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Medical Image Compression Scheme Using Number Theoretic Transform

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Computer Vision and Machine Intelligence in Medical Image Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 992))

Abstract

In this paper, a new methodology is proposed for the medical image compression using number theoretic transforms or NTTs. NTTs are the discrete Fourier transforms carried over finite fields and rings. All the arithmetic operations are carried over a modulo number M. From the review of NTTs and their variants, it is found that NTTs involve only real integers, and the transform is reversible and hence no round-off errors in NTT-based algorithms. Another attractive feature is that NTTs of regular structures are also regular. These factors lay the foundation for the proposed lossless compression scheme of medical images. The variant of NTT known as Fermat number transform (FNT) is used for the proposed compression scheme as it involves less or no multiplications. The results obtained are favorable in terms of compression ratio and reduced number of computations. Further study and research is in progress to optimize the algorithm in terms of computations and hardware implementation of NTTs for real medical images. It is forecasted that with the use of dedicated hardware and optimization of these digital transforms, much higher compression ratio at faster speed may be achieved.

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References

  1. Jain, A.K.: Fundamentals of Digital Image Processing, 2nd edn

    Google Scholar 

  2. Jain, A.K.: Image data compression: a review. Proc. IEEE 69, 349–389 (1981)

    Article  Google Scholar 

  3. Useitch, B.: A tutorial on modern lossy wavelet image compression, foundations of JPEG 2000, IEEE Signal Process. Mag. (2001)

    Google Scholar 

  4. Wallace, G.: The JPEG still picture compression standard. IEEE Trans. Consum. Electron. (1991)

    Google Scholar 

  5. Xiong, Z., Ramchandran, K., Orchard, M.T., Zhang, Y.-Q.: A comparative study of DCT and wavelet based image coding. IEEE Trans. Circuits Syst. Video Technol. 9(5) (1999)

    Google Scholar 

  6. Said, A., Pearlman, W.: A new fast and efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. Circuits Syst. Video Technol. (1996)

    Google Scholar 

  7. Wohlberg, B., de Jager, G.: A review of the fractal image coding literature. IEEE Trans. Image Process. 8(12) (1999)

    Article  MathSciNet  Google Scholar 

  8. Iano, Y., da Silva, F.S., Cruz, A.L.M.: A fast and efficient hybrid fractal-wavelet image coder. IEEE Trans. Image Process 15(1) (2006)

    Article  Google Scholar 

  9. Miaou, S.-G., Keand, F.-S., Chen, S.-C.:A lossless compression method for medical image sequences using JPEG—LS and interframe coding. IEEE Trans. Inf. Technol. Bio Med. 13(5) (2009)

    Google Scholar 

  10. Rabbani, M., Joshi, R.: An overview of the JPEG2000 still image compression standard. Signal Process. Image Commun. (2002)

    Google Scholar 

  11. Pollard, J.M.: The fast fourier transform in a finite field. Math. Comput. 25, 365–374 (1971)

    Article  MathSciNet  Google Scholar 

  12. Rabiner, L.R., Gold B.: Theory and Application of Digital Signal Processing, pp. 419–433. Prentice-Hall, London (19751)

    Google Scholar 

  13. Agarwal, R.C, Cooley, J.W.: New algorithms for digital convolution. IEEE Trans. ASSP-25 106–124 (1977)

    Google Scholar 

  14. Gudvangen, S., Buskerud, H.: Practical Applications of Number Theoretic Transforms. AUI, EMR, Kongsberg, Norway

    Google Scholar 

  15. Siu, W.C.: Number theoretic transform and its applications to digital signal processing. In: Proceedings of IERE HK Section Workshop on Adv. Micro, and DSP, Hong Kong, pp. 76–10 (1982)

    Google Scholar 

  16. Agarwall, R.C., Burrus, C.S.: Fast convolution using Fermat number transform with application to digital filtering. ibid. ASSP-22, pp. 87–97 (1974)

    Google Scholar 

  17. Rader, C.M., Discrete convolution via Mersenne transform. IEEETrans. C-21, 1269–1273 (1972)

    Google Scholar 

  18. Agarwal, R.C., Burrus, C.S.: Number theoretic transforms to implement fast digital convolution. In: Proceedings of the IEEE, vol. 63, pp. 550–560 (1975)

    Article  MathSciNet  Google Scholar 

  19. Veg, E., Leibowitz, L.M.: Fast complex convolution using number theoretic transforms, p. 7935. Naval Research Lab, Washington, DC (1975)

    Google Scholar 

  20. Toivonen, T., Heikkila, J.: Video filtering with Fermat number theoretic transforms using residue number system. IEEE Trans. Circuits Syst. Video Technol. 16(1) (2006)

    Article  Google Scholar 

  21. Conway, R.: Modified overlap technique using Fermat and Mersenne transforms. IEEE Trans. Circuits Syst.-II: Express Briefs, 53(8) (2006)

    Article  Google Scholar 

  22. Tamori, H.: Asymmetric fragile watermarking using a number theoretic transform. IEICE Trans. Fundam. E92-A(3) (2009)

    Article  Google Scholar 

  23. Pedrouzo-Ulloa, A., Troncoso-Pastoriza, J.R., Pérez-González, F.: Number theoretic transforms for secure signal processing. IEEE Trans. Info. Forensics Secur. 12(5) (2017)

    Article  Google Scholar 

  24. Boussakta, S. Shakaff, A.Y., Marir, F., Holt, A.G.J.: Number theoretic transforms of periodic structures and their applications. In: IEE Proceedings, vol. 135. Pt. G (1988)

    Google Scholar 

  25. Hegde, S., Nagapadma, R.: Lossless compression scheme for regular images. IJCA 158(9), 7–12 (2017)

    Article  Google Scholar 

  26. Nicholson, P.J.: Algebraic theory of finite fourier transforms. J. Comput. Syst. Sci. 5, 524–527 (1971)

    Article  MathSciNet  Google Scholar 

  27. Eskicioglu, M., Fisher, P.S.: Image quality measures and their performance. IEEE Trans. Commun. 43(12), 2959–2965 (1995)

    Article  Google Scholar 

  28. Truong, T.K., Yeh, C.S., Reed, I.S., Chang, J.J.: VLSI design of number theoretic transforms for a fast convolution. In: Proceedings of the IEEE International Conference on Compute Design, VLSl in Computing, ICCD, New York. U.S.A, pp. 200–203 (1983)

    Google Scholar 

  29. Towers, P.J., Pajayakrit, A., Holt, A.G.J.: Cascadable NMOS VLSl circuit for implementing a fast convolution using Fermat number transforms. In: IEE Proceedings of the G Electronic Circuits and Systems, vol. 134, no. 2, pp. 57–66 (1987)

    Google Scholar 

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Acknowledgements

This research is carried out at research Lab, NIE, Mysore. We would like to thank Dr. Narasimha Koulgoud, Professor, Department of ECE, NIE, Mysore, INDIA, for his valuable suggestions.

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Authors and Affiliations

  1. NIE Institute of Technology, Mysore, India

    Salila Hegde

  2. National Institute of Engineering, Mysore, India

    Rohini Nagapadma

Authors
  1. Salila Hegde
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  2. Rohini Nagapadma
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Corresponding author

Correspondence to Salila Hegde .

Editor information

Editors and Affiliations

  1. Department of Computer Applications, Sikkim Manipal Institute of Technology, East Sikkim, Sikkim, India

    Mousumi Gupta

  2. Department of Computer Science and Engineering, Sikkim Manipal Institute of Technology, East Sikkim, Sikkim, India

    Debanjan Konar

  3. Department of Information Technology, RCC Institute of Information Technology, Kolkata, West Bengal, India

    Siddhartha Bhattacharyya

  4. Machine Intelligence Unit, Indian Statistical Institute, Kolkata, West Bengal, India

    Sambhunath Biswas

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Hegde, S., Nagapadma, R. (2020). Medical Image Compression Scheme Using Number Theoretic Transform. In: Gupta, M., Konar, D., Bhattacharyya, S., Biswas, S. (eds) Computer Vision and Machine Intelligence in Medical Image Analysis. Advances in Intelligent Systems and Computing, vol 992. Springer, Singapore. https://doi.org/10.1007/978-981-13-8798-2_5

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