for accelerated MRI reconstruction and in several phasebased applications in comparison to 2-channel real-valued networks. Methods: Several complex-valued activation functions for MRI reconstruction were implemented, and their performance was compared. Complex-valued convolution was implemented and tested on an unrolled network architecture and a U-Net-based architecture over a wide range of network widths and depths with knee, body, and phase-contrast datasets. Results: Quantitative and qualitative results demonstrated that complex-valued CNNs with complex-valued convolutions provided superior reconstructions compared to real-valued convolutions with the same number of trainable parameters for both an unrolled network architecture and a U-Net-based architecture, and for 3 different datasets. Complex-valued CNNs consistently had superior normalized RMS error, structural similarity index, and peak SNR compared to real-valued CNNs. Conclusion: Complex-valued CNNs can enable superior accelerated MRI reconstruction and phase-based applications such as fat-water separation, and flow quantification compared to real-valued convolutional neural networks.

Artificial intelligence algorithms based on principles of deep learning (DL) have made a large impact on the acquisition, reconstruction, and interpretation of MRI data. Despite the large number of retrospective studies using DL, there are fewer applications of DL in the clinic on a routine basis. To address this large translational gap, we review the recent publications to determine three major use cases that DL can have in MRI, namely, that of model-free image synthesis, model-based image reconstruction, and image or pixel-level classification. For each of these three areas, we provide a framework for important considerations that consist of appropriate model training paradigms, evaluation of model robustness, downstream clinical utility, opportunities for future advances, as well recommendations for best current practices. We draw inspiration for this framework from advances in computer vision in natural imaging as well as additional healthcare fields. We further emphasize the need for reproducibility of research studies through the sharing of datasets and software. Level of Evidence: 5 Technical Efficacy Stage: 2

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