Adaptive Fractional-order Multi-scale Method for Image Denoising
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The total variation model proposed by Rudin, Osher, and Fatemi performs very well for removing noise while preserving edges. However, it favors a piecewise constant solution in BV space which often leads to the staircase effect, and small details such as textures are often filtered out with noise in the process of denoising. In this paper, we propose a fractional-order multi-scale variational model which can better preserve the textural information and eliminate the staircase effect. This is accomplished by replacing the first-order derivative with the fractional-order derivative in the regularization term, and substituting a kind of multi-scale norm in negative Sobolev space for the L 2 norm in the fidelity term of the ROF model. To improve the results, we propose an adaptive parameter selection method for the proposed model by using the local variance measures and the wavelet based estimation of the singularity. Using the operator splitting technique, we develop a simple alternating projection algorithm to solve the new model. Numerical results show that our method can not only remove noise and eliminate the staircase effect efficiently in the non-textured region, but also preserve the small details such as textures well in the textured region. It is for this reason that our adaptive method can improve the result both visually and in terms of the peak signal to noise ratio efficiently.
KeywordsImage denoising Fractional-order derivative Parameter selection Operator splitting
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- 3.Chan, T.F., Esedoglu, S., Park, F.E.: A fourth order dual method for staircase reduction in texture extraction and image restoration problems. UCLA CAM Report, 05-28 (2005) Google Scholar
- 9.Lieu, L., Vese, L.: Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev space. UCLA CAM Report, 05-33 (2005) Google Scholar
- 11.Zhang, J., Wei, Z.H.: A class of multi-scale models for image denoising in negative Hilbert-Sobolev spaces. In: International Conference on Emerging Intelligent Computing and Applications. Lecture Notes in Control and Information Science, vol. 345, pp. 584–592. Springer, Berlin (2006) Google Scholar