We present a new split-type algorithm for the minimization
of a p-harmonic energy with added data fidelity
term. The half-quadratic splitting reduces the
original problem to two straightforward problems, that
can be minimized efficiently. The minimizers to the two
sub-problems can typically be computed pointwise and
are easily implemented on massively parallel processors.
Furthermore the splitting method allows for the
computation of solutions to a large number of more advanced
directional regularization problems. In particular
we are able to handle robust, non-convex data terms,
and to define a 0-harmonic regularization energy where
we sparsify directions by means of an L0 norm.