Cone-adapted continuous shearlet transform and reconstruction formula

Volume 9, Issue 1, pp 262--269 http://dx.doi.org/10.22436/jnsa.009.01.25

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Authors

Devendra Kumar - Department of Mathematics, Faculty of Science, Al-Baha University, P. O. Box 1988, Alaqiq, Al-Baha-65431, Saudi Arabia, KSA. Shiv Kumar - Department of Mathematics, D. A. V. College, Jalandhar (Pb.), India. - Research Scholar, I.K. Gujral Punjab Technical University, Kapurthala (Jalandhar) (Pb.), India. Balbir Singh - College of Management and Technology, Nurpura, Post Ofice Halwara, District Ludhiana (Pb.), India.

Abstract

The shearlet system generated by unitary representation of the shearlet group becomes unattractive due to biasedness towards one axis. Therefore, in this paper we study the cone-adapted shearlet system to cover whole \(\mathbb{R}^2\) and for giving equal treatment of all directions. Since the horizontal and vertical cones are treated similarly by just interchanging \(w_1\) and \(w_2,w = (w_1;w_2) \in \mathbb{R}^2\), we study only horizontal cone and derived some basic results concerning to continuous shearlet transform.

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Keywords

• Shearlets
• continuous shearlet transform
• cone-adapted shearlet system
• Parseval formula.

MSC

•  42C40
•  68U10
•  47G20

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