Second-order partial differential equations have been studied as a useful tool for noise
removal. The Perona?Malik model [P. Perona, Malik, Scale space and edge detection
using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 629?
639] has an edge preserving property but have sometimes the undesirable red effect.
In this paper, we propose improved models by combining Catte? et al.s model [F. Catte,
P.L. Lions, J.M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear
diffusion, SIAM J. Numer. Anal. 129 (1992) 182?193] with fourth-order terms. We
prove the existence and uniqueness of the proposed models. Then, we show numerical
evidence of the power of resolution of these models with respect to other known models
as the Perona?Malik model, the Catte? et al.s model, the modified total variation model
by Chan et al. [T. Chan, A. Marquina, P. Mulet, Second order differential functionals in
total variation-based image restoration. Available from : http:www.math.ucla.edu chan, etc.