Source :
SIAM Journal on Imaging Sciences
Descriptors :
inverse problems , convex optimization , color image restoration , vectorial total variation , collaborative norms , duality , proximal operators
Abstract :
Even after two decades, the total variation (TV) remains one of the most popular regularizations
for image processing problems and has sparked a tremendous amount of research, particularly on
moving from scalar to vector-valued functions. In this paper, we consider the gradient of a color
image as a three-dimensional matrix or tensor with dimensions corresponding to the spatial extent,
the intensity differences between neighboring pixels, and the spectral channels. The smoothness of
this tensor is then measured by taking different norms along the different dimensions. Depending
on the types of these norms, one obtains very different properties of the regularization, leading
to novel models for color images. We call this class of regularizations collaborative total variation
(CTV). On the theoretical side, we characterize the dual norm, the subdifferential, and the proximal
mapping of the proposed regularizers. We further prove, with the help of the generalized concept of
singular vectors, that an
∞
channel coupling makes the most prior assumptions and has the greatest
potential to reduce color artifacts. Our practical contributions consist of an extensive experimental
section, where we compare the performance of a large number of collaborative TV methods for
inverse problems such as denoising, deblurring, and inpainting.
Title of Article :
Collaborative Total Variation: A General Framework for Vectorial TV Models
Author/Authors :
Duran, J. , Moeller, M. , Sbert, C. , Cremers, D.
Author/Authors - جزئيات :
