Abstract
Modern computer technology devices do not keep pace with the high growth rate of quantitative and qualitative characteristics of digital images. The computational complexity of the wavelet transform must be reduced for the hardware-friendly implementation of wavelet image processing methods on microelectronic devices. This paper proposes a new approach to reduce the computational complexity of wavelet image processing based on the Winograd method. Group pixel processing using Winograd method reduces the asymptotic computational complexity by up to 72.9% compared to the traditional pixel-by-pixel processing approach, according to the results obtained. A theoretical evaluation of the resource costs of a wavelet image processing device based on the unit-gate model showed that Winograd method reduces device delay to 73.62% and device area to 34.03% compared to the direct implementation. The greatest reduction in resource costs is observed mainly when obtaining fragments of the processed image with 5 pixels. At the same time, the greatest rate of resource reduction is observed when obtaining fragments of the processed image with 3 pixels. Further increase in the fragments size leads to a significantly smaller reduction in resource costs while increasing the complexity of circuits design. Separation of filters into several components is more hardware-friendly when using high-order wavelets. Verification of all obtained results on field-programmable gate arrays and application-specific integrated circuits is a promising direction for further research.
REFERENCES
H. G. D. Avenido and R. V. Crisostomo, “Image reconstruction from a large number of projections in proton and 12C ions computed tomography using sequential and parallel ART algorithms,” Procedia Comput. Sci. 197, 126–134 (2022). https://doi.org/10.1016/J.PROCS.2021.12.126
G. Gebremeskel, “A critical analysis of the multi-focus image fusion using discrete wavelet transform and computer vision,” Soft Comput. 26, 5209–5225 (2022). https://doi.org/10.1007/s00500-022-06998-w
A. Lavin and S. Gray, “Fast algorithms for convolutional neural networks,” in Proc. IEEE Comput. Soc. Conf. Computer Vision Pattern Recognition, 2016 (IEEE, 2016), 4013–4021. https://doi.org/10.1109/CVPR.2016.435
P. Lyakhov, M. Valueva, G. Valuev, and N. Nagornov, “A method of increasing digital filter performance based on truncated multiply-accumulate units,” Appl. Sci. 10, 9052 (2020). https://doi.org/10.3390/app10249052
P. Lyakhov and A. Abdulsalyamova, “On the algorithmic complexity of digital image processing filters with Winograd calculations,” in Mathematics and Its Applications in New Computer Systems. MANCS 2021, Lecture Notes in Networks and Systems, Vol. 424 (Springer, Cham, 2021), pp. 71–89. https://doi.org/10.1007/978-3-030-97020-8_8
A. Mehrabian, M. Miscuglio, Y. Alkabani, V. J. Sorger, and T. El-Ghazawi, “A Winograd-based integrated photonics accelerator for convolutional neural networks,” IEEE J. Sel. Top. Quantum Electron. 26, 6100312 (2020). https://doi.org/10.1109/JSTQE.2019.2957443
S. Mittal and Vibhu, “A survey of accelerator architectures for 3D convolution neural networks,” J. Syst. Archit. 115, 102041 (2021). https://doi.org/10.1016/J.SYSARC.2021.102041
Q. Qin, J. Dou, and Z. Tu, “Deep ResNet based remote sensing image super-resolution reconstruction in discrete wavelet domain,” Pattern Recognit. Image Anal. 30, 541–550 (2020). https://doi.org/10.1134/S1054661820030232
R. Ravi and K. Subramaniam, “Image compression using optimized wavelet filter derived from grey wolf algorithm,” J. Ambient. Intell. Human Comput. 12, 6677–6688 (2020). https://doi.org/10.1007/s12652-022-03990-y
D. Rossinelli, G. Fourestey, F. Schmidt, B. Busse, and V. Kurtcuoglu, “High-throughput lossy-to-lossless 3D image compression,” IEEE Trans. Med. Imaging 40, 607–620 (2021). https://doi.org/10.1109/TMI.2020.3033456
J. Shen, Y. Huang, M. Wen, and C. Zhang, “Toward an efficient deep pipelined template-based architecture for accelerating the entire 2-D and 3-D CNNs on FPGA,” IEEE Trans. Comput. Des. Integr. Circuits Syst. 39, 1442–1455 (2020). https://doi.org/10.1109/TCAD.2019.2912894
M. Valueva, P. Lyakhov, G. Valuev, and N. Nagornov, “Digital filter architecture with calculations in the residue number system by Winograd method F(2×2,2×2),” IEEE Access 9, 143331–143340 (2021). https://doi.org/10.1109/ACCESS.2021.3121520
X. Wang, C. Wang, J. Cao, L. Gong, and X. Zhou, “WinoNN: Optimizing FPGA-based convolutional neural network accelerators using sparse Winograd algorithm,” IEEE Trans. Comput. Des. Integr. Circuits Syst. 39, 4290–4302 (2020). https://doi.org/10.1109/TCAD.2020.3012323
S. Winograd, Arithmetic Complexity of Computations (SIAM, Philadelphia, Pa., 1980). https://doi.org/10.1137/1.9781611970364
D. Wu, X. Fan, W. Cao, and L. Wang, “SWM: A high-performance sparse-winograd matrix multiplication CNN accelerator,” IEEE Trans. Very Large Scale Integr. Syst. 29, 936–949 (2021). https://doi.org/10.1109/TVLSI.2021.3060041
J. Yepez and S.-B. Ko, “Stride 2 1-D, 2-D, and 3-D Winograd for convolutional neural networks,” IEEE Trans. Very Large Scale Integr. Syst. 28, 853–863 (2020). https://doi.org/10.1109/TVLSI.2019.2961602
X. Zhang, “A modified artificial bee colony algorithm for image denoising using parametric wavelet thresholding method,” Pattern Recognit. Image Anal. 28, 557–568 (2018). https://doi.org/10.1134/S1054661818030215
R. Zimmermann, Binary Adder Architectures for Cell-Based VLSI and Their Synthesis (Hartung-Gorre, Zürich, 1998).
ACKNOWLEDGMENTS
The authors express gratitude to the North-Caucasus Center for Mathematical Research for providing the material and technical base.
Funding
The research in section 3 was supported by the Russian Science Foundation (project no. 22-71-00009). The research in the remaining sections was supported by the Russian Science Foundation (project no. 21-71-00017).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
COMPLIANCE WITH ETHICAL STANDARDS
This article is a completely original work of its authors; it has not been published before and will not be sent to other publications until the PRIA Editorial Board decides not to accept it for publication.
CONFLICT OF INTEREST
The process of writing and the content of the article does not give grounds for raising the issue of a conflict of interest.
Additional information
Pavel Alekseyevich Lyakhov. Born 1988. Graduated from Stavropol State University, specialty “Mathematics” in 2009. Candidate of Physical and Mathematical Sciences. Head of the Department of Mathematical Modeling, North-Caucasus Federal University, Head of the Department of Modular Computing and Artificial Intelligence, regional scientific and educational mathematical center “North-Caucasus Center for Mathematical Research”. Research interests are digital signal and image processing, artificial intelligence, neural networks, modular arithmetic, parallel computing, high-performance computing, digital circuits and hardware accelerators. Author of more than 200 publications.
Nikolay Nikolaevich Nagornov. Born 1992. Graduated from North-Caucasus Federal University, specialty “Applied Mathematics and Computer Science” in 2014. Candidate of Computer Sciences. Associate Professor of the Department of Mathematical Modeling, North-Caucasus Federal University. Research interests are digital image processing, modular arithmetic, parallel computing, high-performance computing, digital circuits and hardware accelerators. Author of more than 30 publications.
Nataliya Fedorovna Semyonova. Born 1951. Graduated from the Faculty of Physics and Mathematics of the Stavropol State Pedagogical Institute in 1972. Candidate of Physical and Mathematical Sciences. Associate Professor of the Department of Mathematical Modeling, North-Caucasus Federal University. Research interests are mathematical modeling, parallel computing, residue number system, modular arithmetic, diagonal function. Author of more than 60 publications.
Albina Shikhaevna Abdulsalyamova. Born 2000. Graduated from North-Caucasus Federal University, specialty “Mathematics and Computer Science” in 2022. Laboratory assistant of the Department of Modular Computing and Artificial Intelligence, regional scientific and educational mathematical center “North-Caucasus Center for Mathematical Research”. Research interests are digital image processing, computational complexity, high-performance computing and digital circuits.
Rights and permissions
About this article
Cite this article
Lyakhov, P.A., Nagornov, N.N., Semyonova, N.F. et al. Reducing the Computational Complexity of Image Processing Using Wavelet Transform Based on the Winograd Method. Pattern Recognit. Image Anal. 33, 184–191 (2023). https://doi.org/10.1134/S1054661823020074
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1054661823020074