### Abstract

A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

Original language | English |
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Title of host publication | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |

Publisher | IEEE Institute of Electrical and Electronic Engineers |

Pages | 226-230 |

ISBN (Print) | 978-1-4799-5186-4 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

MoE publication type | A4 Article in a conference publication |

Event | 2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States Duration: 29 Jun 2014 → 4 Jul 2014 |

### Publication series

Series | IEEE International Symposium on Information Theory. Proceedings |
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Volume | 2014 |

ISSN | 2157-8095 |

### Conference

Conference | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |
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Country | United States |

City | Honolulu, HI |

Period | 29/06/14 → 4/07/14 |

### Fingerprint

### Cite this

*2014 IEEE International Symposium on Information Theory, ISIT 2014*(pp. 226-230). [6874828] IEEE Institute of Electrical and Electronic Engineers . IEEE International Symposium on Information Theory. Proceedings, Vol.. 2014 https://doi.org/10.1109/ISIT.2014.6874828

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*2014 IEEE International Symposium on Information Theory, ISIT 2014.*, 6874828, IEEE Institute of Electrical and Electronic Engineers , IEEE International Symposium on Information Theory. Proceedings, vol. 2014, pp. 226-230, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 29/06/14. https://doi.org/10.1109/ISIT.2014.6874828

**Signal recovery using expectation consistent approximation for linear observations.** / Kabashima, Yoshiyuki; Vehkaperä, Mikko.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Signal recovery using expectation consistent approximation for linear observations

AU - Kabashima, Yoshiyuki

AU - Vehkaperä, Mikko

PY - 2014/1/1

Y1 - 2014/1/1

N2 - A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

AB - A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

UR - http://www.scopus.com/inward/record.url?scp=84906536415&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2014.6874828

DO - 10.1109/ISIT.2014.6874828

M3 - Conference article in proceedings

AN - SCOPUS:84906536415

SN - 978-1-4799-5186-4

T3 - IEEE International Symposium on Information Theory. Proceedings

SP - 226

EP - 230

BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014

PB - IEEE Institute of Electrical and Electronic Engineers

ER -