Ng et al. present a generalization of a theorem proven by A. Chambolle [1], where an L² regularization of the total variation norm (min_u TV(u) + 1/2&lgr;)||u-g||₂², with TV(u) = ∫_&OHgr; |▿ u(x, y)|, dx dy) is used to de-noise an image g to obtain u.

In this paper, the authors relax some of the smoothness assumptions of the Chambolle paper, most notably the smoothness of the gradient operator, where semi-smooth operators are allowed. The latter operators are obtained as convex envelopes of smooth operators, by applying the machinery of sub-differentials [2].

The paper, which is careful in presenting proofs, concludes by displaying the results of several numerical experiments on standard images.