### Abstract

The Gabor expansion is studied for the purpose of image compression. First, the mathematical conditions required to obtain complete sets of Gabor functions in L_{2}(R) are presented. The concept of Gabor expansion is further interpreted in terms of the compression of real digital images: the problems of both complete and partial Gabor expansions of images are stated and an optimization algorithm which provides the coefficients of these expansions is proposed. This iterative algorithm based on the conjugate gradient algorithm converges in a finite number of iterations and in the mean time it is not computationally too costly (O(n^{2}) calculations per iteration). For complete expansions, a new and tight bound on the number of iterations required to achieve exact reconstructions is given. For partial expansions, the study shows that very good reconstructed images can be obtained with bit rates as low as 0.6 bit per pixel.

Original language | English (US) |
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Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Place of Publication | Piscataway, NJ, United States |

Publisher | Publ by IEEE |

Pages | 251-254 |

Number of pages | 4 |

Volume | 1 |

ISBN (Print) | 0780312813 |

State | Published - 1993 |

Event | 1993 IEEE International Symposium on Circuits and Systems - Chicago, IL, USA Duration: May 3 1993 → May 6 1993 |

### Other

Other | 1993 IEEE International Symposium on Circuits and Systems |
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City | Chicago, IL, USA |

Period | 5/3/93 → 5/6/93 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(Vol. 1, pp. 251-254). Piscataway, NJ, United States: Publ by IEEE.

**Near optimal algorithm for image compression using Gabor expansion.** / Gouronc, Jean Louis; Si, Jennie.

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

*Proceedings - IEEE International Symposium on Circuits and Systems.*vol. 1, Publ by IEEE, Piscataway, NJ, United States, pp. 251-254, 1993 IEEE International Symposium on Circuits and Systems, Chicago, IL, USA, 5/3/93.

}

TY - GEN

T1 - Near optimal algorithm for image compression using Gabor expansion

AU - Gouronc, Jean Louis

AU - Si, Jennie

PY - 1993

Y1 - 1993

N2 - The Gabor expansion is studied for the purpose of image compression. First, the mathematical conditions required to obtain complete sets of Gabor functions in L2(R) are presented. The concept of Gabor expansion is further interpreted in terms of the compression of real digital images: the problems of both complete and partial Gabor expansions of images are stated and an optimization algorithm which provides the coefficients of these expansions is proposed. This iterative algorithm based on the conjugate gradient algorithm converges in a finite number of iterations and in the mean time it is not computationally too costly (O(n2) calculations per iteration). For complete expansions, a new and tight bound on the number of iterations required to achieve exact reconstructions is given. For partial expansions, the study shows that very good reconstructed images can be obtained with bit rates as low as 0.6 bit per pixel.

AB - The Gabor expansion is studied for the purpose of image compression. First, the mathematical conditions required to obtain complete sets of Gabor functions in L2(R) are presented. The concept of Gabor expansion is further interpreted in terms of the compression of real digital images: the problems of both complete and partial Gabor expansions of images are stated and an optimization algorithm which provides the coefficients of these expansions is proposed. This iterative algorithm based on the conjugate gradient algorithm converges in a finite number of iterations and in the mean time it is not computationally too costly (O(n2) calculations per iteration). For complete expansions, a new and tight bound on the number of iterations required to achieve exact reconstructions is given. For partial expansions, the study shows that very good reconstructed images can be obtained with bit rates as low as 0.6 bit per pixel.

UR - http://www.scopus.com/inward/record.url?scp=0027284586&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027284586&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027284586

SN - 0780312813

VL - 1

SP - 251

EP - 254

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -