Finite element approximation of a forward and backward anisotropic diffusion model in image denoising and form generalization

A new forward–backward anisotropic diffusion model is introduced. The two limit cases are the Perona‐Malik equation and the Total Variation flow model. A fully discrete finite element scheme is studied using C⁰‐piecewise linear elements in space and the backward Euler difference scheme in time. A priori estimates are proven. Numerical results in image denoising and form generalization are presented.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008