Abstract
In this paper, we propose a novel framework for restoring color images using nonlocal total variation (NLTV) regularization. We observe that the discrete local and nonlocal gradient of a color image can be viewed as a 3D matrix/or tensor with dimensions corresponding to the spatial extend, the differences to other pixels, and the color channels. Based on this observation we obtain a new class of NLTV methods by penalizing the ℓp,q,r norm of this 3D tensor. Interestingly, this unifies several local color total variation (TV) methods in a single framework. We show in several numerical experiments on image denoising and deblurring that a stronger coupling of different color channels – particularly, a coupling with the ℓ ∞ norm – yields superior reconstruction results.
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Duran, J., Moeller, M., Sbert, C., Cremers, D. (2015). A Novel Framework for Nonlocal Vectorial Total Variation Based on ℓp,q,r −norms. In: Tai, XC., Bae, E., Chan, T.F., Lysaker, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932. Springer, Cham. https://doi.org/10.1007/978-3-319-14612-6_11
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DOI: https://doi.org/10.1007/978-3-319-14612-6_11
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