A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement
We present a robust nonlinear parabolic partial
differential equation (PDE)-based denoising scheme in this article.
Our approach is based on a second-order anisotropic diffusion model
that is described first. Then, a consistent and explicit numerical
approximation algorithm is constructed for this continuous model by
using the finite-difference method. Finally, our restoration
experiments and method comparison, which prove the effectiveness
of this proposed technique, are discussed in this paper.
[1] F. Guichard, L. Moisan and J. M. Morel, “A review of P.D.E. models in
image processing and image analysis”, Journal de Physique, no. 4, 2001,
pp. 137–154.
[2] R. Gonzalez and R. Woods, Digital Image Processing. Prentice Hall, 2nd
ed., 2001.
[3] P. Perona, J. Malik, “Scale-space and edge detection using anisotropic
diffusion“, Proceedings of IEEE Computer Society Workshop on
Computer Vision, 1987, pp. 16–22.
[4] T. Chan, J. Shen and L. Vese, “Variational PDE Models in Image
Processing”, Notices of the AMS, 50, No. 1, 2003.
[5] L. Rudin, S. Osher and E. Fatemi, “Nonlinear total variation based noise
removal algorithms”, Physica D: Nonlinear Phenomena, 60 (1), 1992,
pp. 259-268.
[6] A. Buades, B. Coll and J. M. Morel, ”The staircasing effect in
neighborhood filters and its solution”, IEEE Transactions on Image
Processing, 15, 6, 2006, pp. 1499-1505. [7] T. Barbu, A. Favini, ”Rigorous mathematical investigation of a
nonlinear anisotropic diffusion-based image restoration model”,
Electronic Journal of Differential Equations, 129, 2014, pp. 1-9.
[8] T. Barbu, “A Novel Variational PDE Technique for Image Denoising”,
Lecture Notes in Computer Science (Proceedings of the 20th
International Conference on Neural Information Processing, ICONIP
2013, part III, Daegu, Korea, Nov. 3-7, 2013), vol. 8228, 2013, pp. 501
– 508.
[9] T. Barbu, ”A PDE based Model for Sonar Image and Video Denoising“,
Analele Stiințifice ale Universitătii Ovidius, Constanta, Seria
Matematică, 19, Fasc. 3, 2011, pp. 51-58, 2011.
[10] T. Barbu, ”PDE-based Restoration Model using Nonlinear Second and
Fourth Order Diffusions”, Proceedings of the Romanian Academy,
Series A, 16 (2), April-June 2015.
[11] D. Gleich, Finite Calculus: A Tutorial for Solving Nasty Sums. Stanford
University, 2005.
[12] K. H. Thung and P. Raveendran, ”A survey of image quality measures”,
Proc. International Conference for Technical Postgraduates
(TECHPOS), 2009, pp. 1–4.
[1] F. Guichard, L. Moisan and J. M. Morel, “A review of P.D.E. models in
image processing and image analysis”, Journal de Physique, no. 4, 2001,
pp. 137–154.
[2] R. Gonzalez and R. Woods, Digital Image Processing. Prentice Hall, 2nd
ed., 2001.
[3] P. Perona, J. Malik, “Scale-space and edge detection using anisotropic
diffusion“, Proceedings of IEEE Computer Society Workshop on
Computer Vision, 1987, pp. 16–22.
[4] T. Chan, J. Shen and L. Vese, “Variational PDE Models in Image
Processing”, Notices of the AMS, 50, No. 1, 2003.
[5] L. Rudin, S. Osher and E. Fatemi, “Nonlinear total variation based noise
removal algorithms”, Physica D: Nonlinear Phenomena, 60 (1), 1992,
pp. 259-268.
[6] A. Buades, B. Coll and J. M. Morel, ”The staircasing effect in
neighborhood filters and its solution”, IEEE Transactions on Image
Processing, 15, 6, 2006, pp. 1499-1505. [7] T. Barbu, A. Favini, ”Rigorous mathematical investigation of a
nonlinear anisotropic diffusion-based image restoration model”,
Electronic Journal of Differential Equations, 129, 2014, pp. 1-9.
[8] T. Barbu, “A Novel Variational PDE Technique for Image Denoising”,
Lecture Notes in Computer Science (Proceedings of the 20th
International Conference on Neural Information Processing, ICONIP
2013, part III, Daegu, Korea, Nov. 3-7, 2013), vol. 8228, 2013, pp. 501
– 508.
[9] T. Barbu, ”A PDE based Model for Sonar Image and Video Denoising“,
Analele Stiințifice ale Universitătii Ovidius, Constanta, Seria
Matematică, 19, Fasc. 3, 2011, pp. 51-58, 2011.
[10] T. Barbu, ”PDE-based Restoration Model using Nonlinear Second and
Fourth Order Diffusions”, Proceedings of the Romanian Academy,
Series A, 16 (2), April-June 2015.
[11] D. Gleich, Finite Calculus: A Tutorial for Solving Nasty Sums. Stanford
University, 2005.
[12] K. H. Thung and P. Raveendran, ”A survey of image quality measures”,
Proc. International Conference for Technical Postgraduates
(TECHPOS), 2009, pp. 1–4.
@article{"International Journal of Information, Control and Computer Sciences:73444", author = "Tudor Barbu", title = "A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement", abstract = "We present a robust nonlinear parabolic partial
differential equation (PDE)-based denoising scheme in this article.
Our approach is based on a second-order anisotropic diffusion model
that is described first. Then, a consistent and explicit numerical
approximation algorithm is constructed for this continuous model by
using the finite-difference method. Finally, our restoration
experiments and method comparison, which prove the effectiveness
of this proposed technique, are discussed in this paper.", keywords = "Image denoising and restoration, nonlinear PDE
model, anisotropic diffusion, numerical approximation scheme, finite
differences.", volume = "10", number = "8", pages = "1440-4", }
