Distributions of audio DCT coefficients

doi:10.7523/j.issn.2095-6134.2011.6.008

Abstract

Abstract:

Considering the non-gaussian property of discrete cosine transform(DCT) coefficients of audio and the limitation of modeling the DCT coefficient distribution with a single distribution such as generalized gaussian distribution(GGD) or alpha stable distribution, we propose a mixed model. This mixed model is a linearly weighted average of GGD and alpha stable distribution, while the weight values are obtained using a genetic algorithm. The model accuracy is measured with the Kullback-Leibler Divergence, a metric for evaluating the difference between two probability distributions. Experiment results show that the mixed model is close to the true distribution of DCT coefficients and is of practical use in the field of audio retrieval and steganalysis.

Key words: DCT, mixture model, generalized Gaussian distribution, alpha stable distribution, genetic algorithm, KL divergence

CLC Number:

TP391

WANG Cui-Ping, GUO Li, WANG Yu-Jie, CHEN Yun-Bi. Distributions of audio DCT coefficients[J]. , 2011, 28(6): 752-758.

References

[1] Ma Y P, Han J Q. Audio watermarking in DCT: embedding strategy and algorithm
[J]. Chinese Journal of Electronics, 2006, 34(7): 1260-1264(in Chinese). 马翼平, 韩纪庆. DCT域音频水印:嵌入对策和算法
[J]. 电子学报, 2006, 34(7): 1260-1264.

[2] Wang Q S, Sun S H. A novel algorithm for embedding watermarks into digital audio signals
[J]. Acta Acustica, 2001, 26(5): 464-467(in Chinese). 王秋生, 孙圣和. 一种在数字音频信号中嵌入水印的新算法
[J]. 声学学报, 2001, 26(5): 464-467.

[3] Ma Y P, Han J Q. Choice approach for embedding position of audio watermarking in the DCT domain
[J]. Computer Science, 2005, 32(11): 139-141(in Chinese). 马翼平, 韩纪庆. DCT 域音频水印算法的嵌入位置选择策略
[J]. 计算机科学, 2005, 32(11): 139-141.

[4] Zhou Z P, Zhou L H. A novel algorithm for robust audio watermarking based on quantification DCT domain //Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing. Kaohsiung, 2007: 441-444.

[5] Liu Q, Sung A, Qiao M. Spectrum steganalysis of WAV audio streams //Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition. 2009: 582-593.

[6] Li C, Zeng W, Ai H, et al. Steganalysis of spread spectrum hiding based on DWT and GMM //International Conference on Networks Security, Wireless Communications and Trusted Computing Wuhan. 2009: 240-243.

[7] Liu Q, Sung A, Qiao M. Temporal derivative-based spectrum and mel-cepstrum audio steganalysis
[J]. IEEE Transactions on Information Forensics and Security, 2009, 4(3): 359-368.

[8] Liu S, Ma L, Yao H X, et al. Universal steganalysis based on statistical models using reorganization of block-based DCT coefficients //Fifth International Conference on Information Assurance and Security. Xi'an, 2009:778-781.

[9] Reininger R, Gibson J. Distributions of the two-dimensional DCT coefficients for images
[J]. IEEE Transactions on Communications, 1983, 31(6): 835-839.

[10] Lam E, Goodman J. A mathematical analysis of the DCT coefficient distributions for images
[J]. IEEE Transactions on Image Processing, 2000, 9(10): 1661-1666.

[11] Muller F. Distributions shape of two-dimensional DCT coefficients for nature images
[J]. Electronics Letters, 1993, 29(22): 1935-1936.

[12] Tanabe N, Farvardin N. Subband image coding using entropy-coded quantization over noisy channels
[J]. IEEE Journal on Selected Areas in Communications, 1992, 10(5): 926-943.

[13] Eude T, Grkel R. On the distribution of the DCT coefficients //International Conference on Acoustics, Speech, and Signal Processing, ICASSP-94. Adelaide, 1994 (5):365-368.

[14] Yu R, Xiao L, Rahardja S, et al. A statistics study of the MDCT coefficient distribution for audio //IEEE International Conference on Multimedia and Expo,2004, ICME'04. Taipei, 2004, 2: 1483-1486.

[15] Yaroslavsky L, Wang Y. DFT, DCT, MDCT, DST and signal fourier spectrum analysis //European Signal Processing Conference. Finlande, 2000: 1065-1068.

[16] Sharifi K, Leon-Garcia A. Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video
[J]. IEEE Transactions on Circuits and Systems for Video Technology, 1995, 5(1): 52-56.

[17] Do M, Vetterli M. Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance
[J]. IEEE Transactions on Image Processing, 2002, 11(2): 146-158.

[18] Nolan J. Maximum likelihood estimation and diagnostics for stable distributions
[M]. Lévy Processes: Theory and Applications, 2001: 379-400.

[19] Nolan J. Parameterizations and modes of stable distributions
[J]. Statistics & Probability Letters, 1998, 38(2): 187-195.

[20] Bilmes J. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models . U C Berkely, TR-97-021, 1998.

[21] Houck C, Joines J, Kay M. A genetic algorithm for function optimization: a Matlab implementation //NCSU-IE TR95-09. 1995.