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The Nonnegative Zero-Norm Minimization Under GeneralizedZ-Matrix Measurement

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Abstract

In this paper, we consider the zero-norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalizedZ-matrix for a rectangular matrix, we show that this zero-norm minimization with such a kind of measurement matrices and nonnegative observations can be exactly solved via the correspondingp-norm minimization withp in the open interval from zero to one. Moreover, the lower bound of sample number for exact recovery is allowed to be the same as the sparsity of the original image or signal by the underlying zero-norm minimization. A practical application in communications is presented, which satisfies the generalizedZ-matrix recovery condition.

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Acknowledgements

This research was supported by the National Basic Research Program of China (2010CB732501), the National Natural Science Foundation of China (11101248), and the State Key Laboratory of Rail Traffic Control and Safety (Contract No. RCS2012ZQ001), Beijing Jiaotong University.

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Authors and Affiliations

  1. State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, P.R. China

    Ziyan Luo

  2. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, P.R. China

    Linxia Qin, Lingchen Kong & Naihua Xiu

Authors
  1. Ziyan Luo

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  2. Linxia Qin

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  3. Lingchen Kong

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  4. Naihua Xiu

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Corresponding author

Correspondence toZiyan Luo.

Additional information

Communicated by Vaithilingam Jeyakumar.

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Luo, Z., Qin, L., Kong, L.et al. The Nonnegative Zero-Norm Minimization Under GeneralizedZ-Matrix Measurement.J Optim Theory Appl160, 854–864 (2014). https://doi.org/10.1007/s10957-013-0325-5

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