Fast data acquisition in Magnetic Resonance Imaging (MRI) is vastly in demand and scan time directly depends on the number of acquired k-space samples. The data-driven methods based on deep neural networks have resulted in promising improvements, compared to the conventional methods, in image reconstruction algorithms. The connection between deep neural network and Ordinary Differential Equation (ODE) has been observed and studied recently. The studies show that different residual networks can be interpreted as Euler discretization of an ODE. In this paper, we propose an ODE-based deep network for MRI reconstruction to enable the rapid acquisition of MR images with improved image quality. Our results with undersampled data demonstrate that our method can deliver higher quality images in comparison to the reconstruction methods based on the standard UNet network and Residual network.
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