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

Abstract

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.

Keywords: MRI; complex-valued models; convolutional neural networks; image reconstruction; learning representations.