### Abstract

In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying N dimensional random vector, by collecting at most K arbitrary projections of it. The N components of the latent vector represent sub-channels states, that change dynamically from 'busy' to 'idle' and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in which the CR can sense K out of the N sub-channels, as well as the typical static setting of Compressive Sensing, in which the CR observes K linear combinations of the N dimensional sparse vector. The CR opportunistic choice of the sensing matrix should balance the desire of revealing the state of as many dimensions of the latent vector as possible, while not exceeding the limits beyond which the vector support is no longer uniquely identifiable.

Original language | English (US) |
---|---|

Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3195-3199 |

Number of pages | 5 |

ISBN (Print) | 9781479951864 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

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

### Other

Other | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |
---|---|

Country | United States |

City | Honolulu, HI |

Period | 6/29/14 → 7/4/14 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 3195-3199). [6875424] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6875424

**The Cognitive Compressive Sensing problem.** / Bagheri, Saeed; Scaglione, Anna.

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

*IEEE International Symposium on Information Theory - Proceedings.*, 6875424, Institute of Electrical and Electronics Engineers Inc., pp. 3195-3199, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 6/29/14. https://doi.org/10.1109/ISIT.2014.6875424

}

TY - GEN

T1 - The Cognitive Compressive Sensing problem

AU - Bagheri, Saeed

AU - Scaglione, Anna

PY - 2014

Y1 - 2014

N2 - In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying N dimensional random vector, by collecting at most K arbitrary projections of it. The N components of the latent vector represent sub-channels states, that change dynamically from 'busy' to 'idle' and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in which the CR can sense K out of the N sub-channels, as well as the typical static setting of Compressive Sensing, in which the CR observes K linear combinations of the N dimensional sparse vector. The CR opportunistic choice of the sensing matrix should balance the desire of revealing the state of as many dimensions of the latent vector as possible, while not exceeding the limits beyond which the vector support is no longer uniquely identifiable.

AB - In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying N dimensional random vector, by collecting at most K arbitrary projections of it. The N components of the latent vector represent sub-channels states, that change dynamically from 'busy' to 'idle' and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in which the CR can sense K out of the N sub-channels, as well as the typical static setting of Compressive Sensing, in which the CR observes K linear combinations of the N dimensional sparse vector. The CR opportunistic choice of the sensing matrix should balance the desire of revealing the state of as many dimensions of the latent vector as possible, while not exceeding the limits beyond which the vector support is no longer uniquely identifiable.

UR - http://www.scopus.com/inward/record.url?scp=84906569187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906569187&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2014.6875424

DO - 10.1109/ISIT.2014.6875424

M3 - Conference contribution

AN - SCOPUS:84906569187

SN - 9781479951864

SP - 3195

EP - 3199

BT - IEEE International Symposium on Information Theory - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -