  Euler's elastica model has been extensively studied and applied to image
processing tasks. However, due to the high nonlinearity and nonconvexity of the
involved curvature term, conventional algorithms suffer from slow convergence
and high computational cost. Various fast algorithms have been proposed, among
which, the augmented Lagrangian based ones are very popular in the community.
However, parameter tuning might be very challenging for these methods. In this
paper, a simple cutting-off strategy is introduced into the augmented
Lagrangian based algorithms for minimizing the Euler's elastica energy, which
leads to easy parameter tuning and fast convergence. The cutting-off strategy
is based on an observation of inconsistency inside the augmented Lagrangian
based algorithms. When the weighting parameter of the curvature term goes to
zero, the energy functional boils down to the ROF model. So, a natural
requirement is that its augmented Lagrangian based algorithms should also
approach the augmented Lagrangian based algorithms formulated directly for
solving the ROF model from the very beginning. Unfortunately, this is not the
case for certain existing augmented Lagrangian based algorithms. The proposed
cutting-off strategy helps to decouple the tricky dependence between the
auxiliary splitting variables, so as to remove the observed inconsistency.
Numerical experiments suggest that the proposed algorithm enjoys easier
parameter-tuning, faster convergence and even higher quality of image
restorations.
