Tensor completion for estimating missing values in visual data
Tensor completion for estimating missing values in visual data
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DOI：
10.1109/iccv.2009.5459463
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
Ji Liu;Przemyslaw Musialski;P. Wonka;Jieping Ye
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文献类型：
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作者：
Ji Liu;Przemyslaw Musialski;P. Wonka;Jieping Ye
本文提出了一种估计视觉数据张量缺失值的算法。由于获取过程中的问题，或者由于用户手动识别不需要的异常值，这些值可能会丢失。我们的算法即使在少量的样本中也能工作，并且它可以传播结构来填充更大的缺失区域。我们的方法是建立在最近关于使用矩阵跟踪范数的矩阵补全研究的基础上的。本文的贡献是通过奠定理论基础，然后建立一个工作算法，将矩阵情况扩展到张量情况。首先，我们提出了张量迹范数的定义，推广了矩阵迹范数的定义。其次，与矩阵补全类似，张量补全被表述为一个凸优化问题。不幸的是，由于多个约束之间的依赖关系，直接的问题扩展比矩阵情况更难解决。为了解决这一问题，我们采用松弛技术分离依赖关系，并使用块坐标下降（BCD）方法获得全局最优解。我们的实验显示了我们的算法的潜在应用，定量评价表明我们的方法比启发式方法更准确和健壮。
In this paper we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process, or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by laying out the theoretical foundations and then by building a working algorithm. First, we propose a definition for the tensor trace norm, that generalizes the established definition of the matrix trace norm. Second, similar to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we employ a relaxation technique to separate the dependant relationships and use the block coordinate descent (BCD) method to achieve a globally optimal solution. Our experiments show potential applications of our algorithm and the quantitative evaluation indicates that our method is more accurate and robust than heuristic approaches.