  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, very few low-frequency k-space data are
added. Training the deep learning net involves input and output images that are
pairs of Fourier transforms of the subsampled and fully sampled k-space data.
Numerous experiments show the remarkable performance of the proposed method;
only 29% of k-space data can generate images of high quality as effectively as
standard MRI reconstruction with fully sampled data.
