We have in a previous study introduced a novel elliptic operator Delta((p,q))u = vertical bar del u vertical bar(q) Delta(1)u + (p - 1) vertical bar del u vertical bar(p-2)Delta(infinity) u, p >= 1, q >= 0, as a generalization of the p-Laplace operator. In this paper, we establish the well-posedness of the parabolic equation u(t) =vertical bar del u vertical bar(1-q) Delta((1+q,q)), where q = q(vertical bar del u vertical bar) is continuous and has range in [0, 1], in the framework of viscosity solutions. We prove the consistency and convergence of the numerical scheme of finite differences of this parabolic equation. Numerical simulations shows the advantage of this operator applied to image enhancement.