Color Bregman TV
Color Bregman TV
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DOI：
10.1137/130943388
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发表时间：
2013-10
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影响因子：
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通讯作者：
Michael Möller;Eva-Maria Brinkmann;M. Burger;Tamara Seybold
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文献类型：
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作者：
Michael Möller;Eva-Maria Brinkmann;M. Burger;Tamara Seybold
本文提出了一种利用布雷格曼距离进行多通道图像和数据重建的迭代方法。我们采用这种方法的动机是，在许多应用程序中，多个通道在适当的正则化方面共享一个公共的子梯度。这意味着在总变差（TV）的情况下，有一个共同的边集（以及法线到水准线的共同方向）。因此，我们建议通过使用与前一次迭代的所有其他图像通道的布雷格曼距离的加权线性组合来正则化每个通道来确定每次迭代。在这个意义上，我们推广了Osher等人在[多尺度模型]中提出的Bregman迭代。同时。多通道图像，4 (2005),pp. 460—489]。我们证明了该方案的收敛性，分析了平稳点，并给出了彩色图像去噪的数值实验，结果表明，与TV相比，我们的方法具有优越的性能，TV在每个ch上都有Bregman迭代。
In this paper we present a novel iterative procedure for multichannel image and data reconstruction using Bregman distances. The motivation for our approach is that in many applications multiple channels share a common subgradient with respect to a suitable regularization. This implies desirable properties such as a common edge set (and a common direction of the normals to the level lines) in the case of the total variation (TV). Therefore, we propose to determine each iterate by regularizing each channel with a weighted linear combination of Bregman distances to all other image channels from the previous iteration. In this sense we generalize the Bregman iteration proposed by Osher et al. in [Multiscale Model. Simul., 4 (2005), pp. 460--489] to multichannel images. We prove the convergence of the proposed scheme, analyze stationary points, and present numerical experiments on color image denoising, which show the superior behavior of our approach in comparison to TV, TV with Bregman iterations on each ch...