### Abstract

Original language | English |
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Title of host publication | 2011 IEEE Information Theory Workshop |

Pages | 553-557 |

ISBN (Electronic) | 978-1-4577-0437-6, 978-1-4577-0436-9 |

DOIs | |

Publication status | Published - 21 Dec 2011 |

MoE publication type | A4 Article in a conference publication |

Event | 2011 IEEE Information Theory Workshop, ITW 2011 - Paraty, Brazil Duration: 16 Oct 2011 → 20 Oct 2011 |

### Conference

Conference | 2011 IEEE Information Theory Workshop, ITW 2011 |
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Country | Brazil |

City | Paraty |

Period | 16/10/11 → 20/10/11 |

### Fingerprint

### Cite this

*2011 IEEE Information Theory Workshop*(pp. 553-557). [6089563] https://doi.org/10.1109/ITW.2011.6089563

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*2011 IEEE Information Theory Workshop.*, 6089563, pp. 553-557, 2011 IEEE Information Theory Workshop, ITW 2011, Paraty, Brazil, 16/10/11. https://doi.org/10.1109/ITW.2011.6089563

**Analysis of MMSE estimation for compressive sensing of block sparse signals.** / Vehkaperä, Mikko; Chatterjee, Saikat; Skoglund, Mikael.

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

TY - GEN

T1 - Analysis of MMSE estimation for compressive sensing of block sparse signals

AU - Vehkaperä, Mikko

AU - Chatterjee, Saikat

AU - Skoglund, Mikael

PY - 2011/12/21

Y1 - 2011/12/21

N2 - Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly distributed across the vector of interest, the information bearing components appear here in large mutually dependent clusters. Using the replica method from statistical physics, we derive a simple closed-form solution for the MMSE obtained by the optimum estimator. We show that the MMSE is a version of the Tse-Hanly formula with system load and MSE scaled by a parameter that depends on the sparsity pattern of the source. It turns out that this is equal to the MSE obtained by a genie-aided MMSE estimator which is informed in advance about the exact locations of the non-zero blocks. The asymptotic results obtained by the non-rigorous replica method are found to have an excellent agreement with finite sized numerical simulations.

AB - Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly distributed across the vector of interest, the information bearing components appear here in large mutually dependent clusters. Using the replica method from statistical physics, we derive a simple closed-form solution for the MMSE obtained by the optimum estimator. We show that the MMSE is a version of the Tse-Hanly formula with system load and MSE scaled by a parameter that depends on the sparsity pattern of the source. It turns out that this is equal to the MSE obtained by a genie-aided MMSE estimator which is informed in advance about the exact locations of the non-zero blocks. The asymptotic results obtained by the non-rigorous replica method are found to have an excellent agreement with finite sized numerical simulations.

UR - http://www.scopus.com/inward/record.url?scp=83655202644&partnerID=8YFLogxK

U2 - 10.1109/ITW.2011.6089563

DO - 10.1109/ITW.2011.6089563

M3 - Conference article in proceedings

AN - SCOPUS:83655202644

SN - 978-1-4577-0438-3

SP - 553

EP - 557

BT - 2011 IEEE Information Theory Workshop

ER -