Proceedings of Machine Learning Research – Under Review:1–10, 2022 Full Paper – MIDL 2022 submission Learned Half-Quadratic Splitting Network for Magnetic Resonance Image Reconstruction Bingyu Xin 1 bx64@rutgers.edu Timothy S. Phan 2 Timothy.S.Phan@nyulangone.org Leon Axel 2 Leon.Axel@nyulangone.org Dimitris N. Metaxas 1 dnm@cs.rutgers.edu 1 Department of Computer Science, Rutgers University, Piscataway, NJ 08854, USA. 2 Department of Radiology, New York University, New York, NY 10016, USA. Editors: Under Review for MIDL 2022 Abstract Magnetic Resonance (MR) image reconstruction from highly undersampled k-space data is critical in accelerated MR imaging (MRI) techniques. In recent years, deep learning-based methods have shown great potential in this task. This paper proposes a learned half- quadratic splitting algorithm for MR image reconstruction and implements the algorithm in an unrolled deep learning network architecture. We compare the performance of our proposed method on a public cardiac MR dataset against DC-CNN and LPDNet, and our method outperforms other methods in both quantitative results and qualitative results with fewer model parameters and faster reconstruction speed. Finally, we enlarge our model to achieve superior reconstruction quality, and the improvement is 1.76 dB and 2.74 dB over LPDNet in peak signal-to-noise ratio on 5× and 10× acceleration, respectively. Code for our method is publicly available at https://github.com/hellopipu/HQS-Net. Keywords: MR reconstruction, k-space, Compressed sensing, Deep Learning, Cardiac 1. Introduction Magnetic resonance imaging (MRI) has been widely used in clinical disease diagnosis as a non-invasive imaging technique with a high spatio-temporal signal-to-noise ratio (SNR). However, the main limitation for MRI is the slow acquisition procedure, which usually lasts between 15 to 90 minutes per subject. For dynamic cardiac MRI, subjects are required to hold their breath and stay still to reduce imaging artifacts during the acquisition process, which is challenging or even impossible for those with breathing difficulties. In MRI physics, k-space is the 2D or 3D Fourier transform of the MR image, and MR raw data is acquired in k-space. The recent fast MRI techniques aim to reduce the MRI acquisition time by scanning undersampled k-space data, which are then used to reconstruct the MR images by applying an inverse Fourier transform. This data undersampling process violates the Nyquist Theorem, and therefore the reconstructed images will be heavily aliased, which will result in imaging artifacts and low SNR. Traditional compressed sensing MR image reconstruction methods (Ma et al., 2008) (Ravishankar and Bresler, 2010)(Boyd et al., 2011)(Lingala et al., 2011) are time-consuming, and the reconstruction quality is often not satisfactory. The recent use of deep learn- ing methods for MR image reconstruction has resulted in improved reconstruction quality, higher SNR with significant efficiency gains at runtime. © 2022 B. Xin, T.S. Phan, L. Axel & D.N. Metaxas. arXiv:2112.09760v2 [eess.IV] 21 Dec 2021