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A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement

Authors: Tudor Barbu

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125641

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References:


[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.