A backward–forward regularization of the Perona–Malik equation

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Guidotti, Patrick. “A backward–forward Regularization of the Perona–Malik Equation”. Journal of Differential Equations, vol. 252, no. 4, 2012, pp. 3226-44, https://doi.org/10.1016/j.jde.2011.10.022.
Guidotti, P. (2012). A backward–forward regularization of the Perona–Malik equation. Journal of Differential Equations, 252(4), 3226-3244. https://doi.org/10.1016/j.jde.2011.10.022
Guidotti, Patrick. “A backward–forward Regularization of the Perona–Malik Equation”. Journal of Differential Equations 252, no. 4 (2012): 3226-44. https://doi.org/10.1016/j.jde.2011.10.022.
Guidotti P. A backward–forward regularization of the Perona–Malik equation. Journal of Differential Equations. 2012;252(4):3226-44.
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Mathematics
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Category Category Repetition
Science: Mathematics22
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods19
Science: Mathematics: Instruments and machines: Electronic computers. Computer science7
Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics5
Technology: Mechanical engineering and machinery4
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Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software2
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Citations
Title Journal Journal Categories Citations Publication Date
A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional

 Transactions of the American Mathematical Society
  • Science: Mathematics
 1 2023
A Non-Local Diffusion Equation for Noise Removal Acta Mathematica Scientia
  • Science: Mathematics
 2022
ADMM algorithm for some regularized Perona–Malik equation and applications to image denoising Signal, Image and Video Processing
  • Technology: Electrical engineering. Electronics. Nuclear engineering: Electric apparatus and materials. Electric circuits. Electric networks
  • Technology: Photography
  • Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics
  • Technology: Engineering (General). Civil engineering (General)
 1 2022
Wavefront solutions to reaction-convection equations with Perona-Malik diffusion Journal of Differential Equations
  • Science: Mathematics
 1 2022
Existence of solutions for quasilinear problem with Neumann boundary conditions

 Boletim da Sociedade Paranaense de Matemática
  • Science: Mathematics
  • Science: Mathematics
 1 2022
Citations Analysis
Category Category Repetition
Science: Mathematics14
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods7
Science: Mathematics: Instruments and machines: Electronic computers. Computer science5
Technology: Electrical engineering. Electronics. Nuclear engineering: Telecommunication3
Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics3
Technology: Engineering (General). Civil engineering (General)3
Medicine: Medicine (General): Medical technology3
Science: Physics2
Technology: Technology (General): Industrial engineering. Management engineering: Information technology2
Science: Science (General): Cybernetics: Information theory2
Technology: Electrical engineering. Electronics. Nuclear engineering: Electric apparatus and materials. Electric circuits. Electric networks2
Technology: Photography2
Technology: Chemical technology: Biotechnology2
Medicine: Medicine (General): Computer applications to medicine. Medical informatics1
Science: Biology (General)1
Science: Mathematics: Analysis1
Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software1
Technology: Mechanical engineering and machinery1
The category Science: Mathematics 14 is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Image Restoration with a New Class of Forward-Backward-Forward Diffusion Equations of Perona--Malik Type with Applications to Satellite Image Enhancement and was published in 2013. The most recent citation comes from a 2023 study titled A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional. This article reached its peak citation in 2022, with 4 citations. It has been cited in 18 different journals, 27% of which are open access. Among related journals, the Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization cited this research the most, with 2 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year