Fourier Transforms in Image Compression: How Math Powers JPEG and MP3 Files
Abstract
The use of Fourier Transforms for Image and Audio Compression is described in the research paper, specifically for their applications in JPEG and MP3. Compression of images removes redundant data, optimizing storage and transmission effectiveness, while compression of audio limits the inaudible frequencies in order to retain perceptual quality. The study cross-checks the mathematical foundation of the Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT), founded on their performance in converting components of signals into frequencies for purposes of compression. Two databases, an audio (Royalty-Free Audio) and an image (Live1-Classic5-BSDS500) database are used. Fourier-based compression techniques are employed by research study. The performances are verified using measures such as Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM). Outcomes indicate that increased compression ratios reduce file size without sacrificing sufficient quality, and that SSIM will increase with increasing Bits Per Pixel (BPP). The article identifies Fourier Transform-based compression as the best way to reconcile data reduction with perceptual/aoustic accuracy. Additionally, the research identifies current gaps in terms of areas of future work such as AI-improvement and live optimization on power-constrained hardware.
Downloads
References
S. Dhawan, "A review of image compression and comparison of its algorithms," Int. J. Electron. Commun. Technol., vol. 2, no. 1, pp. 22–26, 2011.
C. Christopoulos, A. Skodras, and T. Ebrahimi, "The JPEG2000 still image coding system: An overview," IEEE Trans. Consum. Electron., vol. 46, no. 4, pp. 1103–1127, Nov. 2000.
M. Stirner and G. Seelmann, "Improved redundancy reduction for JPEG files," in Proc. Picture Coding Symp. (PCS 2007), Nov. 2007.
A. Ennaciri, M. Erritali, M. Mabrouki, and J. Bengourram, "Comparative study of wavelet image compression: JPEG2000 standard," Indones. J. Electr. Eng. Comput. Sci., vol. 16, no. 1, pp. 83–90, 2015.
Gallagher, Thomas A., Alexander J. Nemeth, and Lotfi Hacein-Bey. "An introduction to the Fourier transform: relationship to MRI." American journal of roentgenology 190, no. 5 (2008): 1396-1405.
S. L. Brunton and J. N. Kutz, Data-driven science and engineering: Machine learning, dynamical systems, and control, Cambridge, U.K.: Cambridge Univ. Press, 2019.
Salman, Diaa. "Optimized Image Compression Using Sparse Representations and Fourier Transform." East Journal of Engineering 1, no. 1 (2025): 62-75.
Tran, Trac D. "Modern transform design for practical audio/image/video coding applications." In Signal Processing and Machine Learning Theory, pp. 495-536. Academic Press, 2024.
Podgorelec, David, Damjan Strnad, Ivana Kolingerová, and Borut Žalik. "State-of-the-Art Trends in Data Compression: COMPROMISE Case Study." Entropy 26, no. 12 (2024): 1032.
Basheer, Muhammed, S. K. Ramya, A. Durai Ganesh, Brinda Halambi, and L. S. Geethanjali. "COMPLEX ANALYSIS METHODS FOR IMAGE AND SIGNAL PROCESSING."
Tola, Krisel L. "Comparative study of compression functions in modern web programming languages." In 2023 International Conference on Electromechanical and Energy Systems (SIELMEN), pp. 1-5. IEEE, 2023.
Xue, Xingsi, Raja Marappan, Sekar Kidambi Raju, Rangarajan Raghavan, Rengasri Rajan, Osamah Ibrahim Khalaf, and Ghaida Muttashar Abdulsahib. "Modelling and analysis of hybrid transformation for lossless big medical image compression." Bioengineering 10, no. 3 (2023): 333.
Shukla, Neha. "Review on DCT based Binary Arithmetic Coders Approach for Image Compression."
Pinto, A. C., M. D. Maciel, M. S. Pinho, R. R. Medeiros, and A. O. Moraes. "Evaluation of lossy compression algorithms using discrete cosine transform for sounding rocket vibration data." Measurement Science and Technology 34, no. 1 (2022): 015117.
KLEPÁRNÍK, PETR. "On-the-fly compression in time-domain ultrasound simulations."
Zieliński, Tomasz P., and Tomasz P. Zieliński. "Image Processing." Starting Digital Signal Processing in Telecommunication Engineering: A Laboratory-based Course (2021): 439-482.
A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, 2nd ed., John Wiley & Sons, Inc. Hoboken, New Jersey, 2009.
The Scientist and Engineer's Guide to Digital Signal Processing (Chapter 12), 1997. Retrieved March 2010, from http://www.dspguide.comlchI2/2.htrn.
N. Ahmed, et al., "Discrete cosine transform," IEEE transactions on Computers, vol. C-23, no. 1, pp. 90-93, 1974.
Novamizanti, L., Budiman, G., and Astuti, E. N. F., "Robust audio watermarking based on transform domain and SVD with compressive sampling framework," TELKOMNIKA Telecommunication, Computing, Electronics and Control, vol. 18, no. 2, pp. 1079-1088, 2020
D. Salomon and G. I. Motta, "Handbook of Data Compression," Springer, 5th Edition, 2010.
https://www.kaggle.com/datasets/darshan1504/royaltyfree-audio-dataset
https://www.kaggle.com/datasets/mingyuouyang/live1-valid-dataset-fullsize
Downloads
Published
Issue
Section
License
Copyright (c) 2025 International Journal of Scientific Research in Computer Science, Engineering and Information Technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
