HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation
نویسندگان
چکیده
منابع مشابه
HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation
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 ...
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We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in a bounded open set Ω ⊆ R, with Neumann boundary conditions. If n = 1, we prove some a priori estimates on u and ux. Then we consider the semi-discrete scheme obtained by replacing the space derivatives by finite differences. Extending the previous estimates to the discrete setting we prove a compactness re...
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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.
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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...
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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...
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ژورنال
عنوان ژورنال: The Scientific World Journal
سال: 2014
ISSN: 2356-6140,1537-744X
DOI: 10.1155/2014/417486