J. K. Su, J. J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. IEEE Trans. Signal Proc.: Special Issue on Information Theoretic Issues in Digital Watermarking, 81(6), Jun. 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....theory, this problem can be seen as reliably transmiting a message over a noisy channel, noise being due to modification or attacks of the host document. The attacks are often modeled as the addition of white Gaussian noise (AWGN channel) 1, 2] or as linear filtering plus additive noise [3, 4]. The perceptual sensitivity of the host signal is often taken into account for choosing embedding sites and strength. After presenting the watermarking general scheme in Sec. 2, we introduce side information principles in Sec. 3. Then digital watermarking is revisited in light of a general ....

....watermarking scheme. In the case of embedding in the Fourier domain, convolutionnal filtering can be seen as a kind of scaling. 2. PROBLEM STATEMENT Many approaches introduced so far assume that the signal can be modelled as an ergodic zero mean wide sense stationary Gaussian random process [2, 3]. This assumption is rarely satisfied for real signals or for content adaptive watermarks. We assume instead that the host signal can be modelled as the realization of a set of non stationary Gaussian random variables 1920 230 9 9 # . Let 0 40030 ....

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J. K. Su, J. J. Eggers, and B. Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," IEEE Trans. Signal Proc.: Special Issue on Information Theoretic Issues in Digital Watermarking, vol. 81, no. 6, Jun. 2001.

....very general method may not produce acceptable performance for detecting a specific steganography algorithm. Therefore, choosing the right steganalysis algorithm is in itself a open research problem. Closest in spirit to the work presented in this paper can be found in the watermarking literature [20,28,26]. Here, linear filtering techniques are employed to get an estimate of an embedded watermark. Conditions for resistance against this attack can also be found in these references. As we will see in later sections, the proposed work is significantly di#erent from these. The approach, analysis, ....

J.K. Su, J.J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. Signal Processing, 81, June 2001.

....various forms of channel characterizations. The perceptual sensitivity of the host signal is often taken into account for choos ing embedding sites and strength [1, 7] The attacks are often modelled as the addition of White Gaussian noise (AWGN) 8, 4] or as linear filtering plus additive noise [9, 3]. The authors in [10] show that the optimum attack is obtained by Wiener filtering and that to be maximally robust, the watermark should have a power spectrum matching the one of the original signal. The problem of robust embedding and extraction based on spread spectrum is revisited here in ....

....extraction scheme. 2 PROBLEM STATEMENT Let b = b ,b2, bn with bi 6 1, 1 Vi 6 1,2, n be the message to be embedded in a host signal x. Many approaches introduced so far assume that the signal x can be modelled as an ergodic zero mean wide sense stationary Gaussian random pro cess [4, 9]. This assumption is rarely satisfied for real signals or for content adaptive watermarks. We assume instead that the host signal x can be modelled as the realization of a set of non stationary Gaus sian random variables X = X,X2, Xm where Xi Af(O, axe) The information is then used as a ....

[Article contains additional citation context not shown here]

J. K. Su, J. J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. IEEE Trans. Signal Proc.: Special Issue on Information Theoretic Issues in Digital Watermark- ing, 81(6), Jun. 2001.

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J. K. Su, J. J. Eggers, and Bernd Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Accepted to Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking., Apr. 2000.

....A key assumption used throughout this paper is that the detector is fixed and does not compensate for the attack. Some recent information theoretic papers have adopted a game theoretic approach and consider the ideal situation in which the receiver knows the attack and can compensate for it [18] [19]. There are several reasons, primarily pragmatic, for the assumption of a fixed detector. First, we assume the use of a correlation detector, which is popular in many watermarking schemes in the current literature. Correlation detection is optimal for detecting a known signal (i.e. the watermark ....

....It is thus reasonable to examine the behavior of a fixed detector when its assumptions are violated. For example, Voloshynovskiy et al. 20] have proposed an effective attack in which outliers are introduced to confuse the correlation detector. Second, when watermarking is viewed as a game [18] [19], the watermarker and attacker are opponents who alternately improve their respective methods. In theory, the game continues until one player wins or a stable equilibrium is reached. In practice, however, once the watermarking system has been specified and deployed, the watermarker can no longer ....

[Article contains additional citation context not shown here]

J. K. Su, J. J. Eggers, and B. Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Signal Process., vol. 81, pp. 1141--1175, 2001. Special issue on information theoretic issues in digital watermarking.

....of Non White Host Data So far, white host data statistics were assumed. In practice, most data will be colored. Due to space constraints, we cannot discuss this case here. A more detailed discussion and further references for watermark communication in case of colored host data can be found in [3, 8]. There, the data is decomposed into sub channels which contain approximately white data. For each sub channel watermarking schemes like SCS and attacks like the GTC can be applied. The optimal allocation of the watermark power and the attack power can be found numerically. This approach can be ....

....Data Authentication of a gray scale image is investigated. An 8 x 8 block DCT was used to decompose thc image into 64 sub channels; each frequency is considered a sub channel. Only the 2nd to 21 th coefficients in zig zag scan were selected for watermark embedding according to the results in [3, 8]. The DC coefficient is not watermarked to avoid block artifacts due to the structure of the decomposition. Besides SCS authentication, a reference scheme 1979 based on spread spectrum (SS) watermarking as in [9] was imple mented. The simulations were conducted for the test image girl of size ....

J. K. Su, J. J. Eggers, and Bemd Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Accepted to Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking., Apr 2000.

....has no effect on the performance of the watermarking scheme and consequently is neglected here. A. SAWN Attacks and Effective AWN Attacks Fig. 5 depicts the investigated communication scenario. The shown scenario is more general than those investigated by Moulin et al. 2, 13] and Suet al... [14] due to the amplitude scaling by g, at the embedder s side. The embedder chooses w and g, to transmit the watermark message m with embedding distortion DE. The attacker chooses ga and v constrained to the attack dis tortion D to disturb the watermark communication as much as possible. To solve ....

....D which can never exceeds the original signal power be concluded from (19) Further, it can be observed that ge,opt 1 for practically relevant ratios D a. Thus, the amplinde scaling by g, at the embedder s side does not give a significant performance improvement over the schemes considered in [2, 13, 14], but in principle an improvement is achieved. Further note that we defined the watermark signal w to be the difference between the original and the watermarked signal which is here w = s x = g, 1)x g,w . 25) Thus, for E w x = 0, x and w are correlated for all g, 1, which contradicts ....

J. K. Su, J. J. Eggers, and B. Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking, vol. 81, June 2001.

....WNR necessary to reach the error floor of the turbo codes is depicted for different rates. In all cases, the error floor is at pc 10 . 3. THEORETICAL ROBUSTNESS ANALYSIS The robustness of digital watermarks against linear filtering and additive noise attacks was studied theoretically in [8]. All signals are treated as (colored) Gaussian random processes. With the power spectra of the host signal and watermark given, the attack finds the best combination of LSI filtering and additive colored Gaussian noise to minimize the channel capacity for a desired attacked signal distortion. It ....

....are treated as (colored) Gaussian random processes. With the power spectra of the host signal and watermark given, the attack finds the best combination of LSI filtering and additive colored Gaussian noise to minimize the channel capacity for a desired attacked signal distortion. It was shown in [9, 8] that LSI filtering and noise yields a more effective attack than additive noise alone. Equations for the filter transfer function and noise power spectrum appear in [8] The investigation produced a rule of thumb for resisting the attack when using mean squared error (MSE) distortion. Namely, ....

[Article contains additional citation context not shown here]

J. K. Su, J. J. Eggers, and Bernd Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Submitted to Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking., Apr. 2000.

....WNR necessary to reach the error floor of the turbo codes is depicted for different rates. In all cases, the error floor is at p# # ## . 3. THEORETICAL ROBUSTNESS ANALYSIS The robustness of digital watermarks against linear filtering and additive noise attacks was studied theoretically in [8]. All signals are treated as (colored) Gaussian random processes. With the power spectra of the host signal and watermark given, the attack finds the best combination of LSI filtering and additive colored Gaussian noise to minimize the channel capacity for a desired attacked signal distortion. It ....

....are treated as (colored) Gaussian random processes. With the power spectra of the host signal and watermark given, the attack finds the best combination of LSI filtering and additive colored Gaussian noise to minimize the channel capacity for a desired attacked signal distortion. It was shown in [9, 8] that LSI filtering and noise yields a more effective attack than additive noise alone. Equations for the filter transfer function and noise power spectrum appear in [8] The investigation produced a rule of thumb for resisting the attack when using mean squared error (MSE) distortion. Namely, ....

[Article contains additional citation context not shown here]

J. K. Su, J. J. Eggers, and Bernd Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Submitted to Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking., Apr. 2000.

....has no effect on the performance of the watermarking scheme and consequently is neglected here. A. SAWN Attacks and Effective AWN Attacks Fig. 5 depicts the investigated communication scenario. The shown scenario is more general than those investigated by Moulin et al. 2, 13] and Su et al. [14] due to the amplitude scaling by g e at the embedder s side. The embedder chooses w # and g e to transmit the watermark message m with embedding distortion DE . The attacker chooses g a and v constrained to the attack distortion DA to disturb the watermark communication as much as possible. To ....

....original signal power # 2 x , which can be concluded from (19) Further, it can be observed that g e,opt # 1 for practically relevant ratios DE # 2 x . Thus, the amplitude scaling by g e at the embedder s side does not give a signicant performance improvement over the schemes considered in [2, 13, 14], but in principle an improvement is achieved. Further note that we dened the watermark signal w to be the difference between the original and the watermarked signal which is here w = s x = g e 1)x g e w # . 25) Thus, for E w # x =0, x and w are correlated for all g e #=1, which ....

J. K. Su, J. J. Eggers, and B. Girod, "Analysis of digital watermarks subjected to optimum linear ltering and additive noise," Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking, vol. 81, June 2001.

....knowledge of the watermarking key. Again, signal dependent watermarks might be resistant against the copy attack. ESTIMATION BASED ATTACKS Here, we consider attacks that take into account the knowledge of watermarking technology and exploit statistics of the original data and watermark signal [4 8, 10]. In addition, we emphasize that for the design of attacks against watermarking schemes, the distortion of the attacked document and the success of watermark impairment has to be considered. Within the scope of these attacks, we present the concept of estimation based attacks. This concept is ....

....be masked by the HVS. At the same time, the attacker can use the NVF to automatically determine the flat regions, edges and textures. This attack is schematically shown in Figure 5b. The practical power of this attack was first demonstrated in [4] and a further theoretical analysis can be found in [7, 8]. Figure 5. The data hider strategy exploiting the texture masking function of the HVS (a) the attacker strategy using denoising and perceptual remodulation (b) b) Marked image Watermark embedding Original image a) Edges and textures Flat regions Masked Visible Attacked image ....

[Article contains additional citation context not shown here]

J. K. Su, J.J. Eggers and B. Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Signal Processing, Special Issue on Information Theoretic Issues in Digital Watermarking, 2001.

....of Non White Host Data So far, white host data statistics were assumed. In practice, most data will be colored. Due to space constraints, we cannot discuss this case here. A more detailed discussion and further references for watermark communication in case of colored host data can be found in [3, 8]. There, the data is decomposed into sub channels which contain approximately white data. For each sub channel watermarking schemes like SCS and attacks like the GTC can be applied. The optimal allocation of the watermark power and the attack power can be found numerically. This approach can be ....

....Image Data Authentication of a gray scale image is investigated. An 8 8 block DCTwas used to decompose the image into 64 sub channels; each frequency is considered a sub channel. Only the 2nd to 21th coefficients in zig zag scan were selected for watermark embedding according to the results in [3, 8]. The DC coefficient is not watermarked to avoid block artifacts due to the structure of the decomposition. Besides SCS authentication, a reference scheme 3 based on spread spectrum (SS) watermarking as in [9] was implemented. The simulations were conducted for the test image girl of size ....

J. K. Su, J. J. Eggers, and Bernd Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," Accepted to Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking., Apr. 2000.

....The RD SI scenario appears in the bottom diagram of Fig. 1. A # #### # ## source produces # realizations to form a sequence # # . The encoder and decoder communicate 1 Equality does not necessarily hold for non Gaussian channels. 2 A theoretically optimum attack is investigated in [11]. without error at a rate of # bits per source symbol. The decoder also has an observation # # # ### # # # # #,where # # and # # are independent, # # # # #### # ##,and# # # is known. Then the decoder computes an approximation # # # of the source sequence # # . We wish to ....

J. K. Su, J. J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. Submitted to Signal Processing, Apr. 2000.

....to the AWGN channel. It can also be proven [9] that the optimum defense against this attack results when ### ##### # # # # # # # ## ##### (8) We call (8) the power spectrum condition (PSC) A watermark that satisfies the PSC is said to be PSC compliant.The capacity in this case is [8] ## # # ### # # ## ## # ## # ## # # embed # # # ### # ## # ## ######### # ## embed # # # (9) 2 4. Optimum Attack Contrary to a conventional channel, however, in watermarking ### #### is fixed, and then the attack chooses the filter and noise. Hence, the attacker, rather than the ....

....### #### is fixed, and then the attack chooses the filter and noise. Hence, the attacker, rather than the owner, has a potential power advantage. It was shown in [9] that the effective white noise attack is indeed suboptimal. The optimum attack can be derived using the calculus of variations [8, 9] with Lagrangian cost function # # (integrand of # # ## ) # #(integrand of #) The solutions for ##### and # ## #### are ########### # ## #### # ## ###### ## #### # (10) # ## ######## ###### ##### # # ## #### # ## ###### ## #### # (11) where # # ##### # #, ###. For # ## ######or ### ....

[Article contains additional citation context not shown here]

J. K. Su, J. J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. Submitted to Signal Processing, Special issue on information theoretic issues in digital watermarking, Apr. 2000.

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J. K. Su, J. J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. IEEE Trans. Signal Proc.: Special Issue on Information Theoretic Issues in Digital Watermarking, 81(6), Jun. 2001.

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J.K. Su et al., "Analysis of digital watermarks subjected to optimum linear filtering . . . ," IEEE Trans. Signal Proc., vol. 81, June 2001.

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J. K. Su, J. J. Eggers, B. Girod, Analysis of digital watermarks subjected to optimum linear filtering and additive noise, IEEE Trans. Signal Proc.: Special Issue on Information Theoretic Issues in Digital Watermarking 81 (6). URL http://www.stanford.edu/ bgirod/pdfs/SignalProc2001.pdf

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J. K. Su, J. J. Eggers, and B. Girod, "Analysis of Digital Watermarks Subjected to Optimum Linear Filtering and Additive Noise," Signal Processing, Special Issue on Information Theoretic Issues in Digital Watermarking, Vol. 81, No. 6., pp. 1141-- 1175, 2001.

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J. K. Su, J. J. Eggers, and B. Girod. Analysis of digital watermarks subjected to optimum linear filtering and additive noise. Signal Processing, 81(6):1141--1175, June 2001. Special Issue on Information Theoretic Issues in Digital Watermarking.

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J. K. Su, J. J. Eggers, and B. Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise," IEEE Trans. Signal Proc.: Special Issue on Information Theoretic Issues in Digital Watermarking 81, Jun. 2001.

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J. K. Su, J. J. Eggers, and B. Girod, "Analysis of digital watermarks subjected to optimum linear filtering and additive noise." Preprint, Jan. 2000.

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J. K. Su, J. J. Eggers, and B. Girod, \Analysis of digital watermarks subjected to optimum linear ltering and additive noise." Preprint, Jan. 2000.

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