Olena Kolhanova; Lidiia Tereshchenko; Svitlana Korniienko; Iryna Morozova; Oleksandr Davydov; Volodymyr Shutko; Maksym Zaliskyi

Image Compression via Nonlinear Multiscale Decomposition with Fractional-Rational Approximation

PDF (843KB), PP.48-64

Views: 0 Downloads: 0

Author(s)

Olena Kolhanova ¹ Lidiia Tereshchenko ² Svitlana Korniienko ¹ Iryna Morozova ³ Oleksandr Davydov ⁴ Volodymyr Shutko ^3,* Maksym Zaliskyi ⁵

1. State University “Kyiv Aviation Institute”/Department of Software Engineering, Kyiv, 03058, Ukraine

2. State University “Kyiv Aviation Institute”/Department of Cyber Security, Kyiv, 03058, Ukraine

3. State University “Kyiv Aviation Institute”/Department of Electronics, Robotics, Monitoring and IoT Technologies, Kyiv, 03058, Ukraine

4. Taras Shevchenko National University of Kyiv/Department of Operation Research, Kyiv, 01601, Ukraine

5. State University “Kyiv Aviation Institute”/Department of Telecommunication and Radioelectronic Systems, Kyiv, 03058, Ukraine

* Corresponding author.

DOI: https://doi.org/10.5815/ijigsp.2026.04.03

Received: 18 Jan. 2026 / Revised: 12 Mar. 2026 / Accepted: 6 May 2026 / Published: 8 Aug. 2026

Index Terms

Digital Compression, Nonlinear Method, Wavelet Analysis, Nonlinear Multiscale Decomposition, Aerial Photograph Compression

Abstract

Currently, image compression algorithms are an integral part of modern information systems in various industries and spheres of human activity, including telecommunications, medicine, artificial intelligence, and defense technologies. This paper deals with a novel image compression method based on nonlinear multiscale decomposition with fractional-rational approximation, providing a compact representation of image components while preserving reconstruction quality. The proposed algorithm consists of five steps, including image preprocessing, discretization, nonlinear multiscale decomposition, quantization, and arithmetic compression. The method was evaluated using 1000 test images and demonstrated an average compression ratio of 13.2, with reconstructed image quality of 41.5 dB, outperforming classical wavelet-based approaches under comparable conditions (approximately by 8-10% in average). The computational complexity of the proposed algorithm remains suitable for practical implementation, making it a promising solution for efficient image compression in modern digital systems.

Cite This Paper

Olena Kolhanova, Lidiia Tereshchenko, Svitlana Korniienko, Iryna Morozova, Oleksandr Davydov, Volodymyr Shutko, Maksym Zaliskyi, "Image Compression via Nonlinear Multiscale Decomposition with Fractional-Rational Approximation", International Journal of Image, Graphics and Signal Processing(IJIGSP), Vol.18, No.4, pp. 48-64, 2026. DOI:10.5815/ijigsp.2026.04.03

Reference

[1]D. R. Bull, F. Zhang, Intelligent Image and Video Compression, Academic Press, 2021, 563 p.
[2]S. Liu, F. Saeed, Z. Yang, J. Chen, “A comprehensive review on hyperspectral image lossless compression algorithms,” Remote Sensing, 2025, vol. 17(24), 3966. doi: 10.3390/rs17243966.
[3]V. Shutko, L. Tereshchenko, А. Sitko, V. Kravchenko, V. Volkogon, Zh. Vasylieva-Shalamova, O. Kolhanova, “Method for improving the efficiency of online communication systems based on adaptive multiscale transformation”, In: 10th International Conference on Advanced computer information technologies, 2020, pp. 824–829.
[4]O. Kolhanova, V. Shutko, V. Volkohon, L.Tereshchenko, V. Kravchenko, M. Shutko, N. Mykhalchyshyn, “Mathematical spline processing method for filtering and compressing data”, CEUR Workshop Proceedings, 2022, vol. 2654, pp. 204–214.
[5]O. Holubnychyi, et al., “Self-organization technique with a norm transformation based filtering for sustainable infocommunications within CNS/ATM systems,” In: I. Ostroumov and M. Zaliskyi (eds.), Proceedings of the 2nd International Workshop on Advances in Civil Aviation Systems Development. ACASD 2024. Lecture Notes in Networks and Systems, vol. 992, 2024, pp. 262–278. doi: 10.1007/978-3-031-60196-5_20.
[6]F. J. Yanovsky, “Millimeter Wave Radar: Principles and Applications”, In the book: Millimeter Wave Technology in Wireless PAN, LAN, and MAN, CRC Press, 2008, pp.305-376. https://www.taylorfrancis.com/chapters/edit/10.1201/9780849382284-12/millimeter-wave-radar-principles-applications-felix-yanovsky.
[7]J. Deng, L. Huang, “Synthetic Aperture Radar Image Compression Based on Low-Frequency Rejection and Quality Map Guidance,” Remote Sensing, 2024, vol. 16(5), 891. doi: 10.3390/rs16050891.
[8]C. Schwartz, I. Sander, F. Bruhn, M. Persson, J. Ekblad, C. Fuglesang, “Satellite Image Compression Guided by Regions of Interest,” Sensors, 2023, vol. 23(2), 730. doi: 10.3390/s23020730.
[9]F. J. Yanovsky, A.C.P. Oude Nijhuis, O.A. Krasnov, C.M.H. Unal, H.W.J. Russchenberg, A. Yarovoy, “Turbulence Intensity Estimation Using Advanced Radar Methods,” Proceedings European Radar Conference (EuRAD 2015), Paris, France, pp. 141-144. doi: 10.1109/EuRAD.2015.7346257.
[10]O. Sushchenko, et al., “Algorithm of determining errors of gimballed inertial navigation system,” In: O. Gervasi, et al. (eds.) Computational Science and Its Applications – ICCSA 2024 Workshops. ICCSA 2024. Lecture Notes in Computer Science, vol. 14816, 2024, pp. 206–218. doi: 10.1007/978-3-031-65223-3_14.
[11]R. B. Sinitsyn, F. J. Yanovsky, “Acoustic Noise Atmospheric Radar with Nonparametric Copula Based Signal Processing,” Telecommunications and Radio Engineering, Vol. 71, No. 4, 2012, pp. 327–335. doi: 10.1615/TelecomRadEng.v71.i4.30.
[12]F. J. Yanovsky, “Evolution and Prospects of Airborne Weather Radar Functionality and Technology,” 2005 18th International Conference on Applied Electromagnetics and Communications, Dubrovnik, Croatia, 2005, pp. 1-4, doi: 10.1109/ICECOM.2005.204987.
[13]B. Bross, J. Chen, J. -R. Ohm, G. J. Sullivan, Y. -K. Wang, “Developments in International Video Coding Standardization After AVC, With an Overview of Versatile Video Coding (VVC),” Proceedings of the IEEE, 2021, vol. 109, no. 9, pp. 1463-1493. doi: 10.1109/JPROC.2020.3043399.
[14]V.V. Lukin, S.S. Krivenko, M.K. Chobanu, O.O. Kolganova, “Acceleration and Efficiency Analysis of DCT-based Filtering”, Telecommunications and Radio Engineering, 2013, vol. 72, no 7, pp. 613–626.
[15]V. Shutko, M. Shutko, L. Tereshchenko, M. Zaliskyi, I. Silantieva, “Two-Dimensional Spectral Detector for Baggage Inspection X-ray System”, CEUR Workshop Proceedings, 2018, vol. 2300, pp. 63–66.
[16]S. Han, B. Mo, J. Zhao, J. Xu, S. Sun, B. Jin, “High-Quality Image Compression Algorithm Design Based on Unsupervised Learning,” Sensors, 2024, vol. 24(20), 6503. doi: 10.3390/s24206503.
[17]O. Arefieva, Z. Poberezhna, S. Petrovska, S. Arefiev, Y. Kopcha, “Devising approaches to modeling enterprise business processes under conditions of modern digital technologies,” Eastern-European Journal of Enterprise Technologies, vol. 1, no. 13(127), 2024, pp. 69–79. doi: 10.15587/1729-4061.2024.298143.
[18]R. B. Sinitsyn and F.J. Yanovsky, “Copula ambiguity function for wideband random radar signals,” 2011 IEEE International Conference on Microwaves, Communications, Antennas, (COMCAS 2011), Tel Aviv, Israel, 2011, pp. 1-4, doi: 10.1109/COMCAS.2011.6105843.
[19]F. J. Yanovsky, H. W. J. Russchenberg, L. P. Ligthart and V. S. Fomichev, “Microwave Doppler-polarimetric technique for study of turbulence in precipitation,” IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120), Honolulu, HI, USA, 2000, pp. 2296-2298 vol.5, doi: 10.1109/IGARSS.2000.858387.
[20]F. J. Yanovsky, H. W. J. Russchenberg and C. M. H. Unal, “Retrieval of information about turbulence in rain by using Doppler-polarimetric Radar” in IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 2, pp. 444-450, Feb. 2005, doi: 10.1109/TMTT.2004.840772.
[21]S. Smerichevskyi, Z. Poberezhna, I. Kryvovyazyuk, L. Ivanenko, D. Malnov, “Formation of principles of a customer-oriented approach by transport enterprises in conditions of sustainable development,” E3S Web of Conferences. International Scientific and Practical Conference Innovations in Construction and Smart Building Technologies for Comfortable, Energy Efficient and Sustainable Lifestyle, 2024, vol. 534. doi: 10.1051/e3sconf/202453401022.
[22]T. S. Rappaport, Wireless Communications: Principles and Practice, Prentice Hall communications engineering and emerging technologies series, Prentice Hall, 2002, 126 p.
[23]P. J. Van Fleet, Discrete Wavelet Transformations: An Elementary Approach with Applications. 2nd ed. Wiley, Hoboken, 2019.
[24]E. Liflyand, Harmonic Analysis on the Real Line. Pathways in Mathematics. Birkhäuser, Cham, 2021.
[25]G. Kaiser, A Friendly Guide to Wavelets. Birkhäuser, Boston, 2011.
[26]D. R. Larson, “Unitary systems and wavelet sets,” In: T. Qian, M.I. Vai, Y. Xu, (eds) “Wavelet analysis and applications. Applied and numerical harmonic analysis,” Birkhäuser, Basel, 2007, pp. 143–171. doi: 10.1007/978-3-7643-7778-6_14.
[27]Y. Meyer, Wavelets and Operators, Cambridge, UK: Cambridge University Press, 2009.
[28]R. Gençay, F. Selçuk, B. Whitcher, An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, San Diego, Academic Press, 2002.
[29]S.G. Mallat, A Wavelet Tour of Signal Processing, 3rd edition. Academic Press, 2009.
[30]P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Transactions on Communication, 1983, vol. Com-3l, no. 4, pp. 532-540.
[31]R. Starosolski, “New and Specialized Methods of Image Compression,” Journal of Imaging, 2022, vol. 8(2), 48. doi: 10.3390/jimaging8020048.
[32]V.-I. Ungureanu, P. Negirla, A. Korodi, “Image-Compression Techniques: Classical and “Region-of-Interest-Based” Approaches Presented in Recent Papers,” Sensors, 2024, vol. 24(3), 791. doi: 10.3390/s24030791.
[33]I. A. Urbaniak, “Using Compressed JPEG and JPEG2000 Medical Images in Deep Learning: A Review,” Applied Sciences, 2024, vol. 14(22), 10524. doi: 10.3390/app142210524.
[34]S. K. Deb, W. D. Pan, “Quantum Image Compression: Fundamentals, Algorithms, and Advances,” Computers, 2024, vol. 13(8), 185. doi: 10.3390/computers13080185.
[35]M. Trigka, E. Dritsas, “A Comprehensive Survey of Deep Learning Approaches in Image Processing,” Sensors, 2025, vol. 25(2), 531. doi: 10.3390/s25020531.
[36]F. Yanovsky, “Specified for air safety, monitoring atmospheric phenomena including the volcano dust,” Proceedings, 11th International Radar Symposium IRS-2010, Vol.1, pp.1-4.
[37]S.W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing, 2023.
[38]D. Taubman, M. Marcellin, JPEG2000 Image Compression Fundamentals, Standards and Practice: Image Compression Fundamentals, Standards and Practice. Springer Science & Business Media, 2012.
[39]F. I. Yanovskij, V.A. Panits, “Application of an antenna with controlled polarization for the detection of hail and icing zones,” Izvestiya VUZ: Radioelektronika, 1996, vol. 39 (10), pp. 32–42.
[40]S. Jamil, Md. J. Piran, M. Rahman, O.-J. Kwon, “Learning-driven lossy image compression: A comprehensive survey,” Engineering Applications of Artificial Intelligence. 2023, vol. 123, part B, 106361. doi: 10.1016/j.engappai.2023.106361.
[41]D. Mishra, S. K. Singh, R. K. Singh, “Deep Architectures for Image Compression: A Critical Review,” Signal Processing. 2022, vol. 191, 108346, doi: 10.1016/j.sigpro.2021.108346.
[42]M. Li, W. Zuo, S. Gu, J. You, D. Zhang, “Learning Content-Weighted Deep Image Compression,” IEEE Transactions on Pattern Analysis and Machine Intelligence. 2021, vol. 43, no. 10, pp. 3446-3461. doi: 10.1109/TPAMI.2020.2983926.
[43]H. Zhang, C. Jung, X. Liu, “Frequency-aware learned image compression using channel-wise attention and restormer,” IEEE Access. 2025, vol. 13, pp. 70436-70445. doi: 10.1109/ACCESS.2025.3559937.
[44]K. Yang, et al., “A deep learning-based image compression method for remote sensing-based infrastructure monitoring,” Array. 2026, vol. 30, 100905. doi: 10.1016/j.array.2026.100905.
[45]C.-H. Huang, J.-L. Wu, “Unveiling the Future of Human and Machine Coding: A Survey of End-to-End Learned Image Compression,” Entropy. 2024, vol. 26(5), 357. doi: 10.3390/e26050357.
[46]A. Skodras, C. Christopoulos, T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Processing Magazine, 2001, vol. 18(5), pp. 36–58.
[47]D. Taubman, E. Ordentlich, M. Weinberger, G. Seroussi, I. Ueno, F. Ono, “Embedded block coding in JPEG2000,” Proceedings 2000 International Conference on Image Processing, Vancouver, BC, Canada, 2000, vol. 2, pp. 33–36. doi: 10.1109/ICIP.2000.899218.
[48]G. J. Sullivan, J.-R. Ohm, W.-J. Han, T. Wiegand, “Overview of the High Efficiency Video Coding (HEVC) Standard,” IEEE Transactions on Circuits and Systems for Video Technology, 2012, vol. 22, no. 12, pp. 1649–1668. doi: 10.1109/TCSVT.2012.2221191.
[49]A. Bjelopera, S. Grgić, “Scalable video coding extension of H.264/AVC,” Proceedings ELMAR-2012, Zadar, Croatia, 2012, pp. 7–12.
[50]M. I. Patel, S. Suthar, J. Thakar, “Survey on image compression using machine learning and deep learning,” 2019 International Conference on Intelligent Computing and Control Systems (ICCS), Madurai, India, 2019, pp. 1103–1105. doi: 10.1109/ICCS45141.2019.9065473.
[51]W. Gao, L. Xie, S. Fan, G. Li, S. Liu, W. Gao, “Deep learning-based point cloud compression: An in-depth survey and benchmark,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025, vol. 47, no. 11, pp. 10731–10752. doi: 10.1109/TPAMI.2025.3594355.
[52]T. Lindeberg, “A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time,” Biological Cybernetics, 2023, vol. 117 (1–2), pp. 21–59. doi:10.1007/s00422-022-00953-6.
[53]V. V. Haines, A. G. Jones, “Logarithmic Fourier Transform,” Geophysical Journal, 1988, vol. 92, pp.171–178. doi: 10.1111/j.1365-246X.1988.tb01131.x.
[54]A. C. Bovik, The Essential Guide to Video Processing, Academic Press, 2009, 355 p.
[55]D. Le Gall, A. J. Tabatabai, “Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques,” In: International Conference on Acoustics, Speech, and Signal Processing, 1988, vol. 2, pp. 761–764. doi: 10.1109/ICASSP.1988.196696.
[56]A. Said, W. A. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Transactions on Circuits and Systems for Video Technology, 1996, vol. 6, no. 3, pp. 243–250. doi: 10.1109/76.499834.
[57]M. Unser, T. Blu, “Mathematical properties of the JPEG2000 wavelet filters,” IEEE Transactions on Image Processing, 2003, vol. 12, no. 9, pp. 1080–1090. doi:10.1109/TIP.2003.812329.
[58]C. S. Swartz, Understanding Digital Cinema: A Professional Handbook. Taylor & Francis, 2005, 147 p.

International Journal of Image, Graphics and Signal Processing (IJIGSP)