Weyl – Heisenberg transform capabilities in JPEG compression standard
DOI:
https://doi.org/10.52575/2687-0932-2021-48-1-188-200Keywords:
image compression, JPEG codec, discrete cosine transform, Weyl-Heisenberg transform, downsampling, quantizationAbstract
This article is devoted to the development and research of a new compression technology based on Weyl-Heisenberg bases (WH-technology) for modifying the JPEG compression standard and improving its characteristics. For this purpose, the paper analyzes the main stages of the JPEG compression algorithm, notes its key features and problems that limit further enhancement of its efficiency. To overcome these limitations, it is proposed to use the real version of the two-dimensional discrete orthogonal Weyl-Heisenberg transform (DWHT) instead of the discrete cosine transform (DCT) at the stage of transformation coding. This transformation, unlike DCT, initially has a block structure and is built on the basis of the Weyl-Heisenberg optimal signal basis, the functions of which are orthogonal and well localized both in the frequency and time domains. This feature of DWHT allows for more efficient decorrelation and compression of element values in each block of the image after transformation coding. As a result, it is possible to obtain more efficient selection and screening of insignificant elements at the subsequent stages of quantization and information coding. Based on DWHT, a new version of the JPEG compression algorithm was developed, and convenient criteria for evaluating the compression efficiency and metrics of quality losses were proposed. The results of an experimental study are presented, confirming the higher compression efficiency of the proposed algorithm in comparison with the JPEG compression standard.
Downloads
References
Асирян В.М., Волчков В.П., 2017. Применение ортогонального преобразования Вейля-Гейзенберга для сжатия изображений. Телекоммуникации и информационные технологии, 4 (1): 50–56.
Асирян В.М., Волчков В.П., 2018. Вычислительно эффективная реализация прямого и обратного преобразований Вейля-Гейзенберга. Телекоммуникации и информационные технологии, 5 (1): 5–10.
Ахмед Н., Рао К.Р., 1980. Ортогональные преобразования при обработке цифровых сигналов. Пер. с англ. Под ред. Фоменко И.Б. М., Связь, 248 с. (Ahmed N, Rao K.R., 1975. Orthogonal Transforms for Digital Signal Processing. Berlin, Heidelberg, New York: Springer-Verlag, 264 р.).
Волчков В.П., 2009. Новые технологии передачи и обработки информации на основе хорошо локализованных сигнальных базисов. Научные ведомости БелГУ. Сер. История. Политология. Экономика. Информатика, 15(70): 181–189.
Волчков В.П., Асирян В.М., 2017. Вычислительно эффективный алгоритм формирования оптимального базиса Вейля-Гейзенберга. Фундаментальные проблемы радиоэлектронного приборостроения. М., МИРЭА. Часть 4: 1151–1154.
Волчков В.П., Петров Д.А., 2009. Оптимизация ортогонального базиса Вейля-Гейзенберга для цифровых систем связи, использующих принцип OFDM/OQAM передачи. Научные ведомости БелГУ. Сер. История. Политология. Экономика. Информатика, 1(56):
–112.
Волчков В.П., Петров Д.А., 2009. Условия ортогональности обобщенных базисов Вейля-Гейзенберга для OFTDM сигналов. Научные ведомости БелГУ. Сер. История. Политология. Экономика. Информатика, 15(70): 190–199.
Волчков В.П., Петров Д.А., 2010. Обобщенная теорема Найквиста для OFTDM сигналов. Системы синхронизации, формирования и обработки сигналов, 1(1): 28–32.
Добеши И., 2001. Десять лекций по вейвлетам. Ижевск, РХД, 464 с. (Daubechies I., 1992. Ten Lectures on Wavelets. Philadelphia, Pa.: Society for Industrial and Applied Mathematics, 378 р).
Ahmed N., Natarajan T., and Rao K.R., 1974. Discrete Cosine Transform. IEEE Transac-tions on Computers. C-23 (1): 90–93.
Asiryan V.M., Volchkov V.P., Papulovskaya N.V., 2020. Image Compression Using Dis-crete Weyl-Heisenberg Transform. Proceedings - 2020 Ural Symposium on Biomedical En-gineering, Radioelectronics and Information Technology, USBEREIT 2020, 399–402.
Bolcskei H. et al., 1999. Efficient design of OFDM/OQAM pulse shaping filter. Proceedings of IEEE International Conference on Communications (ICC 99). Vol. 1: 559–564.
Chen W., Pratt W.K., 1984. Scene Adaptive Coder. IEEE Transactions on Communications, 32 (3): 225–232.
Chen W., Smith C., and Fralick S., 1977. A Fast Computational Algorithm for the Discrete Cosine Transform. IEEE Transactions on Communications, 25 (9): 1004–1009.
Digital compression and coding of continuous-tone still images – requirements and guide-lines. 1992. V. 81, CCITT, 186 p.
Gabor D., 1946. Theory of communication. J. Inst. Elect. Eng. (London), 93 (111): 429–457.
Makhoul J., 1980. A fast cosine transform in one and two dimensions. IEEE Transactions on Acoustics, Speech, and Signal Processing. Mathematics. Vol. ASSP-28, No. 1: 27–34.
Volchkov V. et al., 2019. Synthesis of Real Weyl-Heisenberg Signal Frames with Desired Frequency-Time Localization., 2019 24th Conference of Open Innovations Association (FRUCT), Moscow, Russia: 502–508.
Volchkov V.P., 2007. Signal bases with good time-frequency localization. Electrosvyaz, 2: 21–25.
Volchkov V.P., Petrov D.A., 2009. Orthogonal Well-Localized Weyl-Heisenberg Basis Con-struction and Optimization for Multicarrier Digital Communication Systems. Proc. of ICUMT, St. Petersburg: Oct.
Volchkov V.P., Sannikov V.G., 2018. Algebraic approach to the optimal synthesis of real signal Weyl-Heisenberg bases. 2018 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO 2018). Publ: Institute of Electrical and Electronics Engineers (IEEE), POD Publ: Curran Associates, Inc. (Oct 2018): 135–142.
Wexler J., Raz S., 1990. Discrete Gabor expansions. Signal Processing, 21 (3): 207–220.
Abstract views: 114
Share
Published
How to Cite
Issue
Section
Copyright (c) 2021 ECONOMICS. INFORMATION TECHNOLOGIES
This work is licensed under a Creative Commons Attribution 4.0 International License.
