A novel framework for nonlocal vectorial total variation based on ℓp,Q,R-norms

Duran J, Moeller M, Sbert C, Cremers D (2015)

Publication Type: Conference contribution

Publication year: 2015

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer Verlag

Book Volume: 8932

Pages Range: 141-154

Conference Proceedings Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Event location: Hong Kong, CHN

ISBN: 9783319146119

DOI: 10.1007/978-3-319-14612-6_11

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.

Involved external institutions

Universitat de les Illes Balears (IUB) ES Spain (ES) Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Duran, J., Moeller, M., Sbert, C., & Cremers, D. (2015). A novel framework for nonlocal vectorial total variation based on ℓp,Q,R-norms. In Xue-Cheng Tai, Egil Bae, Tony F. Chan, Marius Lysaker (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 141-154). Hong Kong, CHN: Springer Verlag.

MLA:

Duran, Joan, et al. "A novel framework for nonlocal vectorial total variation based on ℓp,Q,R-norms." Proceedings of the 10th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2015, Hong Kong, CHN Ed. Xue-Cheng Tai, Egil Bae, Tony F. Chan, Marius Lysaker, Springer Verlag, 2015. 141-154.

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