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GPU Implementation of Faber Schauder Discrete Wavelet Transform using CUDA

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2021
Assma Azeroual, Karim Afdel

Assma Azeroual and Karim Afdel. GPU Implementation of Faber Schauder Discrete Wavelet Transform using CUDA. International Journal of Computer Applications 183(42):1-8, December 2021. BibTeX

	author = {Assma Azeroual and Karim Afdel},
	title = {GPU Implementation of Faber Schauder Discrete Wavelet Transform using CUDA},
	journal = {International Journal of Computer Applications},
	issue_date = {December 2021},
	volume = {183},
	number = {42},
	month = {Dec},
	year = {2021},
	issn = {0975-8887},
	pages = {1-8},
	numpages = {8},
	url = {},
	doi = {10.5120/ijca2021921815},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


Faber Schauder discrete wavelet transform (FSDWT) has many interesting advantages in image and video processing owing to its simplicity and its multiscale-based theory. It preserves the pixel ranges, has arithmetic operations, and detects edges in multiscale representation. With the increase of image size and the real-time requirement of many applications, the FSDWT computation becomes complex and needs other techniques to deal with it. To solve this problem, the FSDWT is implemented in parallel on a Graphics Processing Unit (GPU) using Compute Unified Device Architecture (CUDA) code. The results demonstrate that the GPU-based FSDWT exceedingly outperforms the CPU FSDWT.


  1. S.G. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, (IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11(7), 1989).
  2. S.G. Mallat, Multifrequency channel decompositions of images and wavelet models, (IEEE Trans. on Acoustics Speech and Signal Processing, vol. 37(12), 1989) p. 2091–2110.
  3. S.G. Mallat, A Wavelet Tour of Signal Processing, (Academic Press, New York, 1998).
  4. S.G. Mallat and S.G., Zhong, Characterization of signals from multiscale edges, (IEEE Trans. on Pattern Analysis and Machine Intelligence , vol. 14(7), 1992).
  5. R.C. Gonzalez and R.E. Woods, Digital Image Processing (Third Edition), (976, Prentice Hall, United States Edition, 2007).
  6. A. Aldroubi and M. Unser Families of multiresolution and wavelet spaces with optimal properties, (Numerical Functional Analysis and Optimization, vol. 14(5-6), 1993) p. 417–446.
  7. A. Cohen, I. Daubechies and J. C. Feauveau Biorthogonal bases of compactly supported wavelets, (Comm. Pure Appl. Math., vol. 45, 1992) p. 485–560.
  8. W. Sweldens The lifting scheme: A custom-design construction of biorthogonal wavelets, (Applied and computational harmonic analysis, vol. 3(2), 1996) p. 186–200.
  9. W. Sweldens The lifting scheme: A construction of second generation wavelets, (SIAM J. Math. Anal., vol. 29(2), 1997) p. 511–546.
  10. H. Douzi, D. Mammass and F. Nouboud Faber-Schauder wavelet transform, application to edge detection and image characterization, (Journal of Mathematical Imaging and Vision, vol. 14(2), 2001) p. 91–101.
  11. M. Amar, R. Harba, H. Douzi, F. Ros, M. El Hajji, R. Riad and K. Gourrame A JND Model Using a Texture-Edge Selector Based on Faber-SchauderWavelet Lifting Scheme, (Image and Signal Processing: 7th International Conference, ICISP 2016, Trois-Rivi`eres, QC, Canada, May 30 - June 1, 2016, Proceedings, 2016) p.328–336.
  12. M. El hajji, H. Douzi and R. Harba Watermarking Based on the Density Coefficients of Faber-Schauder Wavelets, (Image and Signal Processing: 3rd International Conference, ICISP 2008. Cherbourg-Octeville, France, July 1 - 3, 2008. Proceedings) p. 455–462.
  13. M. El Hajji, H. Douzi, D. Mammass and R. Harba A robust wavelet-based watermarking algorithm using mixed scales, (Multimedia Computing and Systems (ICMCS), 2011 International Conference on, 2011) p. 1–5.
  14. A. Azeroual and K. Afdel Low Complexity Image Authentication Based on Singular Value Decomposition and Mixed Scales Faber Schauder Wavelet, (International Review on Computers and Software (IRECOS), vol. 10(12), 2015) p. 1209–1215.
  15. A. Azeroual and K. Afdel Image Authentication Based on Faber Schauder DWT, (2016 13th International Conference on Computer Graphics, Imaging and Visualization (CGiV), Beni Mellal), p. 78–83.
  16. A. Azeroual and K. Afdel A Faber Schauder dominant blocks based fragile watermarking scheme for image tamper detection, (2016 International Conference on Electrical and Information Technologies (ICEIT), Tangiers), p. 380–385.
  17. A. Azeroual and K. Afdel A Fragile Watermarking Scheme for Image Authentication Using Wavelet Transform, (International Conference on Image and Signal Processing ICISP: Image and Signal Processing, 2016) p. 337–345.
  18. A. Azeroual, K. Afdel, M. El Hajji and H. Douzi, On line Key Frame Extraction and Video Boundary Detection using Mixed Scales Wavelets and SVD, (International Journal of Circuits, Systems and Signal Processing, 9, 2015) p. 420–426.
  19. A. Azeroual and K. Afdel Key Frames Based Video Authentication Using Fragile Watermarking and Singular Value Decomposition, (International Review on Computers and Software (IRECOS), vol. 11(5), 2016) p. 420–426.
  20. M. Benabdellah, M. Gharbi, F. Regragui and E. H. Bouyakhf, Choice of reference images for video compression, (Applied Mathematical Sciences, vol. 1(44), 2007) p. 2187–2201.
  21. CUDA C Programming Guide, PG-02829-001 v8.0, September 2016.
  22. CUDA C Best Practices Guide, DG-05603-001 v8.0, September 2016.


Image processing, FSDWT, GPU, CUDA, Multiscale transform