Temporal derivative-based spectrum and mel-cepstrum audio steganalysis

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Temporal Derivative-Based Spectrum and Mel-Cepstrum Audio Steganalysis Qingzhong Liu, Andrew H. Sung, and Mengyu Qiao

Abstract—To improve a recently developed mel-cepstrum audio steganalysis method, we present in this paper a method based on Fourier spectrum statistics and mel-cepstrum coefficients, derived from the second-order derivative of the audio signal. Specifically, the statistics of the high-frequency spectrum and the mel-cepstrum coefficients of the second-order derivative are extracted for use in detecting audio steganography. We also design a wavelet-based spectrum and mel-cepstrum audio steganalysis. By applying support vector machines to these features, unadulterated carrier signals (without hidden data) and the steganograms (carrying covert data) are successfully discriminated. Experimental results show that proposed derivative-based and wavelet-based approaches remarkably improve the detection accuracy. Between the two new methods, the derivative-based approach generally delivers a better performance. Index Terms—Audio, mel-cepstrum, second-order derivative, spectrum, steganalysis, support vector machine (SVM), wavelet.

I. INTRODUCTION TEGANOGRAPHY is the art and science of hiding data in digital media such as image, audio, and video files, etc. To the contrary, steganalysis is the art and science of detecting the information-hiding behaviors in digital media. In recent years, many steganalysis methods have been designed for detecting information-hiding in multiple steganography systems. Most of these methods are focused on detecting digital image steganography. For example, one of the well-known detectors, histogram characteristic function center of mass (HCFCOM), was successful in detecting noise-adding steganography [1]. Another well-known method is to construct the high-order moment statistical model in the multiscale decomposition using wavelet-like transform and then to apply a learning classifier to the high-order feature set [2]. Shi et al. proposed a Markov-process-based approach to detect the information-hiding behaviors in JPEG images [3]. Based on the Markov approach, Liu et al. expanded the Markov features to

S

Manuscript received December 04, 2008; revised May 04, 2009. First published June 10, 2009; current version published August 14, 2009. This work was supported by Institute for Complex Additive Systems Analysis (ICASA), a research division of New Mexico Tech. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Jessica J. Fridrich. Q. Liu and A. H. Sung are with the Department of Computer Science and Engineering and Institute for Complex Additive Systems Analysis, New Mexico Tech, Socorro, NM 87801 USA (e-mail: [email protected]; [email protected]). M. Qiao is with the Department of Computer Science and Engineering, New Mexico Tech, Socorro, NM 87801 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIFS.2009.2024718

the interbands of the discrete cosine transform (DCT) domains and combined the expanded features and the polynomial fitting of the histogram of the DCT coefficients, and successfully improved the steganalysis performance in multiple JPEG images [4]. Other works on image steganalysis have been done by Fridrich [5], Pevny and Fridrich [6], Lyu and Farid [7], Liu and Sung [8], and Liu et al. [9]–[11]. Due to different characteristics of audio signals and images, methods developed for image steganalysis are not directly suitable for detecting information hiding in audio streams, and many research groups have investigated audio steganalysis. Ru et al. presented a method by measuring the features between the signal under detection and a self-generated reference signal via linear predictive coding [12], [13], but the detection performance is poor. Avcibas designed a feature set of content-independent distortion measures for classifier design [14]. Ozer et al. constructed a detector based on the characteristics of the denoised residuals of the audio file [15]. Johnson et al. set up a statistical model by building a linear basis that captures certain statistical properties of audio signals [16]. Craver et al. employed cepstral analysis to estimate a stego-signal’s probability density function in audio signals [17]. Kraetzer and Dittmann recently proposed a mel-cepstrum-based analysis to perform detection of embedded hidden messages [18], [19]. By expanding the Markov approach proposed by Shi et al. for image steganalysis [3], Liu et al. designed expanded Markov features for audio steganalysis [20]. Additionally, Zeng et al. presented new algorithms to detect phase coding steganography based on analysis of the phase discontinuities [21] and to detect echo steganography based on statistical moments of peak frequency [22]. In all these methods, Kraetzer and Dittmann’s proposed mel-cepstrum audio analysis is particularly noticeable, because it is the first time that mel-frequency cepstral coefficients (MFCCs), which are widely used in speech recognition, are utilized for audio steganalysis. In this paper, we propose an audio steganalysis method based on spectrum analysis and mel-cepstrum analysis of the secondorder derivative of audio signal. In spectrum analysis, the statistics of the high-frequency spectrum of the second-order derivative are extracted as spectrum features. To improve Kraetzer and Dittmann’s work [18], we design the features of mel-cepstrum coefficients that are derived from the second-order derivative. Additionally, in comparison to the second-order derivativebased approach, a wavelet-based spectrum and mel-cepstrum method is also designed. Support vector machines (SVMs) with radial basis function (RBF) kernels [35] are employed to detect and differentiate steganograms from innocent signals. Results show that our derivative-based and wavelet-based methods are

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(5) (6) where of the derivatives. We have

and

is the number of samples (7)

Assume that then

is the angle between the vectors

and

,

(8) Since is arbitrary, the expected value of as follows:

is calculated

Fig. 1. Example of edge detection using derivatives [23].

very promising and possess remarkable advantage over Kraetzer and Dittmann’s work. The rest of the paper is organized as follows: Section II presents the second-order derivative for audio steganalysis and the Fourier analysis; Section III introduces Kraetzer and Dittmann’s mel-cepstrum analysis and describes improved mel-cepstrum methods; Section IV presents experiments, followed by discussion in Section V and conclusion in Section VI. II. TEMPORAL DERIVATIVE AND SPECTRUM ANALYSIS In image processing, second-order derivative is widely employed for detecting isolated points, edges, etc. [23]. Fig. 1 shows an example of edge detection by using second-order derivative. With this in mind, we developed a scheme based on the second-order derivative for audio steganalysis, details of which are described as follows. A digital audio signal is denoted as . The second derivative of is , defined as

(1) The stego-signal is denoted , which is modeled by adding into the original signal a noise or error signal (2) The second-order derivatives of error term and signal are denoted as and , respectively. Thus, (3) The discrete Fourier transforms of , are denoted as , , and , respectively,

, and

(9) Divide both sides by (10)

Generally speaking, is far smaller than at low-frequency and middle-frequency components, where the modification caused by the addition of hidden data is negligible. However, the situation changes at high-frequency components. Digital audio signals are generally band-limited, the power spectral density is zero or very close to zero above a certain finite frequency. On the other side, the error term is assumed to be broadband; in such cases, the modification caused by the addition of hidden data is not negligible in high-frequency components. to be a random signal with the expected Assume an error is approximately depicted by a value of zero. The spectrum Gaussian-like distribution [24]. The power is zero at the lowest frequency; as the frequency increases, the spectrum increases. Fig. 2(a) shows a simulated error signal, consisting of 25% for 1s, 50% for 0 s, and 25% for 1 s. In this example, we assume the sampling rate is 1000 Hz. Fig. 2(b) is the spectrum distribution of second-order derivatives (only half the values are plotted due to data symmetry). It demonstrates that the energy of the derivatives is concentrated in high frequency. Regarding the second-order derivative, at the low and middle frequency components, the power spectrum of an audio signal is normally much stronger than the power spectrum of the error is alterm caused by data hiding, in other words, most equal to zero, based on (10); the difference of the spectrum between a cover and the stego-signal is suppressed at low and

(4)

1Available:

http://mathworld.wolfram.com/FourierTransformGaussian.html

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LIU et al.: TEMPORAL DERIVATIVE-BASED SPECTRUM AND MEL-CEPSTRUM AUDIO STEGANALYSIS

Fig. 2. (a) Random error signal consisting of 25% for 1s, 50% for 0 s, and 25% for

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01 s; (b) spectrum of the second-order derivative.

Fig. 3. Spectra of the second derivatives of a cover signal (left) and the stego-signal (right).

middle frequency components. However, the situation is very different at the high-frequency components. As frequency inincreases, and is limited above a certain frecreases, quency, the increase of the spectrum resulted from hidden data is not negligible anymore; hence, the statistics extracted from the high-frequency components give a clue to detect the information-hiding behavior. Fig. 3 shows the spectrum distribution of the second derivative of a 44.1-kHz audio cover and the distribution of the second derivative of the stego-signal that is generated by embedding some data into the cover. It clearly shows that the high-frequency spectrum of the second-order derivative of the stego-signal has higher magnitude values, in comparison with the cover.

In comparing signal spectrum to derivative spectrum, we also observe that Fig. 4 demonstrates the spectra of the same cover and stego-signals without the extraction of the second derivatives. Similarly, the addition of hidden data increases the magnitude in high frequency although the energy is dominated in low frequency. It is worth noting that a comparison between Figs. 3 and 4 shows that the second derivative amplifies the energy in high frequency; especially, it amplifies the energy contributed by the addition of the hidden signal. Therefore, a preprocessing step to extract the second-order derivative could be more effective for detecting the hidden signal. Next, we present the following procedure to extract the statistical characteristics of the spectrum.

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Fig. 4. Spectra of the same cover and stego-signals that are used in Fig. 3.

1) Obtain the Fourier spectrum of the second-order derivative of the audio signal under test. 2) Calculate statistics, including mean value, standard deviation, and skewness, of the different frequency zones over the spectrum. In our experiments, we equally divide the en) zones or tire frequency zone into ( is set to parts, from the lowest to the highest frequency. The mean value, standard deviation, and skewness of the th zone are denoted , , and , respectively. that are extracted from 3) Choose the values , , and the high-frequency spectrum as the features. is given in (9). The expected The expected value of value of the variance is obtained by using the following:

[27]. Recently, Kraetzer and Dittmann proposed a signal-based mel-cepstrum audio steganalysis [18]. Based on (11), we design a second derivative-based mel-cepstrum audio steganalysis to improve Kraetzer and Dittmann’s work. The details are described in Section III. III. IMPROVED MEL-CEPSTRUM AUDIO STEGANALYSIS In speech processing, mel-frequency cepstrum (MFC) is a representation of the short-term power spectrum of a sound, based on a linear cosine transform of a log power spectrum on a nonlinear mel scale of frequency. To convert Hz into mel use the following: (12)

(11) According to (11), the rate of power change in different spectrum bands of the stego-audio is different from the original cover. Generally, the cepstrum may be interpreted as information for the power change; it was defined by Bogert, Healy, and Tukey in [25]. Reynolds and McEachern showed a modified cepstrum called mel-cepstrum for speech recognition [26],

MFCCs are coefficients that collectively make up an MFC. MFCCs are commonly derived from the following processes [28]: 1) take the Fourier transform of (a windowed excerpt of) a signal; 2) map the powers of the spectrum obtained above onto the mel scale, using triangular overlapping windows; 3) take the logs of the powers at each of the mel frequencies; 4) take the DCT of the list of mel log powers, as if it were a signal; 5) the MFCCs are the amplitudes of the resulting spectrum. Fig. 5 (available at http://www.ee.bilkent.edu.tr/ ~onaran/SP-4.pdf) shows a fast Fourier transform (FFT)-based

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and

(16)

Fig. 5. FFT-based mel-cepstrum procedure (available at http://www.ee. bilkent.edu.tr/~onaran/SP-4.pdf).

mel-cepstrum computation; the more technical details are given in [29]. Mel-cepstrum is commonly used for representing the human voice and musical signals. Inspired by the success in speech recognition, Kraetzer and Dittmann proposed mel-cepstrum-based speech steganalysis, including the following two types of mel-cepstrum coefficients [18]: . is the number of 1) MFCCs, MFCCs, for a signal with a sampling rate of 44.1 kHz , calculated by the following equation, where MT indicates the mel-scale transformation:

Temporal derivative-based high-frequency spectrum statistics, described in Section II, and derivative-based mel-cepstrum coefficients, derived from (15) and (16), form the feature vector for detecting the information hiding in digital audio signals. To improve the original mel-cepstrum audio steganalysis, a wavelet-based mel-cepstrum approach is also designed. We apply a wavelet transform to signal and get an approximation denote the detail cosub-band and a detail sub-band. Let and efficient sub-band; we replace in (13) and (14) with obtaine the MFCCs and FMFCCs as follows:

(17)

and (13)

2) Filtered mel-frequency cepstral coefficients (FMFCCs), . is the number of FMFCCs, calculated by the following equation:

(18)

IV. EXPERIMENTS A. Setup (14)

In (14), the role of speech band filtering is to remove the speech relevant bands (the spectrum components between 200 and 6819.59 Hz) [18]. To improve mel-cepstrum-based audio steganalysis, following Kraetzer and Dittmann’s work, we design the second-order derivative-based MFCCs and FMFCCs, obtained by replacing the signal in (13) and (14) with the second-order derivative ; the calculation is listed as follows:

(15)

We obtained 6000 mono and 6000 stereo 44.1-kHz 16-bit quantization in uncompressed, PCM coded WAV audio signal files, covering different types such as digital speech, on-line broadcast in different languages, for instance, English, Chinese, Japanese, Korean, and Spanish, and music (jazz, rock, blues). Each audio has the duration of 19 s. We produced the same amount of the stego-audio signals by hiding different message in these audio signals. The hiding tools/algorithms include Hide4PGP V4.0,2 Invisible Secrets,3 LSB matching [30], and Steghide [31]. The hidden data include voice, video, image, text, and executable codes, which were encrypted before embedding by using different keys. We also produced audio steganograms by hiding random bits. The covert data in any two audio streams are different. All the covers and steganograms are available at http://www.cs.nmt.edu/~IA/steganalysis.html. 2Available: 3Available:

http://www.heinz-repp.onlinehome.de/Hide4PGP.htm http://www.invisiblesecrets.com/

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Fig. 6. P-values in one-way ANOVA analysis for the spectrum features over the whole frequency band. The x-axis corresponds to the low- to high-frequency component, from left to right. The y-axis shows the p-value.

B. Statistical Significance of Spectrum Features To extract the spectrum features, we set 80 to and extract the mean values, standard deviations, and skewness statistics, for a total of 240 features over the whole frequency of the derivatives. Fig. 6 lists the p-values in the one-way analysis of variances (ANOVA) [32], [33] of these features, extracted from Hide4PGP, Invisible Secrets, LSB matching, and Steghide, as well as original covers. It clearly indicates the features extracted from the high-frequency components, which correspond to the small p-values, have better statistical significances than the features from the other frequency components. The ANOVA results are consistent with the analysis of Section II. C. Signal-Based, Derivative-Based, and Wavelet-Based Mel-Cepstrum Audio Steganalysis We compare the signal-based mel-cepstrum audio steganalysis to derivative-based and wavelet-based mel-cepstrum approaches. Since Daubechies wavelets are widely used for signal processing and decomposition [34], we apply a Daubechies wavelet, “db8,” to signal for decomposition. Let MC, D-MC, and W-MC stand for signal-based, derivative-based, and wavelet-based mel-cepstrum steganalysis methods, respectively. Fig. 7 shows the receiver operating characteristic (ROC) curves by performing a cross validation in detecting the audio steganograms by using SVMs with RBF kernels [35]. The experimental results show that wavelet-based and derivative-based mel-cepstrum audio steganalysis methods prominently improve the detection performance of the original

mel-cepstrum method. In comparison with the wavelet-based approach, the derivative-based mel-cepstrum audio steganalysis generally delivers a better performance. Since one-time cross-validation is not statistically significant, to compare these three methods, we perform 100 runs for each method on each type of audio steganograms with a certain information-hiding ratio. In each run, 50% audio samples are randomly assigned to the training set; the remaining 50% audio samples are used for testing. The mean testing accuracy values and the standard errors are listed in Table I. Hiding ratio, the ratio of the size of hidden data to the maximum capacity, is used to measure the embedding strength. As seen in Table I, wavelet-based and derivative-based mel-cepstrum methods are superior to the original signal-based method. Most remarkably, derivative-based mel-cepstrum audio steganalysis delivers the best result by greatly improving the detection performance over the mel-cepstrum method. For instance, it improves the detection accuracy by about 17% for the detection of invisible steganograms with maximum hiding, and about 18% for the detection of LSB matching steganograms with maximum hiding. D. Wavelet-Based and Wavelet-Based Spectrum and Mel-Cepstrum Audio Steganalysis versus AMSL Audio Steganalysis Toolset (AAST) The feature sets of wavelet-based and derivative-based methods include two types: spectrum statistics and mel-cepstrum coefficients. The mel-cepstrum coefficients consist of

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Fig. 7. ROC curves by using signal-based, derivative-based, and wavelet-based mel-cepstrum audio steganalysis, with the legends MC, D-MC, and W-MC, respectively.

TABLE I AVERAGE TESTING ACCURACY VALUES AND STANDARD ERRORS OF ORIGINAL MEL-CEPSTRUM (MC), WAVELET-BASED MEL-CEPSTRUM (W-MC) BY USING “dB8” AND DERIVATIVE-BASED MEL-CEPSTRUM (D-MC) METHODS

constitute a detector for steganalysis of speech audio signals, called AAST [18]. Fig. 8 shows ROC curves by performing a cross validation with the use of these three methods. Table II lists mean testing accuracy values and standard errors of 100 runs. Experimental results show that DSMC and WSMC outperform ASTT. On average, DSMC is superior to WSMC. V. DISCUSSION

MFCCs and FMFCCs, given by (15) and (16) for derivative-based approach, and by (17) and (18) for wavelet-based approach. In wavelet-based method, we adopt the same that is used in the derivative-based approach for spectrum feature extraction, except that we first replace the second derivative with the wavelet detail subband. In both cases, spectrum features consist of mean values, standard deviations, and skewness values from high-frequency components, given by

(19) We abbreviate the methods as DSMC (derivative-based spectrum and mel-cepstrum) and WSMC (wavelet-based spectrum and mel-cepstrum). In Kraetzer and Dittmann’s work, signalbased mel-cepstrum coefficients and other statistical features

Derivative-based and wavelet-based methods are superior to the original solution proposed by Kraetzer and Dittmann for audio steganalysis. Our explanation is that audio signals are generally band-limited while, on the other hand, the embedded hidden data is likely broadband. Consequently, both derivativebased and wavelet-based methods are more accurate since they first obtain the high-frequency information from audio signals. Our experimental results show that the derivative-based method outperforms the wavelet-based method, especially when only mel-cepstrum features are employed for detection. We believe this resulted from different spectrum characteristics between the second-order derivative and wavelet filtering. Fig. 9(a) shows the spectrum of the second derivative of the hidden data in an audio steganogram; Fig. 9(b) plots the spectrum of the detail wavelet sub-band of the same hidden data, filtered by using “db8.” There is a large difference between filtered by the wavelet may be treated these two spectra. The as a white noise signal; the spectrum is almost equally distributed over the whole frequency band, as shown in Fig. 9(b). However, the second derivative suppresses the energy in low

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Fig. 8. ROC curves by using DSMC, WSMC, and AAST, respectively.

TABLE II AVERAGE TESTING ACCURACY VALUES AND STANDARD ERRORS BY USING AAST, WSMC, AND DSMC

frequency and amplifies the energy in high frequency; the spectrum shape is approximately simulated by a half of Gaussian distribution, not equally distributed over the whole frequency band, as shown in Fig. 9(a). Based on (11) in Section II, as the increases, the expected value of the variance of spectrum the audio steganogram will prominently increase, that is, the rate of power change in different spectrum bands will dramatically change. Since the mel-cepstrum coefficients are used to capture the information for power change, the advantage of derivative-based mel-cepstrum approach becomes easily noticeable. With the addition of spectrum features, the wavelet-based method gains a greater improvement than the derivative-based method and thereby narrows the performance gap between the two methods. However, in both methods, mel-cepstrum features make more contributions than spectrum features for detecting

information-hiding; in other words, mel-cepstrum features play key roles in audio steganalysis. We note that different information-hiding systems/algorithms are sensitive to different features, which can be observed by comparing the detection results by using MC and AAST feature sets, shown in Tables I and II, respectively. The testing results by using the AAST feature set are with much higher standard errors. We surmise that some statistical features in AAST feature may not be very significant, as a statistical analysis for each individual feature would indicate. To address this problem, we can discard some insignificant features and choose an optimal feature set from all AAST features. The feature selection problem in steganalysis has been studied in our previous work [10]. The feature optimization for audio steganalysis is currently being conducted. As described and explained in our previous work on image steganalysis [11], besides the information-hiding ratio, image complexity is an important parameter in evaluating steganalysis performance, as the detection performance is necessarily lower for steganalysis of images with high complexity. Similarly, in audio steganalysis, all methods tested in our experiments will not be very effective for steganalysis of audio signals with high complexity, which generally have high magnitude in high frequency. This issue is also currently under our study. VI. CONCLUSION In this paper, we proposed spectrum analysis and improved mel-cepstrum methods for audio steganalysis, derived from the

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Fig. 9. (a) Spectrum of the second-order derivative of a hidden data in a 44.1-kHz audio steganogram, and (b) spectrum of the detail wavelet sub-band of the same hidden data, filtered by using “db8.” The frequency shown in the x-axis of (b) is reduced due to down-sampling of wavelet decomposition to obtain the detail sub-band.

second-order derivative and from the detail wavelet sub-band. Experimental results show that, in steganalysis of audio files produced by Hide4PGP, Invisible Secrets, Steghide, and LSB matching algorithms/tools, our proposed methods deliver good performance and gain significant advantage over a recently designed signal-based mel-cepstrum method. In a comparison of the two new methods, on average, the derivative-based solution is superior to the wavelet-based method. ACKNOWLEDGMENT The authors would like to thank Dr. D. Ellis of Columbia University for his insightful comments and great suggestions, Dr. M. Slaney of Yahoo research and Prof. H. Ai for their helpful discussions, and Dr. J. Dittmann and C. Kraetzer for kindly providing them with the AAST document. Special thanks go to the anonymous reviewers for their insightful comments that helped improve the presentation. REFERENCES [1] J. Harmsen and W. Pearlman, “Steganalysis of additive noise modelable information hiding,” Proc. SPIE, Electronic Imaging, Security, Steganography, and Watermarking of Multimedia Contents, vol. 5020, pp. 131–142, 2003. [2] S. Lyu and H. Farid, “How realistic is photorealistic?,” IEEE Trans. Signal Process., vol. 53, no. 2, pt. 2, pp. 845–850, Feb. 2005. [3] Y. Shi, C. Chen, and W. Chen, “A Markov process based approach to effective attacking JPEG steganography,” in Lecture Notes Comput. Sci., 2007, vol. 437, pp. 249–264. [4] Q. Liu, A. Sung, B. Ribeiro, and R. Ferreira, “Steganalysis of multiclass JPEG images based on expanded Markov features and polynomial fitting,” in Proc. 21st Int. Joint Conf. Neural Networks, 2008, pp. 3351–3356. [5] J. Fridrich, “Feature-based steganalysis for JPEG images and its implications for future design of steganographic schemes,” in Lecture Notes Comput. Sci., 2004, vol. 3200, pp. 67–81. [6] T. Pevny and J. Fridrich, “Merging Markov and DCT features for multiclass JPEG steganalysis,” Proc. SPIE Electronic Imaging, pp. 03–04, Jan. 2007. [7] S. Lyu and H. Farid, “Steganalysis using high-order image statistics,” IEEE Trans. Inf. Forensics Security, vol. 1, no. 1, pp. 111–119, Mar. 2006. [8] Q. Liu and A. Sung, “Feature mining and nuero-fuzzy inference system for steganalysis of LSB matching steganography in grayscale images,” in Proc. of 20th Int. Joint Conf. Artificial Intelligence, 2007, pp. 2808–2813.

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 4, NO. 3, SEPTEMBER 2009

[27] R. H. McEachern, “Hearing it like it is: Audio signal processing the way the ear does it,” DSP Applications, vol. 3, no. 2, pp. 35–47, Feb. 1994. [28] M. Xu, L. Duan, J. Cai, L. Chia, C. Xu, and Q. Tian, “HMM-based audio keyword generation,” in Proc. 5th Pacific Rim Conf. Multimedia, Part III, Lecture Notes in Computer Science, Nov. 30–Dec. 3, 2004, vol. 3333, pp. 566–574. [29] S. Molau, M. Pitz, R. Schlüter, and H. Ney, “Computing mel-frequency cepstral coefficients on the power spectrum,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, Salt Lake City, UT, May 2001, vol. I, pp. 73–76. [30] T. Sharp, “An implementation of key-based digital signal steganography,” in Proc. Information Hiding Workshop (LNCS), 2001, vol. 2137, pp. 13–26. [31] S. Hetzl and P. Mutzel, “A graph-theoretic approach to steganography,” in LNCS, 2005, vol. 3677, pp. 119–128. [32] T. Hill and P. Lewicki, Statistics: Methods and Applications. Tulsa, OK: StatSoft, Inc., 2005, ISBN: 1884233597. [33] R. Agostino, L. Sullivan, and A. Beiser, Introductory Applied Biostatistics. Pacific Grove, CA: Brooks/Cole, 2005. [34] I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992. [35] V. Vapnik, Statistical Learning Theory. Hoboken, NJ: Wiley, 1998.

Andrew H. Sung received the Ph.D. degree from the State University of New York at Stony Brook, in 1984. Dr. Sung is a Professor and the Chairman of the Computer Science and Engineering Department of New Mexico Tech, Socorro, NM. His current research interests include information security and digital forensic analysis, bioinformatics, application algorithms, and soft computing and its engineering applications.

Mengyu Qiao is currently working toward the Ph.D. degree in the Computer Science and Engineering Department, New Mexico Tech, Socorro, NM. He received the B.Eng. degree in software engineering from Beijing University of Posts and Telecommunications, China, in 2006, and the M.S. degree in computer science from New Mexico Tech, in 2009. His research interests include information security, bioinformatics, data mining, image/signal processing, and software engineering.

Qingzhong Liu received the B.Eng. degree from Northwestern Polytechnical University and the M.Eng. degree from Sichuan University in China, and the Ph.D. degree in Computer Science from New Mexico Tech, in 2007. Dr. Liu is currently a Senior Research Scientist and Adjunct Faculty of New Mexico Tech, Socorro, NM. His research interests include data mining, pattern recognition, bioinformatics, multimedia computing, information security, and digital forensic analysis.

Authorized licensed use limited to: NEW MEXICO INST OF MINING & TECH. Downloaded on August 31, 2009 at 18:45 from IEEE Xplore. Restrictions apply.

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