Analysis of deep complex‐valued convolutional neural networks for MRI reconstruction and phase‐focused applications

Purpose Deep learning has had success with MRI reconstruction, but previously published works use real‐valued networks. The few works which have tried complex‐valued 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 phase‐based 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.