Image Compression: Combination of Discrete Transformation and Matrix Reduction

Authors

  • Mardin A Anwer Department of Software and Informatics Engineering, Salahaddin University, IRAQ-KRG
  • Anwar DA Department of Computer science and information technology, Salahaddin University, IRAQ-KRG
  • Anwer SA Department of IT, Erbil Technology Institute, IRAQ-KRG

Keywords:

minimize matrix size, huffman coding, DWT, DCT

Abstract

nowadays, compressing large data using different compression methods increase rapidly. This explains the recent importance and popularity of compressing data of multimedia applications as well as wavelet transforms in this field. Wavelet transforms tend to benefit of block-based transforms, including the Discrete Cosine Trans-form (DCT). DCT is responsible for displaying blocking artifacts while wavelets have compact support and can offer a DCT an adaptable substitute to DCT. The popularity of single-wavelets, formed through converting and expanding of single approximation functions as well as detail functions, offered high multi-resolution function-approximation bases. This paper discusses the idea of the image compression using two levels DWT with two-dimensional DCT on every 8x8 block. Hence, the low-frequency sub-band is reduced. The DC-Column stores the DC-coefficients. As a result of using Huffman coding the DC-Column will be coded. Meanwhile the other AC-Coefficient has to be quantized in order to gain additional zeros, allowing it to be converted easily to bits through the Huffman coding. HL2, HH2, as well as LH2 are other high-frequencies coefficients that are coded using the Minimize-Matrix-Size Algorithm. The mentioned proposed algorithm converts the three high-frequency coefficients into a single real number. Nevertheless, the use of the proposed algorithm; one-dimensional-array that has many real values will be reduced and will be converted it to many bits. The results of the compression algorithm are based on Mean Square Error ( MSE).

References

Tsai, M. & Hung, H., “ DCT and DWT based image watermarking using sub sampling”. In Proceeding of the 2005 IEEE Fourth International Conference on Machine Learning and Cybernetics, China (pp. 5308–5313). 2005.

Grigorios, D., Zervas, N. D., Sklavos, N., & Goutis, C. E “ Design techniques and implementation of low power high-throughput discrete wavelet transform tilters for jpeg 2000 standard”. WASET International Journal of Signal Processing, 4(1), 36–43,2008.

Sayood, K. “ Introduction to data compression (2nd ed.) ”. Morgan Kaufman Publishers: Academic Press.Google Scholar, 2000.

Esakkirajan, S., Veerakumar, T., Senthil Murugan, V., & Navaneethan, P. “ Image compression using multiwavelet and multi-stage vector quantization”. WASET International Journal of Signal Processing, 4(4), 524–531. 2008.

ShivlalMewada, Umesh Kumar Singh, "Measurement Based Performance of Reactive and Proactive Routing Protocols in WMN ", International journal of Advance Research in Computer science and software Engineering,Volume-1,Issue-1, December 2011.

Navpreet Saroya , Prabhpreet Kaur “Analysis Of Image Compression Algorithm Using DCT And DWT Transforms” International Journal of Advanced Research in Computer Science and Software Engineering 4(2), pp. 897-900, February – 2014.

Mohammed Mustafa Siddeq, “ Using Two Levels DWT with Limited Sequential Search Algorithm for Image Compression”,Journal of Signal and Information Processing,3, 51-62 doi:10.4236/jsip.2012.

M.M. Siddeq and M.A. Rodrigues, “ A New 2D Image Compression Technique for 3D Surface Reconstruction ”, 18th International Conference on Circuits, Systems, Communications and Computers, Santorin Island, Greece: 379-386, 2014a

M.M. Siddeq and M.A. Rodrigues, “ A Novel Image Compression Algorithm for high resolution 3D Reconstruction ”, 3D Research-Springer Vol. 5 No.2.DOI 10.1007/s13319-014-0007-6, 2014b.

M.M. Siddeqand RODRIGUES, Marcos, “ Applied sequential-search algorithm for compression-encryption of high-resolution structured light 3D data ”. In: BLASHKI, Katherine and XIAO, Yingcai, (eds.)MCCSIS : Multi-conference on Computer Science and Information Systems 2015. IADIS Press, 195-202, 2015a

M.M. Siddeq and RODRIGUES, Marcos, “ A novel 2D image compression algorithm based on two levels DWT and DCT transforms with enhanced minimize-matrix-size algorithm for high resolution structured light 3D surface reconstruction”. 3D Research-Springer, 6 (3), p. 26. DOI 10.1007/s13319-015-0055-6, 2015b

Downloads

Published

2025-11-11

How to Cite

[1]
A. Mardin A, D. A. Anwar, and S. A. Anwer, “Image Compression: Combination of Discrete Transformation and Matrix Reduction”, Int. J. Comp. Sci. Eng., vol. 5, no. 1, pp. 1–6, Nov. 2025.

Issue

Vol. 5 No. 1 (2017): IJCSE January Edition

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit and that in the event of reuse or distribution, the terms of this license are made clear.