  A modification of the Perona-Malik equation is proposed for which the local
nonlinear diffusion term is replaced by a nonlocal term of slightly reduced
``strength''. The new equation is globally well-posed (in spaces of classical
regularity) and possesses desirable properties from the perspective of image
processing. It admits characteristic functions as (formally linearly
``stable'') stationary solutions and can therefore be reliably employed for
denoising keeping blurring in check. Its numerical implementation is stable,
enhances some of the features of Perona-Malik, and avoids problems known to
affect the latter.
