Collaborative Total Variation
SIAM Journal on Imaging Sciences(2016)
摘要
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 $\ell^{\infty}$ 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.
更多查看译文
关键词
inverse problems,convex optimization,color image restoration,vectorial total variation,collaborative norms,duality,proximal operators,15A60,65F22,65K10,68U10,90C25,90C46,94A08
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要