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Study of shearlet transform using block matrix dilation

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Abstract

In this paper, the shearlet theory is extended from ordinary matrices to block matrices and its properties are investigated. More precisely, the block shearlet group is defined as a semidirect product group and the block shearlet transform is constructed by means of a quasiregular representation of this semidirect product group. In addition, we show that the block shearlet transform can overcome two major issues of the classical shearlet transform: time complexity and redundancy. We also report the result of careful experiments on video denoising which compares our proposed method with state of the art multiscale techniques, including curvelets and 3D shearlet transform.

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Acknowledgements

We would like to thank the referees for their valuable comments and pointing out various references.

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Authors and Affiliations

  1. Department of Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebraic Structures (CEAAS), P.O. Box 1159-91775, Mashhad, Iran

    Z. Amiri & R. A. Kamyabi-Gol

  2. Computer Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

    H. Bagherzadeh & A. Harati

Authors
  1. Z. Amiri
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  2. H. Bagherzadeh
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  3. A. Harati
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  4. R. A. Kamyabi-Gol
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Correspondence to R. A. Kamyabi-Gol.

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Amiri, Z., Bagherzadeh, H., Harati, A. et al. Study of shearlet transform using block matrix dilation. J. Appl. Math. Comput. 56, 665–689 (2018). https://doi.org/10.1007/s12190-017-1120-5

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  • DOI: https://doi.org/10.1007/s12190-017-1120-5

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