informИнформатикаInformatics1816-03012617-6963UIIP NASBinform-254Research ArticleОБРАБОТКА СИГНАЛОВ, ИЗОБРАЖЕНИЙ, РЕЧИ, ТЕКСТА И РАСПОЗНАВАНИЕ ОБРАЗОВSIGNAL, IMAGE, SPEECH, TEXT PROCESSING AND PATTERN RECOGNITIONСИНТЕЗ FPGA-АРХИТЕКТУР БАНКОВ ФИЛЬТРОВ НА ОСНОВЕ БЛОЧНОЙ ЛЕСТНИЧНОЙ ФАКТОРИЗАЦИИ В АЛГЕБРЕ КВАТЕРНИОНОВ (ЧАСТЬ 1)SYNTHESIS OF FPGA ARCHITECTURES OF BLOCK LIFTING-BASED FILTER BANKS IN QUATERNION ALGEBRA (PART 1)https://orcid.org/0000-0001-5807-8685РыбенковЕ. В.RybenkovE. V.

ассистент кафедры электронно-вычислительных систем

Assistant Professor, Department of Computer Engineering

rybenkov@bsuir.byПетровскийН. А.PetrovskyN. A.

доцент кафедры электронно-вычислительных систем,

Associate Professor, Ph. D. (Computer Science), Department of Computer Engineering

nick.petrovsky@bsuir.byБелорусский государственный университет информатики и радиоэлектроникиБеларусьBelarusian State University of Informatics and Radioelectronics, MinskBelarus2018160620181522944Copyright © Рыбенков Е.В., Петровский Н.А., 20182018Рыбенков Е.В., Петровский Н.А.Rybenkov E.V., Petrovsky N.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://inf.grid.by/jour/article/view/254

В настоящее время методологии проектирования систем на кристалле основываются на высокопараметризированных IP-компонентах (IP – intellectual property), которые для конкретного целевого приложения обеспечивают широкий диапазон регулировки затрат ресурсов, форматов данных арифметики с фиксированной запятой и производительности системы. В статье представлен систематический подход к синтезу FPGA-архитектур целочисленных обратимых параунитарных банков фильтров в алгебре кватернионов (Int-Q-ПУБФ) для трансформационного кодирования изображений по схеме L2L (lossless-to-lossy). Показывается, что базовым элементарным преобразованием банка фильтров является операция умножения кватернионов (Q-MUL). Блочная лестничная факторизация данной операции и распределенная арифметика на сумматорах положены в основу параметризируемого Q-MUL IP-компонента.

Nowadays the methodology for designing systems on a chip is based on highly parameterized IP components which provide a wide range of adjustment of costs in resources, fixed point arithmetic data formats and system performance for a specific target application. The article presents a systematic approach for synthesizing FPGA architectures of integer reversible paraunitary filter banks in quaternion algebra (Int-Q-PUBB) for L2L (lossless-to-lossy) image transformed encoding. It is shown that the basic elementary transformation of the filter bank is the operation of quaternion multiplication (Q-MUL), the block-lifting factorization of which and the distributed arithmetic on the adder are the basis of the parametrizable Q-MUL IP-component.

схема lossless-to-lossyкватернионыкомпрессия изображенийFPGAбанк фильтровблочная лестничная факторизацияlossless-to-lossyquaternionsimage compressionFPGAfilter bankblock-lifting factorizationReferencesRao, K. Techniques and Standards for Image, Video, and Audio Coding / K. Rao, J. Hwang. – Prentice Hall, 1996. – 563 p.Rao K., Hwang J. Techniques and Standards for Image, Video, and Audio Coding. Prentice Hall, 1996, 563 p.Vaidyanathan, P. P. Multirate Systems and Filter Banks / P. P. Vaidyanathan. – Englewood Cliffs, NJ : Prentice Hall, 1993. – 911 p.Vaidyanathan P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ, Prentice Hall, 1993, 911 p.Крот, А. М. Теория анализа и синтеза бэнк-фильтров и их применение / А. М. Крот, В. О. Кудрявцев // Успехи современной радиоэлектроники. – 1999. – № 2. – С. 3–17.Krot A. M., Kudrjavcev V. O. Teorija analiza i sinteza bjenk-fil'trov i ih primenenie [Theory of analysis and synthesis filter banks and their application]. Uspehi sovremennoj radiojelektroniki [The Successes of Modern Radio Electronics], 1999, no. 2, pр. 3–17 (in Russian).Suzuki, T. Lifting-based paraunitary filterbanks for lossy/lossless image coding / T. Suzuki, Y. Tanaka, M. Ikehara // Proc. of Intern. Conf. EUSIPCO. – Florence, 2006. – Vol. 6.Suzuki T., Tanaka Y., Ikehara M. Lifting-based paraunitary filterbanks for lossy/lossless image coding. Proc. of Intern. Conf. EUSIPCO. Florence, 2006, vol. 6.Pennebaker, W. B. JPEG: Still Image Compression Standard / W. B. Pennebaker, J. L. Mitchell. – N. Y. : Van Nostrand Reinhold, 1993. – 639 p.Pennebaker W. B., Mitchell J. L. JPEG: Still Image Compression Standard. N. Y., Van Nostrand Reinhold, 1993, 639 p.Taubman, D. JPEG2000: Image Compression Fundamentals, Standards, and Practice / D. Taubman, M. Marcellin. – Boston : Kluwer Academic Publishers, 2002. – 777 p.Taubman D., Marcellin M. JPEG2000: Image Compression Fundamentals, Standards, and Practice. Boston, Kluwer Academic Publishers, 2002, 777 p. doi: 10.1007/978-1-4615-0799-4ISO/IEC 29199-2:2012. Information technology – JPEG XR image coding system. – Part 2: Image coding specification. – 2012.ISO/IEC 29199-2:2012. Information technology – JPEG XR image coding system. – Part 2: Image coding specification. – 2012.Chen, Y. J. Integer discrete cosine transform (IntDCT) / Y. J. Chen, S. Oraintara, T. Nguyen // Proc. of 2nd Intern. Conf. ICICS. – Sydney, 1999. – Vol. 99.Chen Y. J., Oraintara S., Nguyen T. Integer discrete cosine transform (IntDCT). Proc. of 2nd Intern. Conf. ICICS. Sydney, 1999, vol. 99.Liang, J. Fast multiplierless approximations of the DCT with the lifting scheme / J. Liang, T.D. Tran // IEEE Trans. Signal Process. – 2001. – Vol. 49, no. 12. – P. 3032–3044.Liang J., Tran T. D. Fast multiplierless approximations of the DCT with the lifting scheme. IEEE Trans. Signal Process, 2001, vol. 49, no. 12, pр. 3032–3044. doi: 10.1109/78.969511Petrovsky, A. Dynamic reconfigurable on the lifting steps wavelet packet processor with frame-based psychoacoustic optimized time-frequency tiling for real-time audio applications / A. Petrovsky, M. Rodionov, Al. Petrovsky // Design and Architectures for Digital Signal Processing. – Vienna : InTech, 2013. – P. 3–30.Petrovsky A., Rodionov M., Petrovsky Al. Dynamic reconfigurable on the lifting steps wavelet packet processor with frame-based psychoacoustic optimized time-frequency tiling for real-time audio applications. Design and Architectures for Digital Signal Processing. Vienna, InTech, 2013, рр. 3–30. doi: 10.5772/51604Lattice structure for regular paraunitary linear-phase filterbanks and m-band orthogonal symmetric wavelets / S. Oraintara [et. al.] // IEEE Trans. Signal Process. – 2001. – Vol. 49, no. 11. – P. 2659–2672.Oraintara S., Tran T. D., Heller P. N., Nguyen T. Q. Lattice structure for regular paraunitary linear-phase filterbanks and m-band orthogonal symmetric wavelets. IEEE Trans. Signal Process, 2001, vol. 49, no. 11, рр. 2659–2672. doi: 10.1109/78.960413Gan, L. A simplified lattice factorization for linear-phase paraunitary filter banks with pairwise mirror image frequency responses / L. Gan, K.-K. Ma // IEEE Trans. Circuits Syst. II. – 2004. – Vol. 51, no. 1. – P. 3–7.Gan L., Ma K.-K. A simplified lattice factorization for linear-phase paraunitary filter banks with pairwise mirror image frequency responses. IEEE Trans. Circuits Syst. II, 2004, vol. 51, no. 1, рр. 3–7. doi: 10.1109/TCSII.2003.821515Choukroun, D. Novel quaternion Kalman filter / D. Choukroun, I. Bar-Itzhack, Y. Oshman // IEEE Trans. Aerosp. Electron. Syst. – 2006. – Vol. 42, no. 1. – P. 174–190.Choukroun D., Bar-Itzhack I., Oshman Y. Novel quaternion Kalman filter. IEEE Trans. Aerosp. Electron. Syst., 2006, vol. 42, no. 1, рр. 174–190. doi: 10.1109/TAES.2006.1603413Miron, S. Quaternion-MUSIC for vector-sensor array processing / S. Miron, N. Le Bihan, J. Mars // IEEE Trans. Signal Process. – 2006. – Vol. 54, no. 4. – P. 1218–1229.Miron S., Bihan Le N., Mars J. Quaternion-MUSIC for vector-sensor array processing. IEEE Trans. Signal Process, 2006, vol. 54, no. 4, рр. 1218–1229. doi: 10.1109/TSP.2006.870630Parfieniuk, M. Quaternionic building block for paraunitary filter banks / M. Parfieniuk, A. Petrovsky // Proc. of the 12th European Signal Processing Conf. (EUSIPCO). – Austria, Vienna, 2004. – P. 1237–1240.Parfieniuk M., Petrovsky A. Quaternionic building block for paraunitary filter banks. Proc. of the 12th European Signal Processing Conf. (EUSIPCO). Austria, Vienna, 2004, рр. 1237–1240.Парфенюк, М. Параунитарные банки фильтров на основе алгебры кватернионов: теория и применение / М. Парфенюк, А. А. Петровский // Цифровая обработка сигналов. – 2008. – № 1. – С. 22–36.Parfieniuk M., Petrovsky A. Paraunitarnye banki fil'trov na osnove algebry kvaternionov: teorija i primenenie [Quaternion based paraunitary filter banks: theory and applications]. Cifrovaja obrabotka signalov [Journal of Digital Signal Processing], 2008, no. 1, рр. 22–36 (in Russian).Karney, C. Quaternions in molecular modeling / C. Karney // J. Molecular Graphics and Modelling. – 2007. – Vol. 25, no. 5. – P. 595–604.Karney C. Quaternions in molecular modeling. J. Molecular Graphics and Modelling, 2007, vol. 25, no. 5, рр. 595–604.Кантор, И. Л. Гиперкомплексные числа / И. Л. Кантор, А. С. Солодовников. – М. : Наука, 1973. –145 с.Kantor I. L., Solodovnikov A. S. Giperkompleksnye chisla. Hypercomplex Algebra. Moscow, Science Publ., 1973, 145 p. (in Russian).Baker, H. G. Quaternions and orthogonal 4×4 real matrices / H. G. Baker [Electronic resource]. – 1996. – Mode of access: http://archive.gamedev.net/archive/reference/articles/article428.html. – Datе of access: 05.04.2018.Baker H. G. Quaternions and orthogonal 4×4 real matrices, 1996. Available at: http://archive. gamedev.net/archive/reference/articles/article428.html (accessed 05.04.2018).Parfieniuk, M. Inherently lossless structures for eight- and sixchannel linear-phase paraunitary filter banks based on quaternion multipliers / M. Parfieniuk, A. Petrovsky // Signal Process. – 2010. – Vol. 90. – P. 1755–1767.Parfieniuk M., Petrovsky A. Inherently lossless structures for eight- and sixchannel linear-phase paraunitary filter banks based on quaternion multipliers. Signal Process. 2010, vol. 90, рр. 1755–1767. doi: 10.1016/j.sigpro.2010.01.008Gan, L. A simplified lattice factorization for linear-phase perfect reconstruction filter bank / L. Gan, K.-K. Ma // IEEE Signal Process. Lett. – 2001. – Vol. 8, no. 7. – P. 207–209.Gan L., Ma K.-K. A simplified lattice factorization for linear-phase perfect reconstruction filter bank. IEEE Signal Process. Lett, 2001, vol. 8, no. 7, рр. 207–209. doi: 10.1109/97.928679Petrovsky, N. Low read-only memory distributed arithmetic implementation of quaternion multiplier using split matrix approach / N. Petrovsky, A. Stankevich, A. Petrovsky // Electronics Letters. – 2014. – Vol. 50, no. 24. – P. 1809–1811.Petrovsky N., Stankevich A., Petrovsky A. Low read-only memory distributed arithmetic implementation of quaternion multiplier using split matrix approach. Electronics Letters, 2014, vol. 50, no. 24, рр. 1809–1811. doi:10.1049/el.2014.1775Петровский, Н. А. CORDIC-техника для фиксированного угла вращения в операции умножения кватернионов / Н. А. Петровский, А. В. Станкевич, А. А. Петровский // Информатика. – 2015. – № 4(48). – С. 85–108.Petrovsky N. A., Stankevich A. V., Petrovsky A. A. CORDIC-tehnika dlja fiksirovannogo ugla vrashhenija v operacii umnozhenija kvaternionov [CORDIC-techniques for fixed angle of rotation in multiplying operation of quaternions]. Informatika [Informatics], 2015, no. 4(48), рр. 85–108 (in Russian).Бибило П. Н. Основы языка VHDL : учеб. пособие. Изд. 6-е. – М. : Книжный дом «Либроком», 2014. – 328 с.Bibilo P. N. Osnovy jazyka VHDL: uchebnoe posobie. Izd. 6-e. Fundamentals of VHDL: Textbook. Ed. 6th. Moscow, Knizhnyj dom «Librokom» Publ., 2014, 328 p. (in Russian).A systematic approach for synthesizing VLSI architectures of lifting-based filter banks and transforms / R. Bartholoma [et al.] // IEEE Trans. Circuits Syst. I. – 2008. – Vol. 55, no. 7. – P. 1939–1952.Bartholoma R., Greiner T., Kesel F., Rosenstiel W. A systematic approach for synthesizing VLSI architectures of lifting-based filter banks and transforms. IEEE Trans. Circuits Syst. I, 2008, vol. 55, no. 7, рр. 1939–1952.The complexity of the quaternion product : Rep. TR 75-245 / Cornell University. – 1975. – Mode of access: http://www.theworld.com/~sweetser/quaternions/ps/cornellcstr75-245.pdf. – Datе of access: 05.04.2018.The complexity of the quaternion product : Rep. TR 75-245 / Cornell University. – 1975. Available at: http://www.theworld.com/~sweetser/quaternions/ps/cornellcstr75-245.pdf (accessed 05.04.2018).Parfieniuk, M. Quaternion multiplier inspired by the lifting implementation of plane rotations / M. Parfieniuk, A. Petrovsky // IEEE Trans. Circuits Syst. I. – 2010. – Vol. 57, no. 10. – P. 2708–2717.Parfieniuk M., Petrovsky A. Quaternion multiplier inspired by the lifting implementation of plane rotations. IEEE Trans. Circuits Syst. I, 2010, vol. 57, no. 10, рр. 2708–2717. doi: 10.1109/TCSI.2010.2046259Petrovsky, N. A. Design and implementation of reversible integer quaternionic paraunitary filter banks on adderbased distributed arithmetic / N. A. Petrovsky, E. V. Rybenkov, A. A. Petrovsky // Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA 2017). – Poznan, 2017. – P. 17–22.Petrovsky N. A., Rybenkov E. V., Petrovsky A. A. Design and implementation of reversible integer quaternionic paraunitary filter banks on adder-based distributed arithmetic. Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA 2017). Poznan, 2017, рр. 17–22. doi: 10.23919/SPA.2017.8166830Chang, T. S. New distributed arithmetic algorithm and its application to IDCT / T. S. Chang, C. Chen, C. W. Jen // IEE Proceedings – Circuits, Devices and Systems. – 1999. – Vol. 146, no. 4. – P. 159–163.Chang T. S., Chen C., Jen C. W. New distributed arithmetic algorithm and its application to IDCT. IEE Proceedings – Circuits, Devices and Systems, 1999, vol. 146, no. 4, рр. 159–163. doi: 10.1049/ip-cds:19990537

The authors declare that there are no conflicts of interest present.