ANALYSIS OF THE POSSIBILITY OF USING THE SINGULAR VALUE DECOMPOSITION IN IMAGE COMPRESSION

Edyta ŁUKASIK; Emilia ŁABUĆ

doi:10.35784/acs-2022-28

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Published: Dec 3, 2022

DOI: https://doi.org/10.35784/acs-2022-28

DOI

https://doi.org/10.35784/acs-2022-28

Authors

Edyta ŁUKASIK

e.lukasik@pollub.pl

Department of Computer Science, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Lublin,

Emilia ŁABUĆ

e.lukasik@pollub.pl

Department of Computer Science, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Lublin

Abstract

In today’s highly computerized world, data compression is a key issue to minimize the costs associated with data storage and transfer. In 2019, more than 70% of the data sent over the network were images. This paper analyses the feasibility of using the SVD algorithm in image compression and shows that it improves the efficiency of JPEG and JPEG2000 compression. Image matrices were decomposed using the SVD algorithm before compression. It has also been shown that as the image dimensions increase, the fraction of eigenvalues that must be used to reconstruct the image in good quality decreases. The study was carried out on a large and diverse set of images, more than 2500 images were examined. The results were analyzed based on criteria typical for the evaluation of numerical algorithms operating on matrices and image compression: compression ratio, size of compressed file, MSE, number of bad pixels, complexity, numerical stability, easiness of implementation.

Keywords:

singular value decomposition, JPEG2000, JPEG, discrete wavelet transform, discrete cosine transform

References

Anutam, & Rajni. (2014). Comparative Analysis of Filters and Wavelet Based Thresholding Methods for Image Denoising. Computer Science & Amp; Information Technology (CS &Amp; IT ) (pp. 137–148). https://doi.org/10.5121/csit.2014.4515 DOI: https://doi.org/10.5121/csit.2014.4515

Arps, R., & Truong, T. (1994). Comparison of international standards for lossless still image compression. Proceedings of the IEEE, 82(6), 889–899. https://doi.org/10.1109/5.286193 DOI: https://doi.org/10.1109/5.286193

Bovik, A. C. (2009). The Essential Guide to Image Processing (1st ed.). Academic Press. DOI: https://doi.org/10.1016/B978-0-12-374457-9.00001-9

Britanak, V., Yip, P. C., & Rao, K. (2007). CHAPTER 4 – Fast DCT/DST Algorithms. Discrete Cosine and Sine Transforms. General Properties, Fast Algorithms and Integer Approximations (pp. 73–140). Academic Press. https://doi.org/10.1016/b978-012373624-6/50006-0 DOI: https://doi.org/10.1016/B978-012373624-6/50006-0

Cao, L. (2006). SVD applied to digital image processing. Division of Computing Studies, Arizona State University Polytechnic Campus.

Chen, Y., Mukherjee, D., Han, J., Grange, A., Xu, Y., Parker, S., Chen, C., Su, H., Joshi, U., Chiang, C. H., Wang, Y., Wilkins, P., Bankoski, J., Trudeau, L., Egge, N., Valin, J. M., Davies, T., Midtskogen, S., Norkin, A., de Rivaz, P., Design, A., & Liu, Z. (2020). An Overview of Coding Tools in AV1: the First Video Codec from the Alliance for Open Media. APSIPA Transactions on Signal and Information Processing, 9(1), e6. https://doi.org/10.1017/atsip.2020.2 DOI: https://doi.org/10.1017/ATSIP.2020.2

Compton, E. A., & Ernstberger, S. L. (2020). Singular Value Decomposition: Applications to Image Processing. Lagrange College. Journal of Undergraduate Research, 17, 99–105.

Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2005). Wprowadzenie do algorytmów. Wydawnictwo Naukowe PWN.

Davies, E. R. (2017). Computer Vision: Principles, Algorithms, Applications, Learning. Elsevier Gezondheidszorg. Dhawan, S. (2011). A Review of Image Compression and Comparison of its Algorithms. https://www.semanticscholar.org/paper/A-Review-of-Image-Compression-and-Comparison-of-itsDhawan/034dcf50d99bbd9870c5c2e67201f6d792f96a5f

Dumka, A., Ashok, A., Verma, P., & Verma, P. (2020). Advanced Digital Image Processing and Its Applications in Big Data (1st ed.). CRC Press. DOI: https://doi.org/10.1201/9780429351310

Gandhi, T., Patel, H., & Prajapati, D. (2015). Image Compression Using Fractal: Image compression based upon the self-similarities present in the image. LAP LAMBERT Academic Publishing.

Gong, L., Deng, C., Pan, S., & Zhou, N. (2018). Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform. Optics &Amp; Laser Technology, 103, 48–58. https://doi.org/10.1016/j.optlastec.2018.01.007 DOI: https://doi.org/10.1016/j.optlastec.2018.01.007

Hoffman, R. (1997). Data Compression in Digital Systems. Springer Publishing. DOI: https://doi.org/10.1007/978-1-4615-6031-9

Hoffman, R. (2012). Data Compression in Digital Systems. Springer Publishing.

Jackson, D., & Hannah, S. (1993). Comparative analysis of image compression techniques. 1993 (25th) Southeastern Symposium on System Theory (pp. 513–517). IEEE. https://doi.org/10.1109/ssst.1993.522833 DOI: https://doi.org/10.1109/SSST.1993.522833

Jankowska, J., & Jankowski, M. (1988). Przegląd metod i algorytmów numerycznych. Wydawnictwa Naukowo-Techniczne.

Jinchuang, Z., Yan, T., & Wenli, F. (2009). Research of image compression based on Wireless visual sensor networks. 4th International Conference on Computer Science & Education (pp. 353–356). IEEE. https://doi.org/10.1109/iccse.2009.5228430 DOI: https://doi.org/10.1109/ICCSE.2009.5228430

Karwowski, D. (2019). Zrozumieć kompresję obrazu: podstawy technik kodowania stratnego oraz bezstratnego obrazów. Damian Karwowski.

Kostrikin, A. I. (2004). Wstęp do algebry cz. 1 i cz. 2 Podstawy algebry. Wydawnictwo Naukowe PWN.

Lu, Z., & Guo, S. (2016). Lossless Information Hiding in Images (1st ed.). Syngress. DOI: https://doi.org/10.1016/B978-0-12-812006-4.00001-2

Mammeri, A., Hadjou, B., & Khoumsi, A. (2012). A Survey of Image Compression Algorithms for Visual Sensor Networks. International Scholarly Research Notices, 2012, 760320. https://doi.org/10.5402/2012/760320 DOI: https://doi.org/10.5402/2012/760320

Miano, J. (1999). Compressed Image File Formats: JPEG, PNG, GIF, XBM, BMP. Addison-Wesley Professional.

Murray, J. D., & VanRyper, W. (1996). Encyclopedia of Graphics File Formats. O’Reilly & Associates.

Nasri, M., Helali, A., Sghaier, H., & Maaref, H. (2010). Energy-efficient wavelet image compression in Wireless Sensor Network. 2010 International Conference on Wireless and Ubiquitous Systems (pp. 1–7). IEEE. https://doi.org/10.1109/icwus.2010.5670430 DOI: https://doi.org/10.1109/ICWUS.2010.5670430

Nixon, M., & Aguado, A. (2019). Feature Extraction and Image Processing for Computer Vision (4th ed.). Academic Press. DOI: https://doi.org/10.1016/B978-0-12-814976-8.00003-8

Parekh, D. (2021, April 25). Image Compression Standards | Digital Image Processing [Video file]. YouTube. https://www.youtube.com/watch?v=6IuKH7IGspU

Pratt, W., Kane, J., & Andrews, H. (1969). Hadamard transform image coding. Proceedings of the IEEE, 57(1), 58–68. https://doi.org/10.1109/proc.1969.6869 DOI: https://doi.org/10.1109/PROC.1969.6869

Pu, I. M. (2005). Fundamental Data Compression (1st ed.). Butterworth-Heinemann. DOI: https://doi.org/10.1016/B978-075066310-6/50004-0

Salomon, D., Motta, G., & Bryant, D. (2007). Data Compression: The Complete Reference. Springer Publishing.

Sayood, K. (2002). Lossless Compression Handbook. Elsevier Gezondheidszorg. DOI: https://doi.org/10.1201/9781420041163-101

Shih, C. W., Chu, H. C., Chen, Y. M., & Wen, C. C. (2012). The effectiveness of image features based on fractal image coding for image annotation. Expert Systems With Applications, 39(17), 12897–12904. https://doi.org/10.1016/j.eswa.2012.05.003 DOI: https://doi.org/10.1016/j.eswa.2012.05.003

Short, M. N., Manohar, M., & Tilton, J. C. (1994). Planning/Scheduling Techniques for VQ-Based Image Compression. Science Information Management and Data Compression Workshop. 1994 Science Information Management and Data Compression Workshop (pp. 95–104). US Government.

Shukla, K. K., & Prasad, M. V. (2011). Lossy Image Compression: Domain Decomposition-Based Algorithms. Springer Publishing. DOI: https://doi.org/10.1007/978-1-4471-2218-0

Stewart, G. W. (2001). Matrix Algorithms: Volume 2, Eigensystems (1st ed.). SIAM: Society for Industrial and Applied Mathematics. DOI: https://doi.org/10.1137/1.9780898718058

Swathi, H. R., Sohini, S., Surbhi, & Gopichand, G. (2017). Image compression using singular value decomposition. IOP Conference Series: Materials Science and Engineering, 263, 042082. https://doi.org/10.1088/1757-899x/263/4/042082 DOI: https://doi.org/10.1088/1757-899X/263/4/042082

Tanwar, S., Ramani, T., & Tyagi, S. (2018). Dimensionality Reduction Using PCA and SVD in Big Data: A Comparative Case Study. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (pp. 116–125). Springer. https://doi.org/10.1007/978-3-319-73712-6_12 DOI: https://doi.org/10.1007/978-3-319-73712-6_12

Wayner, P. (1999). Compression Algorithms for Real Programmers. Elsevier Gezondheidszorg. What’s the difference between ‘visually lossless’ and real lossless and what does this mean for future encodes? (2019, May 18). Video Production Stack Exchange. Retrieved May 2022 from https://video.stackexchange.com/questions/27656/whats-the-difference-between-visually-lossless-andreal-lossless-and-what-doe

Xiao, F., Zhang, P., Sun, L. J., Wang, J., & Wang, R. C. (2011). Research on image compression and transmission mechanism for wireless multimedia sensor networks. 2011 International Conference on Electrical and Control Engineering (pp. 788–791). IEEE. https://doi.org/10.1109/iceceng.2011.6057601 DOI: https://doi.org/10.1109/ICECENG.2011.6057601

ŁUKASIK, E., & ŁABUĆ, E. (2022). ANALYSIS OF THE POSSIBILITY OF USING THE SINGULAR VALUE DECOMPOSITION IN IMAGE COMPRESSION. Applied Computer Science, 18(4), 53–67. https://doi.org/10.35784/acs-2022-28

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