  Forward-backward methods are a very useful tool for the minimization of a
functional given by the sum of a differentiable term and a nondifferentiable
one and their investigation has experienced several efforts from many
researchers in the last decade. In this paper we focus on the convex case and,
inspired by recent approaches for accelerating first-order iterative schemes,
we develop a scaled inertial forward-backward algorithm which is based on a
metric changing at each iteration and on a suitable extrapolation step. Unlike
standard forward-backward methods with extrapolation, our scheme is able to
handle functions whose domain is not the entire space. Both {an ${\mathcal
O}(1/k^2)$ convergence rate estimate on the objective function values and the
convergence of the sequence of the iterates} are proved. Numerical experiments
on several {test problems arising from image processing, compressed sensing and
statistical inference} show the {effectiveness} of the proposed method in
comparison to well performing {state-of-the-art} algorithms.
