The edges and textures of a digital image may be destroyed by traditional denoising methods, which is a difficult problem in image denoising. In this paper, anisotropic diffusion algorithm based on Partial differential equation is studied. First, image denoising algorithms based on Perona-Malik model are studied. Second, a modified Perona-Malik model is proposed. In the porposed model, the grad...

Image data restoration by diffusion equation is now a well established approach since the pioneering work of Perona and Malik (Perona & Malik, 1990). Originally, image diffusion consists in a convolution by a Gaussian kernel which introduces a scale dimension related to the standard deviation of the Gaussian kernel t 2 = σ . This convolution is equivalent to solve the following linear diffusion...

We are concerned with a wavelet–based treatment of nonlinear diffusion equations in the context of image processing. In particular, we focus on the Perona– Malik model as a suitable instrument for smoothing images while preserving edges. We are not exploring a complete new method of solving the Perona– Malik equation but, inspired by Weickert et.al., we develop a new variant, based on wavelet t...

The Perona-Malik equation is an ill-posed forward-backward parabolic equation with some application in image processing. In this paper, we study the Perona-Malik type equation on a ball in an arbitrary dimension n and show that there exist infinitely many radial weak solutions to the homogeneous Neumann boundary problem for smooth nonconstant radially symmetric initial data. Our approach is to ...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called Homotopy Perturbation Method (HMP) and the correspondent approximated solutions will be obtained for the P-M equation with regard to relevant error analysis. Through ...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Thr...

We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution...

The main theory behind nonlinear diffusion models is to use nonlinear PDEs to create a scale space representation that consists of gradually simplified images where some image features such as edges are maintained or even enhanced. The earliest nonlinear diffusion model proposed in image processing is the so-called anisotropic diffusion1 by Perona and Malik [2]. In their formulation, they repla...

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 so...

A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona-Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and...