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

Abstract

AbstractA 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