Commenced in January 2007
Paper Count: 30121
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125641Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 880
 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.
 R. Gonzalez and R. Woods, Digital Image Processing. Prentice Hall, 2nd ed., 2001.
 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.
 T. Chan, J. Shen and L. Vese, “Variational PDE Models in Image Processing”, Notices of the AMS, 50, No. 1, 2003.
 L. Rudin, S. Osher and E. Fatemi, “Nonlinear total variation based noise removal algorithms”, Physica D: Nonlinear Phenomena, 60 (1), 1992, pp. 259-268.
 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.
 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.
 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.
 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.
 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.
 D. Gleich, Finite Calculus: A Tutorial for Solving Nasty Sums. Stanford University, 2005.
 K. H. Thung and P. Raveendran, ”A survey of image quality measures”, Proc. International Conference for Technical Postgraduates (TECHPOS), 2009, pp. 1–4.