The Perona–Malik inequality and application to image denoising

Atlas, Abdelghafour; Karami, Fahd; Meskine, Driss

doi:10.1016/j.nonrwa.2013.11.006

Cited by 20 publications

(20 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2, 3, 4, and 5) for filtering the images corrupted with noise. As a second experiment, we will keep the same values of the previous parameters and we test the explicit scheme of the Perona-Malik and p-Laplacian (PMPL) proposed in [22] for different values of p Fig. 6.…”

Section: Numerical Results and Simulationsmentioning

confidence: 99%

“…In order to escape the backward regime, a novel kind of regularization [20][21][22] of the classical Perona-Malik model is proposed for image processing. This regularization still allows gradient growth while controls its maximal size which is done by combining two classical models, Perona-Malik and p-Laplacian.…”

Section: Perona-malik and P-laplacian Modelmentioning

confidence: 99%

“…This problem is well posed for a large p, and the existence and uniqueness of the asymptotic behavior as p → ∞ are established in [22]. Letting p → ∞, the problem (1) converges to the following model:…”

Section: Perona-malik and P-laplacian Modelmentioning

confidence: 99%

“…Moreover, u ∈ W ∩ K t is the unique solution of (2) in the following sense: For further details and another sophisticated notion of solutions, we refer to [22]. We remark that the limiting problem can be rewritten as:…”

Section: Perona-malik and P-laplacian Modelmentioning

confidence: 99%

“…[21]). Recently, in [22], the authors proposed a new regularization based on the previous interpolation of PeronaMalik and p-Laplacian with large value of p. Their model is well posed, it reduces the staircase effect and avoids creating new features in the image, they have also done a study of the limiting problem. For a numerical purpose, the authors used an explicit finite difference scheme which is unstable and the condition of stability depends on the parameter p.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration

Karami

Ziad

Sadik

2017

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operator with p → ∞. In Atlas et al., (Nonlinear Anal. Real World Appl 18:57-68, 2014), the authors have proved the existence and uniqueness of the solution of the proposed model. However, in their work, they used the explicit numerical scheme for approximated problem which is strongly dependent to the parameter p. To overcome this, we use in this work an efficient algorithm which is a combination of the classical additive operator splitting and a nonlinear relaxation algorithm. At last, we have presented the experimental results in image filtering show, which demonstrate the efficiency and effectiveness of our algorithm and finally, we have compared it with the previous scheme presented in

show abstract

Section: Numerical Results and Simulationsmentioning

confidence: 99%

Section: Perona-malik and P-laplacian Modelmentioning

confidence: 99%

Section: Perona-malik and P-laplacian Modelmentioning

confidence: 99%

Section: Perona-malik and P-laplacian Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations