Wavelet transform of a halftone image in a finite field

Gorbachyov, V.N., Kazakov, A.Y., Kaĭnarova E.M., Maslenitskaya K.D.

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Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Горбачев В.Н., Казаков А.Я., Кайнарова Е.М., Масленицкая К.Д. Вейвлет-преобразование полутонового изображения в конечном поле // Оптический журнал. 2020. Т. 87. № 5. С. 54–62. http://doi.org/10.17586/1023-5086-2020-87-05-54-62

Gorbachev V.N., Kazakov A.Ya., Kaĭnarova E.M., Maslenitskaya K.D. Wavelet transform of a halftone image in a finite field [in Russian] // Opticheskii Zhurnal. 2020. V. 87. № 5. P. 54–62. http://doi.org/10.17586/1023-5086-2020-87-05-54-62

For citation (Journal of Optical Technology):

V. Gorbachev, A. Kazakov, E. Kaĭnarova, and K. Maslenitskaya, "Wavelet transform of a halftone image in a finite field," Journal of Optical Technology . 87, 293-298 (2020). https://doi.org/10.1364/JOT.87.000293

Abstract:

1. Jabade V.S., Gengaje S.R. Logo based image copyright protection using discrete wavelet transform and fuzzy inference system // Internat. J. Computer Applications. 2012. V. 58. № 10. P. 22–27.

2. Hamghalam M., Mirzakuchaki S., and Akhaee M.A. Geometric modeling of the wavelet coefficients for image watermarking using optimum detector // IET Image Proc. 2014. V. 8. № 3. P. 162–172.

3. Rajan A. and Ramesh G.P. Automated early detection of glaucoma in wavelet domain using optical coherence tomography images // Biosciences Biotechnology Research Asia. 2015. V. 12. № 3. P. 2821–2828.

4. Gokul Kannan K., Ganeshbabu T.R. Glaucoma image classification using discrete orthogonal stockwell transform // Int. J. Adv. Sig. Img. Sci. 2017. V. 3. № 1. URL: https://xlescience.org/index.php/IJASIS/article/download/21/25

5. Hu Y.J., Huang S.K. An algorithm for removable visible watermarking // IEEE. Trans. Circuits and Systems Video Technol. 2006. V. 16. № 1. P. 129–133.

6. Gorbachev V.N., Denisov L.A., Kaynarova E.M., Metelev I.K. A steganographic image-baseg approache for protection of pdf files // Proc. Intern. Conf. Computer Graphycs, Visualization etc, and Image Proc., MCCSIS. Lisbon, Portugal. 20–23 July, 2017. P. 285–289. URL: http://iadisportal.org/mccsis-2017-in-lisbon-portugal

7. Shreyash Shantam. Robust lossless image watermarking in integer wavelet domain using SVD // Intern. J. Research in Appl. Sci. & Eng. Technol. (IJRASET). 2017. V. 5. Iss. VI. P. 2462. URL: https://www.ijraset.com/fileserve.php?FID=8687

8. Лидл Р., Нидеррайтер Г. Конечные поля. В 2-х т. М.: Мир, 1988.

9. Fekri F., Mersereau R.M., Schafer R.W. Theory of wavelet transform over finite fields // Proc. IEEE Intern. Conf.: Acoustics, Speech, and Signal Proc. 1999. V. 3. P. 1213–1216. DOI: 10.1109/ICASSP.1999.756196

10. Caire G., Grossman R.L., Member IEEE, and Poor H.V. Wavelet transforms associated with finite cyclic groups // IEEE Trans. Informmion Theory. 1993. V. 39. № 4. P. 1157.

11. Черников Д.В. Помехоустойчивое кодирование с использованием биортогональных наборов фильтров // Сибирские электронные математические известия. 2015. Т. 12. С. 704–713. URL: https://doi.org/10.17377/semi.2015.12.056.

12. Akansu A.N., Haddad R.A. Multiresolution signal decomposition: Transforms, subbands, and wavelets. Boston, MA: Academic Press, 1992. ISBN 978-0-12-047141-6

13. Daubechies I., Sweldens W. Factoring wavelet transforms into lifting steps // J. Fourier Analysis and Applic. 1998. V. 4. № 3. P. 247–269.

14. Гиш Т.А., Ефимович А.В., Калмыков И.А. Математическая модель дискретного вейвлет преобразования Добеши, реализованного в конечном поле // Современные наукоемкие технологии. 2018. С. 27–31.

15. Gorbachev V.N., Makarov A.H., Kaynarova E.M., Yakovleva E.S. Image watermarking using a cover work with replicated elements // Proc. 45^th Intern. Research Conf. Iarigai, Intern. Assoc. Research Organ. Inform., Media and Graphic Arts Industries. Darmstadt, Germany. 2018. P. 172–177.

Keywords:

discrete wavelet transform, finite field, Dobeshi wavelet db4 and db6.

OCIS codes: 100.2000, 100.7410

References:

1. V. S. Jabade and S. R. Gengaje, “Logo based image copyright protection using discrete wavelet transform and fuzzy inference system,” Int. J. Comput. Appl. 58(10), 22–27 (2012).

2. M. Hamghalam, S. Mirzakuchaki, and M. A. Akhaee, “Geometric modeling of the wavelet coefficients for image watermarking using optimum detector,” IET Image Process. 8(3), 162–172 (2014).

3. A. Rajan and G. P. Ramesh, “Automated early detection of glaucoma in wavelet domain using optical coherence tomography images,” Biomed. Pharmacol. J. 8(2), 641–649 (2015).

4. K. Gokul Kannan and T. R. Ganeshbabu, “Glaucoma image classification using discrete orthogonal Stockwell transform,” Int. J. Adv. Signal Image Sci. 3(1), 1–6 (2017).

5. Y. J. Hu and S. K. Huang, “An algorithm for removable visible watermarking,” IEEE. Trans. Circuits Syst. Video Technol. 16(1), 129–133 (2006).

6. V. N. Gorbachev, L. A. Denisov, E. M. Kaynarova, and I. K. Metelev, “A steganographic image-based approach for protection of PDF files,” in Proceedings of the International Conference on Computer Graphics, Visualization, and Image Processing (MCCSIS) (2017), pp. 285–289.

7. S. Shantam, “Robust lossless image watermarking in integer wavelet domain using SVD,” Int. J. Res. Appl. Sci. Eng. Technol. 5, 2462–2467 (2017).

8. R. Lidl and G. Niederreiter, Finite Fields (Mir, Moscow, 1988).

9. F. Fekri, R. M. Mersereau, and R. W. Schafer, “Theory of wavelet transform over finite fields,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (1999), pp. 1213–1216.

10. G. Caire, R. L. Grossman, and H. V. Poor, “Wavelet transforms associated with finite cyclic groups,” IEEE Trans. Inf. Theory 39(4), 1157–1166 (1993).

11. D. V. Chernikov, “Error-correcting codes using biorthogonal filter banks,” Sibirskie Elektron. Mat. Izv. 12, 704–713 (2015).

12. A. N. Akansu and R. A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets (Academic, Boston, 1992).

13. I. Daubechies and W. Sweldens, “Factoring wavelet transforms into lifting steps,” J. Fourier Anal. Appl. 4(3), 247–269 (1998).

14. T. A. Gish, A. V. Efimovich, and I. A. Kalmykov, “Mathematical model of discrete Daubechies wavelet transform in finite field,” Sovrem. Naukoemkie Tekhnol., 27–31 (2018).

15. V. N. Gorbachev, A. H. Makarov, E. M. Kaynarova, and E. S. Yakovleva, “Image watermarking using a cover work with replicated elements,” in Proceedings of the 45th International Research Conference of the IARIGAI (2018), pp. 172–177.