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The Nonnegative Zero-Norm Minimization Under Generalized Z-Matrix Measurement

Author

Listed:
  • Ziyan Luo

    (Beijing Jiaotong University)

  • Linxia Qin

    (Beijing Jiaotong University)

  • Lingchen Kong

    (Beijing Jiaotong University)

  • Naihua Xiu

    (Beijing Jiaotong University)

Abstract

In this paper, we consider the zero-norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalized Z-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 corresponding p-norm minimization with p 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 generalized Z-matrix recovery condition.

Suggested Citation

  • Ziyan Luo & Linxia Qin & Lingchen Kong & Naihua Xiu, 2014. "The Nonnegative Zero-Norm Minimization Under Generalized Z-Matrix Measurement," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 854-864, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0325-5
    DOI: 10.1007/s10957-013-0325-5
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    References listed on IDEAS

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    1. G. M. Fung & O. L. Mangasarian, 2011. "Equivalence of Minimal ℓ 0- and ℓ p -Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 1-10, October.
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    Cited by:

    1. M. Ruiz Galán, 2017. "A theorem of the alternative with an arbitrary number of inequalities and quadratic programming," Journal of Global Optimization, Springer, vol. 69(2), pages 427-442, October.
    2. Yong Wang & Guanglu Zhou & Xin Zhang & Wanquan Liu & Louis Caccetta, 2016. "The Non-convex Sparse Problem with Nonnegative Constraint for Signal Reconstruction," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1009-1025, September.

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