Nonlinear PDE operators with memory terms for image processing

A model of selective filters based on anisotropic nonlinear diffusion is proposed for image enhancement. In this model the processed image can be obtained on the asymptotic states of its solution. The diffusion tensor is chosen to change dynamically in such a way as to process the image without affecting its interesting features. The proposed anisotropic diffusion can be classed as a nonstandard Volterra equation. Experimental results are shown on test and medical images, which illustrate the ability of our model to detect fine objects in a noisy image.