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.

Automated summary

This study aims to compare the performance of complex-valued convolutional neural networks (CNNs) with real-valued CNNs in MRI reconstruction and phase-based applications. Results demonstrate that complex-valued CNNs outperform real-valued CNNs in reconstruction and have better normalized RMS error, structural similarity index, and peak signal-to-noise ratio.