This paper presents a deep learning method for faster magnetic resonance imaging (MRI) by reducing k-space data with sub-Nyquist sampling strategies and provides a rationale for why the proposed approach works well. Uniform subsampling is used in the time-consuming phase-encoding direction to capture high-resolution image information, while permitting the image-folding problem dictated by the Poisson summation formula. To deal with the localization uncertainty due to image folding, a small number of low-frequency k-space data are added. Training the deep learning net involves input and output images that are pairs of the Fourier transforms of the subsampled and fully sampled k-space data. Our experiments show the remarkable performance of the proposed method; only 29% of the k-space data can generate images of high quality as effectively as standard MRI reconstruction with the fully sampled data.
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