Image restoration with discrete constrained total variation - Part I: Fast and exact optimization
Image restoration with discrete constrained total variation - Part I: Fast and exact optimization
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DOI：
10.1007/s10851-006-8803-0
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发表时间：
2006-12-01
影响因子：
2
通讯作者：
Sigelle, Marc
中科院分区：
文献类型：
--
作者：
Darbon, Jerome;Sigelle, Marc
研究了图像复原中凸数据保真度泛函的总变分最小化问题。我们提出了一个新的和快速的算法，计算的离散框架中的精确解。我们的方法依赖于图像到其水平集的分解。它将原始问题映射为每个层次上独立的二进制马尔可夫随机场优化问题。这些二元问题的精确解是由于图中的最小成本切割技术而找到的。这些二元解被证明是单调增加的水平和产量，从而离散原问题的精确解。此外，我们表明，L-1数据保真度项下的总变差最小化产生一个自对偶对比度不变滤波器。最后我们给出了一些结果。
This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under L-1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.