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Fast 2-D 8×8 discrete cosine transform algorithm for image coding

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Abstract

A new fast two-dimension 8×8 discrete cosine transform (2D 8×8 DCT) algorithm based on the characteristics of the basic images of 2D DCT is presented. The new algorithm computes each DCT coefficient in turn more independently. Hence, the new algorithm is suitable for 2D DCT pruning algorithm of pruning away any number of high-frequency components of 2D DCT. The proposed pruning algorithm is more efficient than the existing pruning 2D DCT algorithms in terms of the number of arithmetic operations, especially the number of multiplications required in the computation.

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References

  1. Pennebaker W B, Mitchell J L. JPEG Still Image Data Compression Standard. New York: Van Nostrand Reinhold, 1993

    Google Scholar 

  2. Mitchell J L, Pennebaker W B, Fogg C E, et al. MPEG Video Compression Standard. New York: Chapman and Hall, 1997

    Google Scholar 

  3. Feig E, Winograd S. Fast algorithms for the discrete cosine transform. IEEE Trans Signal Process, 1992, 40(9): 2174–2193

    Article  MATH  Google Scholar 

  4. Leoffler C, Ligtenberg A, Moschytz G S. Practical fast 1D DCT algorithms with 11 mutiplications. In: Proc. IEEE ICASSP, 1989, 2: 988–991

    Google Scholar 

  5. Lee B G. A new algorithm to compute the discrete cosine transform. IEEE Trans Acoustic, Speech, Signal Process, 1984, 32(12): 1243–1245

    MATH  Google Scholar 

  6. Chen WH, Smith C H, Fralick S C. A fast computational algorithm for the discrete cosine transform. IEEE Trans Commun, 1977, 25(9): 1004–1009

    Article  MATH  Google Scholar 

  7. Ahmed N, Natarajan T, Rao K R. Discrete cosine transform. IEEE Trans Comput, 1974, 23(1): 90–93

    Article  MATH  MathSciNet  Google Scholar 

  8. Vetterli M, Nussbaumer H. Simple FFT and DCT algorithms with reduced number of operations. Signal Process, 1984, 6:267–278

    Article  MathSciNet  Google Scholar 

  9. Suehiro N, Hateri M. Fast algorithms for the DFT and other sinusoidal transforms. IEEE Trans Acoustic, Signal, and Speech Process, 1986, 34(6): 642–644

    Article  Google Scholar 

  10. Arai Y, Agui T, Nakajima M. A fast DCT-SQ scheme for images. Trans IEICE, 1988, 71(11): 1095–1097

    Google Scholar 

  11. Hou H S. A fast recursive algorithm for computing the discrete cosine transform. IEEE Trans Acoustic, Speech, Signal Process, 1987, 35(10): 1445–1461

    Google Scholar 

  12. Duhamel P, Guillemot C. Polynomial transform computation of 2-D DCT. In: Proc. ICASSP, 1990. 1515–1518

  13. Kamanagar F A, Rao K R. Fast algorithms for the 2-D discrete cosine transform. IEEE Trans Comput, 1982, 31(9): 899–906

    Article  Google Scholar 

  14. Huang Y M, Wu J L. A refined fast 2-D discrete cosine transform algorithm. IEEE Trans Signal Process, 1999, 47(3): 904–907

    Article  MATH  MathSciNet  Google Scholar 

  15. Skodras A N. Direct transform to computation. IEEE Signal Process Lett, 1999, 6: 202–204

    Article  Google Scholar 

  16. Liang J. Fast multiplierless approximations of the DCT with the lifting scheme. IEEE Trans Signal Process, 2001, 49(12): 3032–3044

    Article  Google Scholar 

  17. Cho N I, Lee S U. A fast 4×4 algorithm for the recursive 2-D DCT. IEEE Trans Signal Process, 1992, 40(9): 2166–2173

    Article  MATH  Google Scholar 

  18. Cho N I, Lee S U. Fast algorithm and implementation of 2-D discrete cosine transform. IEEE Trans Circuits Syst, 1991, 38: 297–305

    Article  Google Scholar 

  19. Chan S C, Ho K L. A new two-dimensional fast cosine transform. IEEE Trans Signal Process, 1991, 39: 481–485

    Article  MATH  Google Scholar 

  20. Ma C. A fast recursive two-dimensional cosine transform. In: Proc SPIEInt Soc Opt Eng, 1988. 541–548

  21. Vetterli M. Fast 2-D discrete cosine transform. In: Proc. ICASSP, 1985. 1538–1541

  22. Duhamel P, Guillemot C. Polynomial transform computation of 2-D DCT. In: Proc. ICASSP, 1990. 1515–1518

  23. Skodras A N. Fast discrete cosine transform pruning. IEEE Trans Signal Process, 1994, 42(7): 1833–1837

    Article  Google Scholar 

  24. Wang Z. Pruning the fast discrete cosine transform. IEEE Trans Commun, 1991, 39(5): 640–643

    Article  Google Scholar 

  25. Huang Y, Wu J, Chang C. A generalized output pruning algorithm for matrix-vector multiplication and its application to computing pruning discrete cosine transform. IEEE Trans Signal Process, 2000, 48(2): 561–563

    Article  MATH  MathSciNet  Google Scholar 

  26. Walmsley N P, Skodras A N, Curtis K M. A fast picture compression technique. IEEE Trans Consum Elect, 1994, 40(1):11–19

    Article  Google Scholar 

  27. Christopoulos C A, Skodras A N. Pruning the two-dimensional fast cosine transform. In: Proceedings of the VII European Signal Processing Conference (EUSIPCO), Edinburgh, Scotland, UK, 1994. 596–599

  28. Silva A, Navarro A. Fast 8×8 DCT pruning algorithm. In: IEEE International Conference on Image Processing, 2005, 2: 317–320

    Google Scholar 

  29. Ji X H, Zhang C M. A fast IDCT algorithm for image decompression. Chinese J Comput, 2005, 28(12): 2079–2088

    MathSciNet  Google Scholar 

  30. Ji X H. Fast DCT algorithm for low bit-rate image compression. Chinese J Comput-aided Design & Comput Graph, 2004, 16(10): 1355–1359

    Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong Economic University, Jinan, 250014, China

    XiuHua Ji, CaiMing Zhang, JiaYe Wang & S. H. Boey

  2. School of Computer Science and Technology, Shandong University, Jinan, 250061, China

    XiuHua Ji & CaiMing Zhang

Authors
  1. XiuHua Ji
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  2. CaiMing Zhang
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  3. JiaYe Wang
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  4. S. H. Boey
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Correspondence to XiuHua Ji.

Additional information

Supported by the National Basic Research Program of China (Grant No. 2006CB303102), the National Natural Science Foundation of China (Grant Nos. 60573114, 60533030 and 60573181)

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Ji, X., Zhang, C., Wang, J. et al. Fast 2-D 8×8 discrete cosine transform algorithm for image coding. Sci. China Ser. F-Inf. Sci. 52, 215–225 (2009). https://doi.org/10.1007/s11432-009-0038-4

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  • DOI: https://doi.org/10.1007/s11432-009-0038-4

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