High-order total variation-based image restoration

The total variation ( TV) denoising method is a PDE-based technique that preserves edges well but has the sometimes undesirable staircase effect, namely, the transformation of smooth regions ( ramps) into piecewise constant regions ( stairs). In this paper we present an improved model, constructed by adding a nonlinear fourth order diffusive term to the Euler-Lagrange equations of the variational TV model. Our technique substantially reduces the staircase effect, while preserving sharp jump discontinuities ( edges). We show numerical evidence of the power of resolution of this novel model with respect to the TV model in some 1D and 2D numerical examples.