Shanshan Wang^{1}, Huitao Cheng^{1}, Ziwen Ke^{1}, Leslie Ying^{2}, Xin Liu^{1}, Hairong Zheng^{1}, and Dong Liang^{1}

Applying deep learning to fast MR imaging has been new and highly evolved. This direction utilizes networks to draw valuable prior information from available big datasets and then assists fast online imaging. Nevertheless, most existing works adopt real-valued network structures while MR images are complex-valued. This paper proposes a complex-valued residual network learning framework for parallel MR imaging. Specifically, complex-valued convolution and initialization strategy are provided. Residual connections are also adopted to learn a more accurate prior. Experimental results show that the proposed method could achieve improved complex-valued image reconstruction with much less time compared to GRAPPA and SPIRiT.

**Theory and ****method**

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Fig. 1 (a) presents the architecture of the network proposed. (b)
illustrates the detail of complex convolution operator

Fig. 2 From left to right and top to bottom: (a) Ground-truth MR image;
The reconstructions of the GRAPPA (b), SPIRiT (c) and the proposed method (d) with 2D poisson undersampling
mask. The groundtruth phase (e) and phases reconstructed by GRPPA (f), SPIRiT (g) and the proposed method (h).

Tabel 1. Quantitative
comparison of the three methods in reconstructing MR images from 2D Poisson
undersampled data.