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Published in:
2015 | OriginalPaper | Chapter
A Novel Framework for Nonlocal Vectorial Total Variation Based on ℓ p,q,r −norms
Authors : Joan Duran, Michael Moeller, Catalina Sbert, Daniel Cremers
Published in: Energy Minimization Methods in Computer Vision and Pattern Recognition
Publisher: Springer International Publishing
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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 ℓ
p
,
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.