Optimality analysis on partial $$l_1$$ l 1 -minimization recovery

Huan Gao (), Haibin Zhang (), Zhibao Li () and Kai Tu ()
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Huan Gao: Beijing University of Technology
Haibin Zhang: Beijing University of Technology
Zhibao Li: Central South University
Kai Tu: Beijing University of Technology

Journal of Global Optimization, 2018, vol. 70, issue 1, No 8, 159-170

Abstract: Abstract Partially sparse recovery problem is a special sparse recovery optimization problem with part of the support of the solution is known in advance. Such a problem is closely related to the problems on compressive sensing where the $$l_1$$ l 1 -norm of the whole solution vector is minimized. In this paper, we propose the partial range space property to obtain some uniqueness conditions on the solution of the partially sparse recovery problem, it is somewhat stronger than the range space property for general sparse recovery problem. And any pair of solution to partial $$l_0$$ l 0 -minimization problem satisfying the partial range space property is also the unique solution to partial $$l_1$$ l 1 -minimization problem under mild condition.

Keywords: Partially sparse recovery; Partial range space property; Partial $$l_1$$ l 1 -minimization problem; 68Q25; 90C25; 94A08 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-017-0567-0

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