Image compression techniques aim to reduce redundant information in order
to allow data storage and transmission in an efficient way. In this work, we
propose and analyze a lossy image compression method based on the singular
value decomposition using an optimal choice of eigenvalues and an adaptive
mechanism for block partitioning. Experiments are conducted on several images
to demonstrate the effectiveness of the proposed compression method in
comparison with the direct application of the singular value decomposition.
References
[1]
Cho, Z.-H., Jones, J.P. and Singh, M. (1993) Foundations of Medical Imaging. Wiley, New York.
[2]
Jensen, J.R. and Lulla, K. (1987) Introductory Digital Image Processing: A Remote Sensing Perspective. Geocarto International, 2, 65.
https://doi.org/10.1080/10106048709354084
[3]
Crocker, J.C. and Grier, D.G. (1996) Methods of Digital Video Microscopy for Colloidal Studies. Journal of Colloid and Interface Science, 179, 298-310.
https://doi.org/10.1006/jcis.1996.0217
[4]
Wall, M.E., Rechtsteiner, A. and Rocha, L.M. (2003) Singular Value Decomposition and Principal Component Analysis. In: Berrar, D.P., Dubitzky, W. and Granzow, M., Eds., A Practical Approach to Microarray Data Analysis, Springer, Boston, MA, 91-109. https://doi.org/10.1007/0-306-47815-3_5
[5]
Andrews, H. and Patterson, C. (1976) Singular Value Decompositions and Digital Image Processing. IEEE Transactions on Acoustics, Speech, and Signal Processing, 24, 26-53. https://doi.org/10.1109/TASSP.1976.1162766
[6]
Bhavani, S. and Thanushkodi, K.G. (2013) Comparison of Fractal Coding Methods for Medical Image Compression. IET Image Processing, 7, 686-693.
https://doi.org/10.1049/iet-ipr.2012.0041
[7]
Messaoudi, A. and Srairi, K. (2016) Colour Image Compression Algorithm Based on the DCT Transform Using Difference Lookup Table. Electronics Letters, 52, 1685-1686. https://doi.org/10.1049/el.2016.2115
[8]
Qureshi, M.A. and Deriche, M. (2016) A New Wavelet Based Efficient Image Compression Algorithm Using Compressive Sensing. Multimedia Tools and Applications, 75, 6737-6754. https://doi.org/10.1007/s11042-015-2590-9
[9]
Yao, J. and Liu, G. (2017) A Novel Color Image Compression Algorithm Using the Human Visual Contrast Sensitivity Characteristics. Photonic Sensors, 7, 72-81.
https://doi.org/10.1007/s13320-016-0355-3
[10]
Prakash, A., Moran, N., Garber, S., Dilillo, A. and Storer, J. (2017) Semantic Perceptual Image Compression Using Deep Convolution Networks. 2017 Data Compression Conference, Snowbird, UT, 4-7 April 2017, 250-259.
https://doi.org/10.1109/DCC.2017.56
[11]
David, M., George, T., Michele, C., Troy, C., Nick, J., Joel, S., Hwang, S.J., Vincent, D. and Singh, S. (2017) Spatially Adaptive Image Compression Using a Tiled Deep Network. 2017 IEEE International Conference on Image Processing, Beijing, 17-20 September 2017, 2796-2800. https://doi.org/10.1109/ICIP.2017.8296792
[12]
Zhang, Y., Xu, B. and Zhou, N. (2017) A Novel Image Compression-Encryption Hybrid Algorithm Based on the Analysis Sparse Representation. Optics Communications, 392, 223-233. https://doi.org/10.1016/j.optcom.2017.01.061
[13]
Zhao, C., Zhang, J., Ma, S., Fan, X., Zhang, Y. and Gao, W. (2017) Reducing Image Compression Artifacts by Structural Sparse Representation and Quantization Constraint Prior. IEEE Transactions on Circuits and Systems for Video Technology, 27, 2057-2071. https://doi.org/10.1109/TCSVT.2016.2580399
[14]
Ahanonu, E., Marcellin, M. and Bilgin, A. (2018) Lossless Image Compression Using Reversible Integer Wavelet Transforms and Convolutional Neural Networks. 2018 Data Compression Conference, Snowbird, UT, 27-30 March 2018, 395-395.
https://doi.org/10.1109/DCC.2018.00048
[15]
Toderici, G., Vincent, D., Johnston, N., Hwang, S.J., Minnen, D., Shor, J. and Covell, M. (2017) Full Resolution Image Compression with Recurrent Neural Networks. Conference on Computer Vision and Pattern Recognition, Honolulu, HI, 21-26 July 2017, 5435-5443. https://doi.org/10.1109/CVPR.2017.577
[16]
Baxes, G.A. (1994) Digital Image Processing: Principles and Applications. Wiley, New York.
[17]
Sayood, K. (2017) Introduction to Data Compression. Morgan Kaufmann, Burlington, MA.
[18]
Nelson, M. and Gailly, J.-L. (1996) The Data Compression Book. M & T Books, New York.
[19]
Gonzalez, R.C. and Woods, R.E. (2002) Digital Image Processing.
[20]
Rabbani, M. and Jones, P.W. (1991) Digital Image Compression Techniques. SPIE Press, Bellingham, WA.
[21]
Sharma, M. (2010) Compression Using Huffman Coding. International Journal of Computer Science and Network Security, 10, 133-141.
[22]
Connell, J.B. (1973) A Huffman-Shannon-Fano Code. Proceedings of the IEEE, 61, 1046-1047. https://doi.org/10.1109/PROC.1973.9200
[23]
Gonzales, C.A., Anderson, K.L. and Pennebaker, W.B. (1990) DCT-Based Video Compression Using Arithmetic Coding. Electronic Imaging: Advanced Devices and Systems, Santa Clara, CA, 1990, 305-312. https://doi.org/10.1117/12.19522
[24]
Morita, H. and Kobayashi, K. (1989) An Extension of LZW Coding Algorithm to Source Coding Subject to a Fidelity Criterion. 4th Joint Swedish-Soviet Int. Workshop on Information Theory, Gotland, Sweden, 105-109.
[25]
Pountain, D. (1987) Run-Length Encoding. Byte, 12, 317-319.
[26]
Rabbani, M. and Jones, P.W. (1991) Bit Plane Encoding. In: Digital Image Compression Techniques, SPIE Press, Bellingham, WA, 49-62.
[27]
Jain, A.K. (1981) Image Data Compression: A Review. Proceedings of the IEEE, 69, 349-389. https://doi.org/10.1109/PROC.1981.11971
[28]
De Jager, F. (1952) Delta Modulation, a Method of PCM Transmission Using the 1-Unit Code. Philips Research Reports, 7, 23.
[29]
Schindler, H. (1974) Linear, Nonlinear, and Adaptive Delta Modulation. IEEE Transactions on Communications, 22, 1807-1823.
https://doi.org/10.1109/TCOM.1974.1092119
[30]
Rao, K.R. and Yip, P. (2014) Discrete Cosine Transform: Algorithms, Advantages, Applications. Academic Press, Cambridge, MA.
[31]
Lewis, A.S. and Knowles, G. (1992) Image Compression Using the 2-D Wavelet Transform. IEEE Transactions on Image Processing, 1, 244-250.
https://doi.org/10.1109/83.136601
[32]
Watson, A.B. (1994) Image Compression Using the Discrete Cosine Transform. Mathematica Journal, 4, 81.
[33]
Waldemar, P. and Ramstad, T. (1997) Hybrid KLT-SVD Image Compression. 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, Munich, 21-24 April 1997, 2713-2716.
[34]
Rufai, A.M., Anbarjafari, G. and Demirel, H. (2014) Lossy Image Compression Using Singular Value Decomposition and Wavelet Difference Reduction. Digital Signal Processing, 24, 117-123. https://doi.org/10.1016/j.dsp.2013.09.008
[35]
Wang, Z., Bovik, A.C., Sheikh, H.R. and Simoncelli, E.P. (2004) Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Transactions on Image Processing, 13, 600-612. https://doi.org/10.1109/TIP.2003.819861
[36]
Hu, Y.H. (2018) Public-Domain Test Images.
https://homepages.cae.wisc.edu/~ece533/images/index.html
[37]
Ranade, A., Mahabalarao, S.S. and Kale, S. (2007) A Variation on SVD Based Image Compression. Image and Vision Computing, 25, 771-777.
https://doi.org/10.1016/j.imavis.2006.07.004
