### Abstract

Sparse representation is one of the principles for the most effective signal processing, and makes it possible for us to infer from less data. The framework of signal processing based on it is called compressed sensing or compressive sensing, where dictionary matrices play an essential role of the basis for sparse representation. In our previous work, we successfully derived an analytical expression of the probability distribution followed by image dictionaries for the images generated by the Gaussian model [1]. However, we have found that the distribution has a difficulty of a divergent covariance matrix, which is needed for an analytical performance evaluation of image processing by compressed sensing. Therefore, it is the purpose of this paper to solve the difficulty and to open the way to the evaluation.

Original language | English |
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Title of host publication | International Conference on Control, Automation and Systems |

Publisher | IEEE Computer Society |

Pages | 829-832 |

Number of pages | 4 |

Volume | 2018-October |

ISBN (Electronic) | 9788993215151 |

Publication status | Published - Dec 10 2018 |

Event | 18th International Conference on Control, Automation and Systems, ICCAS 2018 - PyeongChang, Korea, Republic of Duration: Oct 17 2018 → Oct 20 2018 |

### Other

Other | 18th International Conference on Control, Automation and Systems, ICCAS 2018 |
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Country | Korea, Republic of |

City | PyeongChang |

Period | 10/17/18 → 10/20/18 |

### Fingerprint

### Keywords

- Compressed sensing
- Covariance matrix
- Dictionary matrix

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*International Conference on Control, Automation and Systems*(Vol. 2018-October, pp. 829-832). [8571653] IEEE Computer Society.

**Covariance matrix of a probability distribution for image dictionaries in compressed sensing.** / Aida, Toshiaki.

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

*International Conference on Control, Automation and Systems.*vol. 2018-October, 8571653, IEEE Computer Society, pp. 829-832, 18th International Conference on Control, Automation and Systems, ICCAS 2018, PyeongChang, Korea, Republic of, 10/17/18.

}

TY - GEN

T1 - Covariance matrix of a probability distribution for image dictionaries in compressed sensing

AU - Aida, Toshiaki

PY - 2018/12/10

Y1 - 2018/12/10

N2 - Sparse representation is one of the principles for the most effective signal processing, and makes it possible for us to infer from less data. The framework of signal processing based on it is called compressed sensing or compressive sensing, where dictionary matrices play an essential role of the basis for sparse representation. In our previous work, we successfully derived an analytical expression of the probability distribution followed by image dictionaries for the images generated by the Gaussian model [1]. However, we have found that the distribution has a difficulty of a divergent covariance matrix, which is needed for an analytical performance evaluation of image processing by compressed sensing. Therefore, it is the purpose of this paper to solve the difficulty and to open the way to the evaluation.

AB - Sparse representation is one of the principles for the most effective signal processing, and makes it possible for us to infer from less data. The framework of signal processing based on it is called compressed sensing or compressive sensing, where dictionary matrices play an essential role of the basis for sparse representation. In our previous work, we successfully derived an analytical expression of the probability distribution followed by image dictionaries for the images generated by the Gaussian model [1]. However, we have found that the distribution has a difficulty of a divergent covariance matrix, which is needed for an analytical performance evaluation of image processing by compressed sensing. Therefore, it is the purpose of this paper to solve the difficulty and to open the way to the evaluation.

KW - Compressed sensing

KW - Covariance matrix

KW - Dictionary matrix

UR - http://www.scopus.com/inward/record.url?scp=85060444593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060444593&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85060444593

VL - 2018-October

SP - 829

EP - 832

BT - International Conference on Control, Automation and Systems

PB - IEEE Computer Society

ER -