TY - JOUR

T1 - Designing Local Orthogonal Bases on Finite Groups II

T2 - Nonabelian Case

AU - Bernardini, Riccardo

AU - Kovačević, Jelena

PY - 2000

Y1 - 2000

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.

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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 -