Journal of Applied Mathematics
Volume 2010 (2010), Article ID 763847, 14 pages
Research Article

Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India

Received 21 August 2009; Revised 13 January 2010; Accepted 11 February 2010

Academic Editor: Malgorzata Peszynska

Copyright © 2010 V. B. Surya Prasath and Arindama Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. By incorporating edges found at multiple scales via an adaptive edge detector-based indicator function, the proposed scheme removes noise while respecting salient boundaries. We create a smooth transition region around probable edges found and reduce the diffusion rate near it by a gradient-based diffusion coefficient. In contrast to the previous anisotropic diffusion schemes, we prove the well-posedness of our scheme in the space of bounded variation. The proposed scheme is general in the sense that it can be used with any of the existing diffusion equations. Numerical simulations on noisy images show the advantages of our scheme when compared to other related schemes.