  Sparse reconstruction is an important aspect of MRI, helping to reduce
acquisition time and improve spatial-temporal resolution. Popular methods are
based mostly on compressed sensing (CS), which relies on the random sampling of
k-space to produce incoherent (noise-like) artefacts. Due to hardware
constraints, 1D Cartesian phase-encode under-sampling schemes are popular for
2D CS-MRI. However, 1D under-sampling limits 2D incoherence between
measurements, yielding structured aliasing artefacts (ghosts) that may be
difficult to remove assuming a 2D sparsity model. Reconstruction algorithms
typically deploy direction-insensitive 2D regularisation for these
direction-associated artefacts. Recognising that phase-encode artefacts can be
separated into contiguous 1D signals, we develop two decoupling techniques that
enable explicit 1D regularisation and leverage the excellent 1D incoherence
characteristics. We also derive a combined 1D + 2D reconstruction technique
that takes advantage of spatial relationships within the image. Experiments
conducted on retrospectively under-sampled brain and knee data demonstrate that
combination of the proposed 1D AliasNet modules with existing 2D deep learned
(DL) recovery techniques leads to an improvement in image quality. We also find
AliasNet enables a superior scaling of performance compared to increasing the
size of the original 2D network layers. AliasNet therefore improves the
regularisation of aliasing artefacts arising from phase-encode under-sampling,
by tailoring the network architecture to account for their expected appearance.
The proposed 1D + 2D approach is compatible with any existing 2D DL recovery
technique deployed for this application.
