Algorithm

Engineering

Undersampling

Image quality

Folding (DSP implementation)

Iterative reconstruction

Computer science

Filter (signal processing)

k-space

Mathematics

Image (mathematics)

Sampling (signal processing)

Mathematical analysis

Nyquist–Shannon sampling theorem

Artificial intelligence

Encoding (memory)

Deep learning

Compressed sensing

Fourier transform

Computer vision

Electrical engineering

Physics in Medicine and Biology

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.

Deep learning for undersampled MRI reconstruction