Abstract Shearlet Transform

In this paper, the shearlet theory is extended from Euclidean spaces to locally compact groups. More precisely, the abstract shearlet group is defined as a 3-fold semidirect product and the abstract shearlet transform is constructed by means of a quasiregular representation of the semidirect product...

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Bibliographic Details
Published in:Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2015-11, Vol.22 (4), p.669-681
Main Authors: Kamyabi-Gol, R.A., Atayi, V.
Format: Article
Language:English
Subjects:
42C40
43A65
quasiregular representation
semidirect product
Shearlet group
shearlet transform
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Summary:In this paper, the shearlet theory is extended from Euclidean spaces to locally compact groups. More precisely, the abstract shearlet group is defined as a 3-fold semidirect product and the abstract shearlet transform is constructed by means of a quasiregular representation of the semidirect product group. Its properties are investigated and results are illustrated by some examples.
ISSN:1370-1444
2034-1970
DOI:10.36045/bbms/1447856066