Leveraging SVD for efficient image compression and robust digital watermarking
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Abstract
In terms of digital files, compression is the act of encoding information using fewer bits than what’s found in the original file. When we say image compression, we have in mind an image that has fewer bytes than the original image but has the most important features that describe the original image. So, the aim of image compression is to reduce the image size without degrading image quality below an acceptable threshold. In MATLAB, an image is stored as a matrix. One approach is to apply the Singular Values Decomposition (SVD) to the image matrix. This method is implemented in MATLAB. In order to divide the matrix of the given image into three other matrices in MATLAB, we can use the function svd(). As performance metrics, we can use PSNR and Compression ratio. Digital Watermarking is defined as the process of hiding a piece of digital data in the cover data which is to be protected and extracted later for ownership verification. In an SVD-based watermarking scheme, the singular values of the cover image are modified to embed the watermark data. All tests and experiments are performed using MATLAB as the computing environment and programming language. Also, in the RStudio programming language we can see the implementation of the SVD method in image compression.
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References
Martin, C. D., & Porter, M. A. (2012). The extraordinary SVD. The American Mathematical Monthly, 119(10), 838-851. https://doi.org/10.4169/amer.math.monthly.119.10.838
Trefethen, L. N. (1992). The definition of numerical analysis. Cornell University.
Baksalary, O. M., & Trenkler, G. (2021). The Moore–Penrose inverse: a hundred years on a frontline of physics research. The European Physical Journal H, 46, 1-10.
Comon, P. (2002). Tensor Decompositions, State of the Art and Applications. Mathematics in Signal Processing. Oxford University Press.
De Lathauwer, L., & De Moor, B. (1998). From matrix to tensor: Multilinear algebra and signal processing. Institute of Mathematics and its Applications Conference Series, 67, 1-16. Oxford University Press.
Sidiropoulos, N. D., Bro, R., & Giannakis, G. B. (2000). Parallel factor analysis in sensor array processing. IEEE Transactions on Signal Processing, 48(8), 2377-2388. https://doi.org/10.1109/78.852018
Vasilescu, M. A. O., & Terzopoulos, D. (2002). Multilinear analysis of image ensembles: Tensorfaces. In Computer Vision—ECCV 2002: 7th European Conference on Computer Vision Copenhagen, Denmark, May 28–31, 2002 Proceedings, Part I 7, 447-460. https://doi.org/10.1007/3-540-47969-4_30
Vasilescu, M. A. O., & Terzopoulos, D. (2002). Multilinear image analysis for facial recognition. 2002 International Conference on Pattern Recognition, 2, 511-514. https://doi.org/10.1109/ICPR.2002.1048350
Vasilescu, M. A. O., & Terzopoulos, D. (2003). Multilinear subspace analysis of image ensembles. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings, 2, 93-99. https://doi.org/10.1109/CVPR.2003.1211457
Savas, B., & Eldén, L. (2007). Handwritten digit classification using higher order singular value decomposition. Pattern Recognition, 40(3), 993-1003. https://doi.org/10.1016/j.patcog.2006.08.004
Kolda, T. G., Bader, B. W., & Kenny, J. P. (2005). Higher-order web link analysis using multilinear algebra. Fifth IEEE International Conference on Data Mining (ICDM'05). https://doi.org/10.1109/ICDM.2005.77
Mucha, P. J., Richardson, T., Macon, K., Porter, M. A., & Onnela, J. P. (2010). Community structure in time-dependent, multiscale, and multiplex networks. Science, 328(5980), 876-878.
https://doi.org/10.1126/science.1184819
Elakkiya, S., & Thivya, K. S. (2022). Comprehensive review on lossy and lossless compression techniques. Journal of The Institution of Engineers (India): Series B, 103(3), 1003-1012. https://doi.org/10.1007/s40031-021-00686-3
Chahal, P. K., Singh, A., & Singh, P. (2013). Digital Watermarking Techniques. International Journal of Computers &Amp; Technology, 11(8), 2903–2909. https://doi.org/10.24297/ijct.v11i8.3009
Tan, L., Zeng, Y., & Zhang, W. (2019). Research on image compression coding technology. Journal of Physics: Conference Series, 1284(1), 012069. https://doi.org/10.1088/1742-6596/1284/1/012069
Gordani, O., & Simoni, A. (2023). The application of SVD method in image compression and digital watermarking. Advanced Engineering Days (AED), 8, 100-102.