### Abstract

When the subband transform coefficients of natural images at the same location are considered a vector, the vector often has an elliptically symmetric distribution where the probabilities are identical on an elliptic surface. This paper treats the coding loss of the scalar entropy coding of a vector information source with an elliptically symmetric distribution. The multidimensional uncorrelated Gaussian distribution has the characteristics that no coding loss occurs even if the components are independently coded, and that the information becomes concentrated in the elliptic shell as the number of dimensions increases. In this paper, we show that the one-dimensional marginal distribution of the multidimensional distribution concentrating in the elliptical shell asymptotically approaches a Gaussian distribution. The classified scalar entropy coding (CSEC) makes use of this fact; we first classify the vector by its normalized norm, entropy-code, the classification index, and each vector component. Next, under the assumption that the elliptically symmetric distribution varies more slowly than the thickness of the Gaussian distribution shell, the coding loss of the CSEC method is derived. We show that the coding loss per dimension asymptotically approaches zero as the number of dimensions increases. Finally, the amount of information of the CSEC method is computed when the amplitude distribution of the subband transform coefficients is modeled by the generalized Gaussian distribution. The result is superior to the unclassified scalar entropy coding method by 0.25 to 0.5 [bits/dim].

Original language | English |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 82 |

Issue number | 2 |

Publication status | Published - Feb 1999 |

### Fingerprint

### Keywords

- Adaptation
- Classification
- Elliptically symmetric distribution
- Gaussian distribution
- Subband transform

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*,

*82*(2), 1-10.

**Classified Scalor Entropy Coding for Information Sources with Elliptically Symmetric Probability Distribution.** / Morikawa, Yoshitaka; Yamane, Nobumoto; Ohira, Hironobu.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 82, no. 2, pp. 1-10.

}

TY - JOUR

T1 - Classified Scalor Entropy Coding for Information Sources with Elliptically Symmetric Probability Distribution

AU - Morikawa, Yoshitaka

AU - Yamane, Nobumoto

AU - Ohira, Hironobu

PY - 1999/2

Y1 - 1999/2

N2 - When the subband transform coefficients of natural images at the same location are considered a vector, the vector often has an elliptically symmetric distribution where the probabilities are identical on an elliptic surface. This paper treats the coding loss of the scalar entropy coding of a vector information source with an elliptically symmetric distribution. The multidimensional uncorrelated Gaussian distribution has the characteristics that no coding loss occurs even if the components are independently coded, and that the information becomes concentrated in the elliptic shell as the number of dimensions increases. In this paper, we show that the one-dimensional marginal distribution of the multidimensional distribution concentrating in the elliptical shell asymptotically approaches a Gaussian distribution. The classified scalar entropy coding (CSEC) makes use of this fact; we first classify the vector by its normalized norm, entropy-code, the classification index, and each vector component. Next, under the assumption that the elliptically symmetric distribution varies more slowly than the thickness of the Gaussian distribution shell, the coding loss of the CSEC method is derived. We show that the coding loss per dimension asymptotically approaches zero as the number of dimensions increases. Finally, the amount of information of the CSEC method is computed when the amplitude distribution of the subband transform coefficients is modeled by the generalized Gaussian distribution. The result is superior to the unclassified scalar entropy coding method by 0.25 to 0.5 [bits/dim].

AB - When the subband transform coefficients of natural images at the same location are considered a vector, the vector often has an elliptically symmetric distribution where the probabilities are identical on an elliptic surface. This paper treats the coding loss of the scalar entropy coding of a vector information source with an elliptically symmetric distribution. The multidimensional uncorrelated Gaussian distribution has the characteristics that no coding loss occurs even if the components are independently coded, and that the information becomes concentrated in the elliptic shell as the number of dimensions increases. In this paper, we show that the one-dimensional marginal distribution of the multidimensional distribution concentrating in the elliptical shell asymptotically approaches a Gaussian distribution. The classified scalar entropy coding (CSEC) makes use of this fact; we first classify the vector by its normalized norm, entropy-code, the classification index, and each vector component. Next, under the assumption that the elliptically symmetric distribution varies more slowly than the thickness of the Gaussian distribution shell, the coding loss of the CSEC method is derived. We show that the coding loss per dimension asymptotically approaches zero as the number of dimensions increases. Finally, the amount of information of the CSEC method is computed when the amplitude distribution of the subband transform coefficients is modeled by the generalized Gaussian distribution. The result is superior to the unclassified scalar entropy coding method by 0.25 to 0.5 [bits/dim].

KW - Adaptation

KW - Classification

KW - Elliptically symmetric distribution

KW - Gaussian distribution

KW - Subband transform

UR - http://www.scopus.com/inward/record.url?scp=0033078111&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033078111&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033078111

VL - 82

SP - 1

EP - 10

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 2

ER -