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Image Denoising Using Directional Adaptive Variable Exponents Model

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Abstract

In this paper, a new variational image denoising model is proposed. The new model could be seen to be a two-step method. In the first step, structure tensor analysis is used to infer something about the local geometry. The eigenvectors and the eigenvalues of the structure tensor are used in the construction of the denoising energy. In the second step, the actual variational denoising takes place. The steps are coupled in the sense that the energy expression is built using the underlying image, not the data. Two variable exponents are incorporated into the regularizer in order to reduce the staircasing effect, which is often present in the methods based on the first-order partial derivatives, and to increase smoothing along the image boundaries. In addition, two pointwise weight functions try to help to preserve small-scale details. In the theoretical part, the existence of a minimizer of a weak form of the original energy is considered. In the numerical part, an algorithm based on iterative minimization is presented and the numerical experiments demonstrate the possible advantages of the new model over some existing variational and partial differential equations methods.

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Acknowledgments

This work was supported by the Academy of Finland and the Vilho, Yrjö and Kalle Väisälä Foundation.

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  1. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014, Oulu, Finland

    Juha Tiirola

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  1. Juha Tiirola
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Correspondence to Juha Tiirola.

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Tiirola, J. Image Denoising Using Directional Adaptive Variable Exponents Model. J Math Imaging Vis 57, 56–74 (2017). https://doi.org/10.1007/s10851-016-0666-4

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  • DOI: https://doi.org/10.1007/s10851-016-0666-4

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