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CURVELET TRANSFORM AS AN EXTENSION OF WAVELET TRANSFORM AND ITS OPERATIONAL CALCULUS

  • Sachin Mane (Department of Mathematics, Shivaji University Kolhapur) ;
  • Bharat Bhosale (Sambhajirao Kadam College) ;
  • Shubham D. Shedge (Department of Mathematics, Rajarshi Chhatrapati Shahu College)
  • 투고 : 2023.09.30
  • 심사 : 2023.12.20
  • 발행 : 2024.05.31

초록

In image and signal processing, the wavelet transform is frequently employed. However, it has the drawback of having weak directionality, which has limited its use in many applications. A recent addition to the wavelet transform, the curvelet transform attempts to address crossing phenomena that occur along curved edges in 2-D images. As an extension of the wavelet transform, we discuss various curvelet transform features in this paper. There are numerous uses for the curvelet and wavelet transforms in image and signal processing.

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참고문헌

  1. G. Beylkin: On the representation of operators in bases of compactly supported wavelets. SIAM Journal on Numerical Analysis 29 (1992), no. 6, 1716-1740. https://doi.org/10.1137/0729097
  2. B. Bhosale: Wavelet analysis of randomized solitary wave solutions. J. Math. Anal. Appl. 1 (2014), no. 1, 20-26.
  3. B. Bhosale: Curvelet Interaction with Artificial Neural Networks Artificial Neural Network Modelling (2016), 109-125. https://doi.org/10.1007/978-3-319-28495-8_6
  4. B. Bhosale, A. Jain & et.al.: Curvelet based multiresolution analysis of graph neural networks. International Journal of Applied Physics and Mathematics 4 (2014), no. 5, 313-316. https://doi.org/10.7763/IJAPM.2014.V4.304
  5. E.J. Cand'es & D.L. Donoho: Ridgelets: A key to higher-dimensional intermittency. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 357 (1999), no. 1760, 2495-2509. https://doi.org/10.1098/rsta.1999.0444
  6. L. Debnath & Shah, F.A. : Wavelet transforms and their applications. Boston: Birkha user (2002), 12-14. https://doi.org/10.1007/978-0-8176-8418-1
  7. D.L. Donoho & M.R. Duncan: Digital curvelet transform: strategy, implementation, and experiments. In Wavelet applications VII SPIE 4056 (2000), 12-30. https://doi.org/10.1117/12.381679
  8. J. Ma & G. Plonka: A review of curvelets and recent applications. IEEE Signal Processing Magazine 27 (2000), no. 2, 118-133.
  9. S.D. Shedge & B.N. Bhosale: Operational Calculus On Wavelet Transform As An Extension Of Fractional Fourier Transform. Journal of the Oriental Institute M.S. University of Baroda 71 (2022), 56-59.
  10. J.S. Walker & Y. Chen: Image denoising using tree-based wavelet subband correlations and shrinkage. Optical Engineering 39 (2000), no. 11, 2900-2908. https://doi.org/10.1117/1.1315571