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    Tensor Completion for Estimating Missing Values in Visual Data

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    Name:
    2012.PAMI.JiLiu.Tensor Completion.pdf
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    2.041Mb
    Format:
    PDF
    Description:
    Accepted Manuscript
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    Type
    Article
    Authors
    Liu, Ji
    Musialski, Przemyslaw
    Wonka, Peter cc
    Ye, Jieping
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Visual Computing Center (VCC)
    Date
    2012-01-25
    Online Publication Date
    2012-01-25
    Print Publication Date
    2013-01
    Permanent link to this record
    http://hdl.handle.net/10754/562566
    
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    Abstract
    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 proposing the first definition of the trace norm for tensors 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, similarly 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 developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC and HaLRTC the former is more efficient to obtain a low accuracy solution and the latter is preferred if a high-accuracy solution is desired. © 1979-2012 IEEE.
    Citation
    Liu J, Musialski P, Wonka P, Ye J (2013) Tensor Completion for Estimating Missing Values in Visual Data. IEEE Transactions on Pattern Analysis and Machine Intelligence 35: 208–220. Available: http://dx.doi.org/10.1109/TPAMI.2012.39.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Pattern Analysis and Machine Intelligence
    DOI
    10.1109/TPAMI.2012.39
    ae974a485f413a2113503eed53cd6c53
    10.1109/TPAMI.2012.39
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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