This work concerns the Perona-Malik equation, which plays essential role in image processing. The first part gives a survey of results on existance, uniqueness and stability of solutions, the second part introduces discretisations of equation and deals with an analysis of discrete problem. In the last part I present some numerical results, in particular with algorithms applied to real images.

We propose time regularizations for ill posed evolution equations of the type of the Perona-Malik equation of image processing, prove that they are well posed, and give numerical evidence for their superiority to the widely used space regularizations.

ENWEndNote BIBJabRef, Mendeley RISPapers, Reference Manager, RefWorks, Zotero AMA Gera C, Malik M. Effect of spinal manipulation on cardiopulmonary parameters in patients with functional scoliosis: A randomised controlled pilot trial. Advances Rehabilitation. 2022;36(1):11-17. doi:10.5114/areh.2022.114226. APA Gera, C., & Malik, (2022). Rehabilitation, 36(1), 11-17. https://doi.org/10.5114/areh...

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 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...

Preview: Coma is the most severe form of unresponsiveness, in which a patient is totally unaware of self and surroundings. With the patient so disengaged during examination, management can be particularly challenging. What steps should the primary care physician take to ensure the most appropriate care for a comatose patient? In this article, Drs Malik and Hess describe an evaluation plan, labo...

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...