Journal of Mathematical Imaging and Vision

, Volume 40, Issue 2, pp 188–198

Two Enhanced Fourth Order Diffusion Models for Image Denoising

Open Access

DOI: 10.1007/s10851-010-0256-9

Cite this article as:
Guidotti, P. & Longo, K. J Math Imaging Vis (2011) 40: 188. doi:10.1007/s10851-010-0256-9


This paper presents two new higher order diffusion models for removing noise from images. The models employ fractional derivatives and are modifications of an existing fourth order partial differential equation (PDE) model which was developed by You and Kaveh as a generalization of the well-known second order Perona-Malik equation. The modifications serve to cure the ill-posedness of the You-Kaveh model without sacrificing performance. Also proposed in this paper is a simple smoothing technique which can be used in numerical experiments to improve denoising and reduce processing time. Numerical experiments are shown for comparison.


Nonlinear diffusion Fractional derivatives Image denoising Fourth order 
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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at IrvineIrvineUSA

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