  The proximal gradient method is a generic technique introduced to tackle the
non-smoothness in optimization problems, wherein the objective function is
expressed as the sum of a differentiable convex part and a non-differentiable
regularization term. Such problems with tensor format are of interest in many
fields of applied mathematics such as image and video processing. Our goal in
this paper is to address the solution of such problems with a more general form
of the regularization term. An adapted iterative proximal gradient method is
introduced for this purpose. Due to the slowness of the proposed algorithm, we
use new tensor extrapolation methods to enhance its convergence. Numerical
experiments on color image deblurring are conducted to illustrate the
efficiency of our approach.
