Invertible integer DCT algorithms

Applied and Computational Harmonic Analysis

Volumn 15, Issue 1, 2003, Pages 70-88

  Plonka, Gerlind ^a   Tasche, Manfred ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

Data compression; Discrete cosine transform; Error estimate; Factorization of cosine matrix; Integer DCT; Invertible integer DCT; Lifting matrix; Lossless coding; Rounding off; Worst case error

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COSINE TRANSFORMS; MATRIX ALGEBRA;

FACTORIZATION; PERMUTATIONS;

IMAGE COMPRESSION;

EID: 0242657786     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1063-5203(03)00032-0     Document Type: Article

References (21)

1. V. Bhaskaran, K. Konstantinides, Images and Video Compression Standards: Algorithms and Architectures, Kluwer, Boston, 1997.
2. A.R. Calderbank, I. Daubechies, W. Sweldens, B.L. Yeo, Wavelet transforms that map integers to integers, Appl. Comput. Harmon. Anal. 5 (1998) 332-369.
3. W.K. Cham, P.C. Yip, Integer sinusoidal transforms for image processing, Internat. J. Electron. 70 (1991) 1015-1030.
4. Y.-J. Chen, S. Oraintara, T.Q. Nguyen, Integer discrete cosine transform Int-DCT, Univ. Boston, Preprint, 2000.
5. Y.-J. Chen, S. Oraintara, T.D. Tran, K. Amaratunga, T.Q. Nguyen, Multiplierless approximation of transforms using lifting scheme and coordinate descent with adder constraint, in: Proc. IEEE Internat. Conf. Acoust. Speech Signal Process., Vol. 3, 2002, pp. 3136-3139.
6. L.Z. Cheng, H. Xu, Y. Luo, Integer discrete cosine transform and its fast algorithm, Electron. Lett. 37 (2001) 64-65.
7. I. Daubechies, W. Sweldens, Factoring wavelet transforms into lifting steps, J. Fourier Anal. Appl. 4 (1998) 247-269.
8. K. Komatsu, K. Sezaki, Reversible discrete cosine transform, in: Proc. IEEE Internat. Conf. Acoust. Speech Signal Process., 1998, pp. 1769-1772.
9. K. Komatsu, K. Sezaki, 2D lossless discrete cosine transform, in: Proc. IEEE Internat. Conf. Image Process., 2001, pp. 466-469.
10. J. Liang, T.D. Tran, Fast multiplierless approximations of the DCT: The lifting scheme, IEEE Trans. Signal Process. 49 (2001) 3032-3044.
11. C. Loeffler, A. Lightenberg, G. Moschytz, Practical fast 1-d DCT algorithms with 11 multiplications, in: Proc. IEEE Internat. Conf. Acoust. Speech Signal Process., Vol. 2, 1989, pp. 988-991.
12. M.W. Marcellin, M.J. Gormish, A. Bilgin, M.P. Boliek, An overview of JPEG-2000, in: Proc. Data Compression Conf., 2000, pp. 523-541.
13. W. Philips, Lossless DCT for combined lossy/lossless image coding, in: Proc. IEEE Internat. Conf. Image Process., Vol. 3, 1998, pp. 871-875.
14. G. Plonka, M. Tasche, Split-radix algorithms for discrete trigonometric transforms, Gerhard-Mercator-Univ. Duisburg, Preprint, 2002.
15. G. Plonka, M. Tasche, Integer DCT-II by lifting steps, in: W. Haußmann, K. Jetter, M. Reimer, J. Stöckler (Eds.), Advances in Multivariate Approximation, Birkhäuser, Basel, 2003, in press.
16. K.R. Rao, P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications, Academic Press, Boston, 1990.
17. U. Schreiber, Fast and numerically stable trigonometric transforms (in German), Thesis, Univ. Rostock, 1999.
18. G. Strang, The discrete cosine transform, SIAM Rev. 41 (1999) 135-147.
19. T.D. Tran, The BinDCT: Fast multiplierless approximation of the DCT, IEEE Signal Process. Lett. 7 (2000) 141-144.
20. G.K. Wallace, The JPEG still picture compression standard, Comm. ACM 34 (1991) 32-44.
21. Y. Zeng, L. Cheng, G. Bi, A.C. Kot, Integer DCTs and fast algorithms, IEEE Trans. Signal Process. 49 (2001) 2774-2782.