Commun. Comput. Phys., 1 (2006), pp. 847-858.

An Efficient Operator-Splitting Method for Noise Removal in Images

D. Krishnan 1*, P. Lin 1, X.-C. Tai 2

1 Department of Mathematics, National University of Singapore, Singapore 117453.
2 Department of Mathematics, University of Bergen, Johannes Brunsgate 12, Bergen, N-5008, Norway.

Received 5 October 2005; Accepted (in revised version) 5 March 2006


In this work, noise removal in digital images is investigated. The importance of this problem lies in the fact that removal of noise is a necessary pre-processing step for other image processing tasks such as edge detection, image segmentation, image compression, classification problems, image registration etc. A number of different approaches have been proposed in the literature. In this work, a non-linear PDE-based algorithm is developed based on the ideas proposed by Lysaker, Osher and Tai [IEEE Trans. Image Process., 13 (2004), 1345-1357] . This algorithm consists of two steps: flow field smoothing of the normal vectors, followed by image reconstruction. We propose a finite-difference based additive operator-splitting method that allows for much larger time-steps. This results in an efficient method for noise-removal that is shown to have good visual results. The energy is studied as an objective measure of the algorithm performance.

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Key words: Noise removal; nonlinear PDEs; additive operator splitting (AOS).

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Correspondence to: D. Krishnan , Department of Mathematics, National University of Singapore, Singapore 117453. Email:

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