  Purpose: Compressed sensing MRI (CS-MRI) from single and parallel coils is
one of the powerful ways to reduce the scan time of MR imaging with performance
guarantee. However, the computational costs are usually expensive. This paper
aims to propose a computationally fast and accurate deep learning algorithm for
the reconstruction of MR images from highly down-sampled k-space data.
  Theory: Based on the topological analysis, we show that the data manifold of
the aliasing artifact is easier to learn from a uniform subsampling pattern
with additional low-frequency k-space data. Thus, we develop deep aliasing
artifact learning networks for the magnitude and phase images to estimate and
remove the aliasing artifacts from highly accelerated MR acquisition.
  Methods: The aliasing artifacts are directly estimated from the distorted
magnitude and phase images reconstructed from subsampled k-space data so that
we can get an aliasing-free images by subtracting the estimated aliasing
artifact from corrupted inputs. Moreover, to deal with the globally distributed
aliasing artifact, we develop a multi-scale deep neural network with a large
receptive field.
  Results: The experimental results confirm that the proposed deep artifact
learning network effectively estimates and removes the aliasing artifacts.
Compared to existing CS methods from single and multi-coli data, the proposed
network shows minimal errors by removing the coherent aliasing artifacts.
Furthermore, the computational time is by order of magnitude faster.
  Conclusion: As the proposed deep artifact learning network immediately
generates accurate reconstruction, it has great potential for clinical
applications.
