A new synergetic model based on a pulse neural network and the Perona-Malik anisotropic diffusion algorithm is introduced. The proposed model was developed because of the failure of conventional edge detectors to perform the extraction of geometric structures from low contrast edges and noisy assumed uniform regions. The synergetic model is a variation of the Perona-Malik algorithm that incorpo...

The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed ...

A generalization of the linear fractional integral equation u(t) = u0 + ∂−αAu(t), 1 < α < 2, which is written as a Volterra matrix–valued equation when applied as a pixel–by–pixel technique, has been proposed for image denoising (restoration, smoothing,...). Since the fractional integral equation interpolates a linear parabolic equation and a hyperbolic equation, the solution enjoys intermediat...

Article history: Received 18 February 2011 Revised 28 October 2011 Available online 6 December 2011

The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.

The Perona–Malik (PM) model, a classical anisotropic diffusion, can preserve edges while removing the noise. However, the defect of traditional PM model is tending to contain the staircase effect in the processed image. For this reason, a novel ramp preserving Perona–Malik (RPPM) model based on a new edge indicator is presented. In the RPPM model, the diffusion coefficient of the PM model is ad...