### Abstract

We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one. This, in turn, is used for designing local orthogonal bases obtained by unitary transformations of a single prototype filter. The first part of this work considered the abelian groups of unitary transformations, while here we deal with nonabelian groups. As an example, we show how to build such bases where the group of unitary transformations consists of modulations and rotations. Such bases are useful for building systems for evaluating image quality.

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

Pages (from-to) | 206-231 |

Number of pages | 26 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 6 |

Issue number | 2 |

State | Published - Dec 1 2000 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Knot Theory and its Ramifications*,

*6*(2), 206-231.

**Designing Local Orthogonal Bases on Finite Groups II : Nonabelian Case.** / Bernardini, Riccardo; Kovacevic, Jelena.

Research output: Contribution to journal › Article

*Journal of Knot Theory and its Ramifications*, vol. 6, no. 2, pp. 206-231.

}

TY - JOUR

T1 - Designing Local Orthogonal Bases on Finite Groups II

T2 - Nonabelian Case

AU - Bernardini, Riccardo

AU - Kovacevic, Jelena

PY - 2000/12/1

Y1 - 2000/12/1

N2 - We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one. This, in turn, is used for designing local orthogonal bases obtained by unitary transformations of a single prototype filter. The first part of this work considered the abelian groups of unitary transformations, while here we deal with nonabelian groups. As an example, we show how to build such bases where the group of unitary transformations consists of modulations and rotations. Such bases are useful for building systems for evaluating image quality.

AB - We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one. This, in turn, is used for designing local orthogonal bases obtained by unitary transformations of a single prototype filter. The first part of this work considered the abelian groups of unitary transformations, while here we deal with nonabelian groups. As an example, we show how to build such bases where the group of unitary transformations consists of modulations and rotations. Such bases are useful for building systems for evaluating image quality.

UR - http://www.scopus.com/inward/record.url?scp=0347107216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347107216&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347107216

VL - 6

SP - 206

EP - 231

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 2

ER -