### Abstract

A new theory known as compressed sensing considers the problem to acquire and recover a sparse signal from its linear measurements. In this paper, we propose a new support recovery algorithm from noisy measurements based on the linear programming (LP). LP is widely used to estimate sparse signals, however, we focus on the problem to recover the support of sparse signals rather than the problem to estimate sparse signals themselves. First, we derive an integer linear programming (ILP) formulation for the support recovery problem. Then we obtain the LP based support recovery algorithm by relaxing the ILP. The proposed LP based recovery algorithm has an attracting property that the output of the algorithm is guaranteed to be the maximum a posteiori (MAP) estimate when it is integer valued. We compare the performance of the proposed algorithm to a state-of-the-art algorithm named sparse matching pursuit (SMP) via numerical simulations.

Original language | English |
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Title of host publication | Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 270-274 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523090 |

Publication status | Published - 2017 Feb 2 |

Event | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 - Monterey, United States Duration: 2016 Oct 30 → 2016 Nov 2 |

### Other

Other | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 |
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Country | United States |

City | Monterey |

Period | 16/10/30 → 16/11/2 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Information Systems
- Signal Processing
- Library and Information Sciences

### Cite this

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016*(pp. 270-274). [7840428] Institute of Electrical and Electronics Engineers Inc..

**A note on support recovery of sparse signals using linear programming.** / Horii, Shunsuke; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016.*, 7840428, Institute of Electrical and Electronics Engineers Inc., pp. 270-274, 3rd International Symposium on Information Theory and Its Applications, ISITA 2016, Monterey, United States, 16/10/30.

}

TY - GEN

T1 - A note on support recovery of sparse signals using linear programming

AU - Horii, Shunsuke

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2017/2/2

Y1 - 2017/2/2

N2 - A new theory known as compressed sensing considers the problem to acquire and recover a sparse signal from its linear measurements. In this paper, we propose a new support recovery algorithm from noisy measurements based on the linear programming (LP). LP is widely used to estimate sparse signals, however, we focus on the problem to recover the support of sparse signals rather than the problem to estimate sparse signals themselves. First, we derive an integer linear programming (ILP) formulation for the support recovery problem. Then we obtain the LP based support recovery algorithm by relaxing the ILP. The proposed LP based recovery algorithm has an attracting property that the output of the algorithm is guaranteed to be the maximum a posteiori (MAP) estimate when it is integer valued. We compare the performance of the proposed algorithm to a state-of-the-art algorithm named sparse matching pursuit (SMP) via numerical simulations.

AB - A new theory known as compressed sensing considers the problem to acquire and recover a sparse signal from its linear measurements. In this paper, we propose a new support recovery algorithm from noisy measurements based on the linear programming (LP). LP is widely used to estimate sparse signals, however, we focus on the problem to recover the support of sparse signals rather than the problem to estimate sparse signals themselves. First, we derive an integer linear programming (ILP) formulation for the support recovery problem. Then we obtain the LP based support recovery algorithm by relaxing the ILP. The proposed LP based recovery algorithm has an attracting property that the output of the algorithm is guaranteed to be the maximum a posteiori (MAP) estimate when it is integer valued. We compare the performance of the proposed algorithm to a state-of-the-art algorithm named sparse matching pursuit (SMP) via numerical simulations.

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M3 - Conference contribution

AN - SCOPUS:85015170506

SP - 270

EP - 274

BT - Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -