Dynamic MRI reconstruction using low-rank plus sparse decomposition with
  smoothness regularization
Chee-Ming Ting Fuad Noman Raphaël C. -W. Phan Hernando Ombao
The low-rank plus sparse (L+S) decomposition model has enabled better
reconstruction of dynamic magnetic resonance imaging (dMRI) with separation
into background (L) and dynamic (S) component. However, use of low-rank prior
alone may not fully explain the slow variations or smoothness of the background
part at the local scale. In this paper, we propose a smoothness-regularized L+S
(SR-L+S) model for dMRI reconstruction from highly undersampled k-t-space data.
We exploit joint low-rank and smooth priors on the background component of dMRI
to better capture both its global and local temporal correlated structures.
Extending the L+S formulation, the low-rank property is encoded by the nuclear
norm, while the smoothness by a general \ell_{p}-norm penalty on the local
differences of the columns of L. The additional smoothness regularizer can
promote piecewise local consistency between neighboring frames. By smoothing
out the noise and dynamic activities, it allows accurate recovery of the
background part, and subsequently more robust dMRI reconstruction. Extensive
experiments on multi-coil cardiac and synthetic data shows that the SR-L+S
model outp