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

Ziyan Luo (), Linxia Qin (), Lingchen Kong () and Naihua Xiu ()
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Ziyan Luo: Beijing Jiaotong University
Linxia Qin: Beijing Jiaotong University
Lingchen Kong: Beijing Jiaotong University
Naihua Xiu: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 3, No 8, 854-864

Abstract: 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.

Keywords: Nonnegative l 0 norm minimization; Generalized Z-matrix; k-Sparse solution; Sample number (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0325-5

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