An Image Compression Method Based on Subspace and Downsampling

Year 2023, Volume: 12 Issue: 1, 215 - 225, 22.03.2023

Serkan Keser

https://doi.org/10.17798/bitlisfen.1225312

Cited By: 2

Abstract

In this study, a new Karhunen-Loeve transform based algorithm with acceptable computational complexity is developed for lossy image compression. This method is based on obtaining an autocorrelation matrix by clustering the highly correlated image rows obtained by applying downsampling to the image. The KLT is applied to the blocks created from the downsampled image using the eigenvector (or transform) matrix obtained from the autocorrelation matrix; thus, the transform coefficient matrices are obtained. Then these coefficients were compressed by the lossless coding method. One of the proposed method’s essential features is sufficient for a test image to have one transform matrix, which has low dimensional. While most image compression studies using PCA (or KLT) in the literature are used in hybrid methods, the proposed study presents a simple algorithm that only downsamples images and applies KLT. The proposed method is compared with JPEG, BPG, and JPEG2000 compression methods for the PSNR-HVS and the SSIM metrics. In the results found for the test images, the average PSNR-HVS and SSIM results of the proposed method are higher than JPEG, very close to JPEG2000, and lower than BPG. It has been observed that the proposed method generally gives better results than other methods in images containing low-frequency components with high compression ratios.

Keywords

Image compression, Downsampling, Transform coefficient vectors, KLT

References

• [1] Bhatt, A., Ashutosh, K. B., and Bhatt, K., “Image compression algorithms under JPEG with lapped orthogonal transform and discrete cosine transformation.”, International Journal of Engineering Research and Development, 7(3): 6-10, 2013.
• [2] Katharotiya, A., Patel, S., and Goyani, M., “Comparative Analysis between DCT & DWT Techniques of Image Compression.”, Journal of Information Engineering and Applications, 1(2): 9-17, , 2011.
• [3] Effros, M., and Chou, P. A., “Weighted universal transform coding: Universal image compression with the Karhunen-Loeve transform.” In Proceedings., International Conference on Image Processing, Washington, USA, 61-64, 1995.
• [4] Ahmed, N., Natarajan, T., and Rao, K. R., “Discrete cosine transform.” IEEE transactions on Computers, 100(1): 90-93, 1974.
• [5] Roy A.B., Dey D., Mohanty B. and Banerjee D., “Comparison of FFT, DCT, DWT, WHT compression techniques on electrocardiogram and photo plethysmography signals.” Special Issue of International Journal of Computer Applications (Inte. Conf. on Computing, Communication and Sensor Network, CCSN’2012), 6-11, 2012.
• [6] OH, T. H., and Besar, R., “Medical image compression using JPEG-2000 and JPEG: A comparison study”. Journal of Mechanics in Medicine and Biology, 2(03n04), 313-328, 2002.
• [7] Bharath, K. N., and Padmajadevi, G., “Hybrid compression using dwt-dct and huffman encoding techniques for biomedical image and video applications”. International Journal of Computer Science and Mobile Computing, 2(5), 255-261, 2013.
• [8] Muthukumaran, N., and Ravi, R., “The performances analysis of fast efficient lossless satellite image compression and decompression for wavelet based algorithm”. Wireless Personal Communications, 81(2), 839-859, 2015.
• [9] Ghrare, S.E., and Khobaiz, A.R. “Digital image compression using block truncation coding and Walsh Hadamard transform hybrid technique.” International Conference on Computer, Communications, and Control Technology (I4CT), 477-480, 2014.
• [10] Xie, Y., Jing, X., Sun, S., and Hong, L., “A fast and low complicated image compression algorithm for predictor of JPEG-LS.”, IEEE International Conference on Network Infrastructure and Digital Content, Beijing, China, 353-356, 2009.
• [11] Skodras, A., Christopoulos, C., Ebrahimi, T., “The JPEG 2000 still image compression standard.”, IEEE Signal processing magazine, 18(5): 36-58, 2001.
• [12] Sun, C., Li, Q., and Liu, J., “The study of Digital Image Compression based on wavelets”, International Conference on Audio, Language and Image Processing, Shanghai, China, 312-316, 2010.
• [13] M. A. Engin and B. Cavusoglu, “New Approach in Image Compression: 3D Spiral JPEG,” in IEEE Communications Letters, vol. 15, no. 11, pp. 1234-1236, 2011.
• [14] Ince, I. F., Bulut, F., Kilic, I., Yildirim, M. E., & Ince, O. F. “Low dynamic range discrete cosine transform (LDR-DCT) for high-performance JPEG image compression”. The Visual Computer, 38(5), 1845-1870, 2022.
• [15] Shinde, A. A., and Kanjalkar, P., “The comparison of different transform based methods for ECG data compression.”, International Conference on Signal Processing, Communication, Computing and Networking Technologies, 332-335, 2011.
• [16] Telagarapu, P., Naveen, V. J., Prasanthi, A. L., and Santhi, G. V., “Image compression using DCT and wavelet transformations.”, International Journal of Signal Processing, Image Processing and Pattern Recognition, 4(3): 61-74, 2011.
• [17] Hartung, F., and Girod, B., “Watermarking of uncompressed and compressed video”. Signal processing, 66(3): 283-301, 1998.
• [18] Hofbauer, H., Rathgeb, C., Wagner, J., Uhl, A., and Busch, C., “Investigation of Better Portable Graphics Compression for Iris Biometric Recognition,” 2015 International Conference of the Biometrics Special Interest Group (BIOSIG), Darmstadt, Germany, 1-4, 2015.
• [19] F. Bellard. BPG Image format. http://http://bellard.org/bpg . Access date: 10.06.2019.
• [20] YEE, David, et al. “Medical image compression based on region of interest using better portable graphics (BPG).”, IEEE international conference on systems, man, and cybernetics (SMC), Banff, AB, Canada, 216-221, 2017.
• [21] Sullivan, G. J., Ohm, J. R., Han, W. J., and Wiegand, T., “Overview of the high efficiency video coding (HEVC) standard”. IEEE Transactions on circuits and systems for video technology, 22(12):1649-1668, 2012.
• [22] Chen, Y., Murherjee, D., Han, J., Grange, A., Xu, Y., Liu, Z., and Chiang, C. H., “An overview of core coding tools in the AV1 video codec”. In Picture Coding Symposium (PCS), IEEE, 41-45, 2018.
• [23] A. M. Bruckstein, M. Elad, and R. Kimmel, “Down-scaling for better transform compression,” IEEE Trans. Image Process., 12(9): 1132–1144,2003.
• [24] C. Y. Wang et al., “JPEG-based image coding algorithm at low bit rates with down-sampling and interpolation,” in 4th Int. Conf. On Wireless Communications, Networking and Mobile Computing (WiCOM’08), pp. 1–5, IEEE, Dalian, 1-5, 2008.
• [25] Y. B. Zhang et al., “Interpolation-dependent image downsampling,”IEEE Trans. Image Process. , 20(11): 3291–3296, 2011.
• [26] R. Pournaghi, X. L. Wu, and X. M. Liu, “Low bit-rate image coding via local random down-sampling,” in Picture Coding Symp. (PCS), IEEE, San Jose, California, 329–332, 2013.
• [27] Chen, H., He, X., Ma, M., Qing, L., and Teng, Q., “Low bit rates image compression via adaptive block downsampling and super resolution”. Journal of Electronic Imaging, 25(1): 013004, 2016.
• [28] W. S. Lin and L. Dong, “Adaptive downsampling to improve image compression at low bit rates,” IEEE Trans. Image Process, 15(9): 2513–2521, 2006.
• [29] V. A. Nguyen, Y. P. Tan, and W. S. Lin, “Adaptive downsampling/upsampling for better video compression at low bit rate,” in IEEE Int. Symp. On Circuits and Systems, 1624–1627, 2008.
• [30] Báscones, D., González, C., and Mozos, D., “Hyperspectral image compression using vector quantization, PCA and JPEG2000”. Remote sensing, 10(6), 907, 2018.
• [31] Wang, C. W., and Jeng, J. H., “Image compression using PCA with clustering”. In 2012 International Symposium on Intelligent Signal Processing and Communications Systems IEEE, 458-462, 2012.
• [32] Liu, Y. R., and Kau, L. J., “Scalable face image compression based on Principal Component Analysis and arithmetic Coding”. In 2017 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW), IEEE, 265-266, 2017.
• [33] Vaish, A., and Kumar, M., “WDR coding based image compression technique using PCA”. In 2015 International Conference on Signal Processing and Communication (ICSC), IEEE,360-365, 2015.
• [34] Rafael do Esprito Santo, “Principal Component Analysis applied to digital image compression”, Hospital Israelita Albert Einstein HIAE, Sao Paulo (SP), Brazil, 2012.
• [35] Cheng, Z., Sun, H., Takeuchi, M., and Katto, J., “Deep convolutional autoencoder-based lossy image compression”. In 2018 Picture Coding Symposium (PCS), pp. 253-257, IEEE, 2018.
• [36] BULUT, F., “Huffman Algoritmasıyla Kayıpsız Hızlı Metin Sıkıştırma”. El-Cezeri Journal of Science and Engineering, 3(2), 2016.
• [37] Egiazarian, K., Astola, J., Ponomarenko, N., Lukin, V., Battisti, F., and Carli, M., “New full-reference quality metrics based on HVS.” In Proceedings of the Second International Workshop on Video Processing and Quality Metrics, (4) , 2006.
• [38] Hore, A., and Ziou, D., “Image quality metrics: PSNR vs. SSIM.”, 20th international conference on pattern recognition, Istanbul, Turkey, 2366-2369, 2010.
• [39] Marcellin, M. W., Gormish, M. J., Bilgin, A., and Boliek, M. P. “An overview of JPEG-2000.”, In Proceedings DCC 2000. Data Compression Conference, Snowbird, UT, USA, 523-541, 2000.
• [40] Gonzalez, R. C. and Woods, R. E., Digital Image Processing, 3rd ed., Upper Saddle River, NJ, USA: Prentice-Hall,Inc., 2006.
• [41] P. Brodatz, Textures: A Photographic Album for Artists and Designers. Dover Publications, 1966.
• [42] STex, Salzburg texture image database (STex). Available online at <http://wavelab.at/sources/STex/>, 2009.
• [43] Fei-fei, L., Fergus, R., and Perona, P., “One-shot learning of object categories”. IEEE Trans. PAMI, 2006.