Collaborative Total Variation: A General Framework for Vectorial TV Models
Collaborative Total Variation: A General Framework for Vectorial TV Models
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DOI：
10.1137/15m102873x
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发表时间：
2016-01-01
影响因子：
2.1
通讯作者：
Cremers, D.
中科院分区：
文献类型：
--
作者：
Duran, J.;Moeller, M.;Cremers, D.
即使在二十年后，全变差（TV）仍然是图像处理问题中最流行的正则化方法之一，并引发了大量的研究，特别是从标量到向量值函数的研究。在本文中，我们认为彩色图像的梯度作为一个三维矩阵或张量的维度对应的空间范围，相邻像素之间的强度差，和光谱通道。这个张量的平滑度可以通过在不同的维度上取沿着不同的范数来测量。根据这些规范的类型，人们获得非常不同的正则化特性，从而产生彩色图像的新模型。我们称这类正则化为协作全变差（CTV）。在理论方面，我们刻画了所提出的正则化子的对偶范数、次微分和近似映射。我们进一步证明，广义的奇异向量的概念的帮助下，一个l（无穷大）通道耦合，使最先验的假设，并具有最大的潜力，以减少色彩伪影。我们的实际贡献包括一个广泛的实验部分，在那里我们比较了大量的合作电视方法的逆问题，如去噪，去模糊和修复的性能。
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 l(infinity) 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.