Wavelet transform of a gray-scale image in a finite GF(2) field

Gorbachyov, V.N., Kazakov, A.Y., Savelieva, M.Y.

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Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Горбачев В.Н., Казаков А.Я., Савельева М.Ю. Вейвлет-преобразование полутонового изображения в конечном поле GF(2) // Оптический журнал. 2021. Т. 88. № 2. С. 40–49. http://doi.org/10.17586/1023-5086-2021-88-02-40-49

Gorbachev V.N., Kazakov A.Ya., Savelieva M.Yu. Wavelet transform of a gray-scale image in a finite GF(2) field [in Russian] // Opticheskii Zhurnal. 2021. V. 88. № 2. P. 40–49. http://doi.org/10.17586/1023-5086-2021-88-02-40-49

For citation (Journal of Optical Technology):

V. N. Gorbachev, A. Ya. Kazakov, and M. Yu. Savel’eva, "Wavelet transform of a gray-scale image in a finite GF(2) field," Journal of Optical Technology. 88(2), 87-93 (2021). https://doi.org/10.1364/JOT.88.000087

Abstract:

A biorthogonal wavelet transform in a finite GF(2) field is studied for gray-scale images. The wavelet transform is implemented on the basis of binary filters of length 4 and 8, with the initial image resolved into bit planes. As an example, an arrangement of embedded digital watermarks into blocks of wavelet coefficients is considered. It is shown that the proposed technique makes it possible to eliminate the averaging errors that accompany the standard approach.

Keywords:

discrete wavelet transform, finite field, digital image

OCIS codes: 100.2000, 100.7410

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