Lossy Image Compression Using Karhunen-Loeve Transform Based Methods

Year 2022, Volume: 9 Issue: 2, 424 - 435, 31.05.2022

Serkan Keser

https://doi.org/10.31202/ecjse.951417

Abstract

In this paper, we discuss image compression techniques based on the eigenvector matrices used the Karhunen-Loeve Transform (KLT) is obtained. Two novel methods are proposed for the grouping of eigenvectors via vector quantization in the KLT subspace. Various codebook sizes are tested for image compression purposes. The first grouping approach uses eigenvectors of autocorrelation matrices for geometrically clustering into fewer numbers of vectors. In this approach, the quantization is performed using principal component directions of the eigenvector matrices. The second approach has used the eigenvectors according to their usage frequencies. The qualities of reconstructed test images are compared with DCT based JPEG and Wavelet Transform based JPEG2000 compression methods using the PSNR metric. Experimental results show that the proposed methods, particularly the second method, give plausible and competitive results.

Keywords

Image compression, eigenvector clustering, codebooks, KLT

Karhunen-Loeve Dönüşümüne Dayalı Yöntemleri Kullanarak Kayıplı Görüntü Sıkıştırma

Abstract

Bu yazıda, Karhunen-Loeve Dönüşümü (KLT) kullanılarak elde edilen özvektör matrislerine dayalı görüntü sıkıştırma teknikleri tartışılmaktadır. KLT alt uzayında vektör niceleme yoluyla özvektörlerin gruplandırılması için iki yöntem önerilmiştir. Görüntü sıkıştırma amaçları için çeşitli kod kitabı boyutları test edilir. İlk gruplama yaklaşımı, geometrik olarak daha az sayıda vektöre kümeleme için otokorelasyon matrislerinin özvektörlerini kullanır. Bu yaklaşımda nicemleme, özvektör matrislerinin temel bileşen yönleri kullanılarak gerçekleştirilir. İkinci yaklaşım, özvektörleri kullanım frekanslarına göre kullanmıştır. Yeniden oluşturulmuş test görüntülerinin nitelikleri, PSNR metriği kullanılarak DCT tabanlı JPEG ve Wavelet Dönüşümü tabanlı JPEG2000 sıkıştırma yöntemleriyle karşılaştırılır. Deneysel sonuçlar, önerilen yöntemlerin, özellikle ikinci yöntemin makul ve rekabetçi sonuçlar verdiğini göstermektedir.

Keywords

Görüntü sıkıştırma, öz vektör kümeleme, kod kitapları, KLT

References

• [1]. Anil Kumar Katharotiya, Swati Patel, Mahesh Goyani, “Comparative Analysis between DCT & DWT Techniques of Image Compression”. Journal of Information Engineering and Applications, Vol. 1, No. 2, 2011.
• [2]. CLARKE, Roger John. Transform coding of images. Astrophysics, 1985.
• [3]. Ahmed, N., Natarajan, T., Rao, K. R., 1974. Discrete cosine transform. IEEE transactions on Computers. 100(1), 90-93.
• [4]. Roy A.B., Dey D., Mohanty B. and Banerjee D. Comparison of FFT, DCT, DWT, WHT compression techniques on electro cardiogram and photo plethysmography signals. Int. J. Comp. Appl. 2012; 975-888.
• [5]. W. B. Pennebaker and J. L. Mitchell, “JPEG –Still Image Data Compression Standard,”Newyork: International Thomsan Publishing, 1993.
• [6]. Singh H, Sharma S. Hybrid image compression using DWT, DCT and Huffman encoding techniques. Int J Emerg Technol Adv Eng 2012; 2: 300-306.
• [7]. Goyal, V. K., 2001. Theoretical foundations of transform coding. IEEE Signal Processing Magazine. 18(5), 9-21.
• [8]. A. Oliva and A. Torralba, (2001) "Modeling the shape of the scene: a holistic representation of the spatial envelope," International Journal of Computer Vision, vol. 42, no. 3, pp. 145-175.
• [9]. Xie Y, Jing X, Sun S, Hong L. A fast and low complicated image compression algorithm for predictor of JPEG-LS. In IEEE IC-NIDC, 2009; 353-356.
• [10]. Skodras, A., Christopoulos, C., Ebrahimi, T., 2001. The JPEG 2000 still image compression standard. IEEE Signal processing magazine. 18(5), 36-58.
• [11]. Chuanwei S, Quanbin L, Jingao L. The study of digital image compression based on wavelets. ICALIP 2010.
• [12]. Ruey-Feng Chang and Wei-Ming Chen, Adaptive Edge-Based Side-Match Finite-State Classified Vector Quantization with Quadtree Map, IEEE Transactions on Image Processing, Vol. 5, No. 2, pp. 378-383, 2001
• [13]. Keser, S., Gerek, Ö. N., Seke, E., and Gülmezoğlu, M. B. (2017). A subspace based progressive coding method for speech compression. Speech Communication, 94, 50-61.
• [14]. Walaa M, Abd E, Wajeb G. Color image compression algorithm based on DCT blocks. Int. J.Comp. Sci. Issue 2012; 9: 323-328.
• [15]. Zhang SQ, Zhang SF, Wang XN, Wang Y. The image compression method based on adaptive segment and adaptive quantified. IEEE Icicic 2008; 8: 353-353.
• [16]. Jain, A. K.,2010. Data clustering: 50 years beyond K-means. Pattern recognition letters. 31(8), 651-666.
• [17]. Hartung, F., & Girod, B. (1998). Watermarking of uncompressed and compressed video. Signal processing, 66(3), 283-301.
• [18]. L. Fei-Fei and P. Perona, (2005) "A bayesian hierarchical model for learning natural scene categories," in In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, volume 2, pages 524–531, Washington, DC, USA, 2005., Washington, DC, USA.
• [19]. Das, Dipankar. "Scene classification using pyramid histogram of multi-scale block local binary pattern." Int. J. Comput. Sci. Appl. (IJCSA) 4.4 (2014): 15-25.
• [20]. S. Lazebnik, C. Schmid and J. Ponce, (2006) "Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories," in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, New York, NY, USA.
• [21]. Waldemar, P., & Ramstad, T. A. (1997, April). Hybrid KLT-SVD image compression. In 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (Vol. 4, pp. 2713-2716). IEEE.
• [22]. Kassim, A. A., & Lee, W. S. (2003). Embedded color image coding using SPIHT with partially linked spatial orientation trees. IEEE Transactions on Circuits and Systems for Video Technology, 13(2), 203-206.
• [23]. Ashin, R., Morimoto, A., & Vaillancourt, R. (2005). Image compression with multiresolution singular value decomposition and other methods. Mathematical and Computer Modelling, 41(6-7), 773-790.
• [24] Blanes, I., & Serra-Sagristà, J. (2010). Pairwise orthogonal transform for spectral image coding. IEEE Transactions on Geoscience and Remote Sensing, 49(3), 961-972.