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Sparse Structure for Visual Information Sensing: Theory and Algorithms

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High-Dimensional and Low-Quality Visual Information Processing

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This chapter proposes to utilize sparse structure for visual information sensing and understanding. In detail, concentered on the fundamental theory of compressive sensing, we will discuss the problem of low-rank structure learning (LRSL) from sparse outliers. Different from traditional approaches, which directly utilize convex norms to measure the sparseness, our method introduces more reasonable non-convex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization–minimization (MM)-type algorithm. From the theoretic perspective, we have proved that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve a number of computer vision and information processing tasks, e.g., face image enhancement, object tracking, and time series clustering.

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Notes

  1. 1.

    In cases, the weighting matrices may cause complex numbers due to the inverse operation. In such condition, we use the approximating matrices \(\mathbf {W}_Y=\mathbf {U}(\Sigma +\delta \mathbf {I}_m)^{-1/2}\mathbf {U}^T\) and \(\mathbf {W}_Z=\mathbf {V}(\Sigma +\delta \mathbf {I}_m)^{-1/2}\mathbf {V}^T\) in LHR.

  2. 2.

    The optimization for \(p\)HR is very similar by changing the weight matrices.

  3. 3.

    We only report the result of \(p=1/3\) here since in the previous numerical simulation, \(p\)HR (\(p=1/3\)) achieves higher recovery accuracy than \(p\)HR with \(P=2/3\).

  4. 4.

    For example, in the industrial category of drug manufactures, it is not possible to get the historical data of CIPILA.LTD from [28] which is the only the interface for us to get the stock prices in USA.

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Authors and Affiliations

  1. Automation Department, Tsinghua Nationality Laboratory for Information Science and Technology (TNList), Tsinghua University, Beijing, China

    Yue Deng

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  1. Yue Deng
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Correspondence to Yue Deng .

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Deng, Y. (2015). Sparse Structure for Visual Information Sensing: Theory and Algorithms. In: High-Dimensional and Low-Quality Visual Information Processing. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44526-6_2

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  • DOI: https://doi.org/10.1007/978-3-662-44526-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44525-9

  • Online ISBN: 978-3-662-44526-6

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