  We consider a variable metric linesearch based proximal gradient method for
the minimization of the sum of a smooth, possibly nonconvex function plus a
convex, possibly nonsmooth term. We prove convergence of this iterative
algorithm to a critical point if the objective function satisfies the
Kurdyka-Lojasiewicz property at each point of its domain, under the assumption
that a limit point exists. The proposed method is applied to a wide collection
of image processing problems and our numerical tests show that our algorithm
results to be flexible, robust and competitive when compared to recently
proposed approaches able to address the optimization problems arising in the
considered applications.
