  Total variation denoising is a nonlinear filtering method well suited for the
estimation of piecewise-constant signals observed in additive white Gaussian
noise. The method is defined by the minimization of a particular
non-differentiable convex cost function. This paper describes a generalization
of this cost function that can yield more accurate estimation of piecewise
constant signals. The new cost function involves a non-convex penalty
(regularizer) designed to maintain the convexity of the cost function. The new
penalty is based on the Moreau envelope. The proposed total variation denoising
method can be implemented using forward-backward splitting.
