×

zbMATH — the first resource for mathematics

Invertible integer DCT algorithms. (English) Zbl 1030.65144
The paper presents two new algorithms for the integer DCT-II (discrete cosine transform) and integer DCT-IV of radix-2 length. Then it estimates the worst case error between the resulting vectors of the exact DCT and the corresponding integer DCT. Some numerical experiments for the integer DCT-II of length 8 and for the 2-dimensional integer DCT-II of size \(8\times 8\) are also presented.

MSC:
65T50 Numerical methods for discrete and fast Fourier transforms
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65G50 Roundoff error
Software:
binDCT
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bhaskaran, V.; Konstantinides, K., Images and video compression standards: algorithms and architectures, (1997), Kluwer Boston
[2] Calderbank, A.R.; Daubechies, I.; Sweldens, W.; Yeo, B.L., Wavelet transforms that map integers to integers, Appl. comput. harmon. anal., 5, 332-369, (1998) · Zbl 0941.42017
[3] Cham, W.K.; Yip, P.C., Integer sinusoidal transforms for image processing, Internat. J. electron., 70, 1015-1030, (1991)
[4] Y.-J. Chen, S. Oraintara, T.Q. Nguyen, Integer discrete cosine transform Int-DCT, Univ. Boston, Preprint, 2000
[5] Chen, Y.-J.; Oraintara, S.; Tran, T.D.; Amaratunga, K.; Nguyen, T.Q., Multiplierless approximation of transforms using lifting scheme and coordinate descent with adder constraint, (), 3136-3139
[6] Cheng, L.Z.; Xu, H.; Luo, Y., Integer discrete cosine transform and its fast algorithm, Electron. lett., 37, 64-65, (2001)
[7] Daubechies, I.; Sweldens, W., Factoring wavelet transforms into lifting steps, J. Fourier anal. appl., 4, 247-269, (1998) · Zbl 0913.42027
[8] Komatsu, K.; Sezaki, K., Reversible discrete cosine transform, (), 1769-1772
[9] Komatsu, K.; Sezaki, K., 2D lossless discrete cosine transform, (), 466-469
[10] Liang, J.; Tran, T.D., Fast multiplierless approximations of the DCT: the lifting scheme, IEEE trans. signal process., 49, 3032-3044, (2001)
[11] Loeffler, C.; Lightenberg, A.; Moschytz, G., Practical fast 1-d DCT algorithms with 11 multiplications, (), 988-991
[12] Marcellin, M.W.; Gormish, M.J.; Bilgin, A.; Boliek, M.P., An overview of JPEG-2000, (), 523-541
[13] Philips, W., Lossless DCT for combined lossy/lossless image coding, (), 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 · Zbl 1036.65118
[16] Rao, K.R.; Yip, P., Discrete cosine transform: algorithms, advantages, applications, (1990), Academic Press Boston · Zbl 0726.65162
[17] U. Schreiber, Fast and numerically stable trigonometric transforms (in German), Thesis, Univ. Rostock, 1999
[18] Strang, G., The discrete cosine transform, SIAM rev., 41, 135-147, (1999) · Zbl 0939.42021
[19] Tran, T.D., The bindct: fast multiplierless approximation of the DCT, IEEE signal process. lett., 7, 141-144, (2000)
[20] Wallace, G.K., The JPEG still picture compression standard, Comm. ACM, 34, 32-44, (1991)
[21] Zeng, Y.; Cheng, L.; Bi, G.; Kot, A.C., Integer DCTs and fast algorithms, IEEE trans. signal process., 49, 2774-2782, (2001) · Zbl 1369.65195
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.