(50-3) 08 * << * >> * Russian * English * Content * All Issues

High-performance discrete wavelet transform for JPEG XS standard
P.A. Lyakhov1,2, M.V. Bergerman2, N.N. Nagornov1, A.S. Abdulsalyamova2

1 Department of Mathematical Modeling, North-Caucasus Federal University, 355017, Stavropol, Russia, Pushkin st. 1;
2 North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017, Stavropol, Russia, Pushkin st. 1

  Full text (PDF)

DOI: 10.18287/COJ 1725

Article ID: 1725

Language: English

Abstract:
This paper presents a high-speed method for forward and inverse discrete wavelet transform (DWT) intended for the JPEG XS image compression standard. Unlike state-of-the-art approaches, which process pixels sequentially, the proposed algorithm employs the Winograd method to compute groups of 2-5 pixels in parallel within a single clock cycle. We determine the minimum fractional bit-widths required for fixed-point arithmetic to ensure reconstructed image quality with a peak signal-to-noise ratio (PSNR) of at least 40 dB. Hardware modeling using the OpenLane environment demonstrates that the proposed method increases throughput by up to 109% for forward DWT and up to 144% for inverse DWT compared to state-of-the-art techniques. The optimal configurations are 3-pixel fragments for forward and 4-pixel fragments for inverse transforms. The proposed DWT approach is recommended for real-time systems where processing speed is critical, particularly in medical imaging and satellite data processing.

Keywords:
digital image processing, Le Gall filter, hardware modeling, Winograd computation.

Acknowledgements:
Research is section 3 was funded by the Russian Science Foundation (Project No. 24-71-10016). The rest of the paper was funded by the Russian Science Foundation (Project No. 23-71-10013).

Citation:
Lyakhov PA, Bergerman MV, Nagornov NN, Abdulsalyamova AS. High-performance discrete wavelet transform for JPEG XS standard. Computer Optics 2026; 50(3): 1725. doi: 10.18287/COJ 1725.

References:

  1. Gonzalez RC, Woods RE. Digital image processing. 4th ed. Harlow: Pearson Education; 2018.
  2. Rao KR, Domínguez HO, Subbarayappa S. JPEG series. 1st ed. Gistrup, Denmark: River Publishers; 2021. 346 p.
  3. Sai SV, Zinkevich AV, Fomina ES. Comparison of discrete cosine and wavelet transforms in RAW image compression systems. Computer Optics 2022; 46(6): 929-938. doi:10.18287/2412-6179-CO-1094.
  4. Descampe A, Richter T, Ebrahimi T, Foessel S, Keinert J, Bruylants T, Pellegrin P, Buysschaert C, Rouvroy G. JPEG XS -- a new standard for visually lossless low-latency lightweight image coding. Proc IEEE 2021; 109(9): 1559-1577. doi:10.1109/JPROC.2021.3080916.
  5. Guo T, Zhang T, Lim E, López-Benítez M, Ma F, Yu L. A review of wavelet analysis and its applications: challenges and opportunities. IEEE Access 2022; 10: 58869-58903. doi:10.1109/ACCESS.2022.3179517.
  6. Álvarez-Cortés S, Serra-Sagristà J, Bartrina-Rapesta J, Marcellin MW. Regression wavelet analysis for near-lossless remote sensing data compression. IEEE Trans Geosci Remote Sens 2020; 58(2): 790-798. doi:10.1109/TGRS.2019.2940553.
  7. Meyer A, Brand F, Kaup A. Learned wavelet video coding using motion compensated temporal filtering. IEEE Access 2023; 11: 113390-113401. doi:10.1109/ACCESS.2023.3295512.
  8. Sahoo GR, Freed JH, Srivastava M. Optimal wavelet selection for signal denoising. IEEE Access 2024; 12: 45369-45380. doi: 10.1109/access.2024.3377664.
  9. Stokfiszewski K, Wieloch K, Yatsymirskyy M. An efficient implementation of one-dimensional discrete wavelet transform algorithms for GPU architectures. J Supercomput 2022; 78: 11539-11563. doi:10.1007/s11227-021-04023-3.
  10. Richter T, Keinert J, Descampe A, Rouvroy G. Entropy coding and entropy coding improvements of JPEG XS. In: 2018 Data Compression Conference (DCC); Snowbird, UT, USA; 2018. pp. 87-96. doi:10.1109/DCC.2018.00018.
  11. Tian S, Song Q, He J, Zhang W, Wang Y, Lin Y. Implementation of JPEG XS entropy encoding and decoding on FPGA. J Real-Time Image Process 2024; 21(3-4): 1-17. doi:10.1007/s11554-023-01388-4.
  12. Foessel S, Richter T. Coding techniques in JPEG XS for efficient video production and contribution. In: Proceedings of the 2nd Mile-High Video Conference (MHV'23); 2023. pp. 72-77.
  13. Le Gall D, Tabatabai A. Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques. In: Proc IEEE Int Conf Acoust Speech Signal Process (ICASSP-88); 1988; vol. 2. pp. 761-764.
  14. Sweldens W. The lifting scheme: a construction of second generation wavelets. SIAM J Math Anal 1997; 29(2): 511-546. doi:10.1137/S0036141095289051.
  15. Winograd S. Arithmetic complexity of computations. 1st ed. Philadelphia, PA: SIAM; 1980. 96 p.
  16. Anand R, Reddy A, Babu G, et al. Winograd transform-based fast detection of heart disease using ECG signals and chest X-ray images. IEEE Access 2025; 13: 57119-57140. doi:10.1109/ACCESS.2025.3555518.
  17. Kai G, Ximing Y, Yu P, Liansheng L. A Winograd-based CNN accelerator for cloud detection on FPGA. In: 2022 China Automation Congress (CAC); Xiamen, China; 2022. pp. 3966-3970. doi:10.1109/CAC57257.2022.10054855.
  18. Bao C, Xie T, Feng W, Chang L, Yu C. A power-efficient optimizing framework FPGA accelerator based on Winograd for YOLO. IEEE Access 2020; 8: 94307-94317. doi:10.1109/ACCESS.2020.2995330.
  19. Wang J, Hou J, Zhang F, Meng Y, Su Y, Yang C. An efficient and parallelism-scalable large integer multiplier architecture using least-positive form and Winograd fast algorithm. IEEE Trans Circuits Syst II Express Briefs 2025; 72(1): 248-252. doi:10.1109/TCSII.2024.3457494.
  20. Lyakhov P, Abdulsalyamova A, Semyonova N, Nagornov N. On the computational complexity of 2D filtering by Winograd method. In: 11th Mediterranean Conference on Embedded Computing (MECO); Budva, Montenegro; 2022. pp. 1-4. doi:10.1109/MECO55406.2022.9797173.
  21. Lyakhov PA, Nagornov NN, Semyonova NF, Abdulsalyamova AS. Development of digital image processing algorithms based on the Winograd method in general form and analysis of their computational complexity. Computer Optics 2023; 47(1): 68-78. doi:10.18287/2412-6179-CO-1146.
  22. Rao KR, Yip PC. The transform and data compression handbook. 1st ed. Boca Raton, FL: CRC Press; 2001. 399 p.
  23. The OpenROAD Project. OpenLane. 2020. Available at: https://github.com/The-OpenROAD-Project/OpenLane.

151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20