350 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 5, NO. 2, JUNE 2010 The rest of the paper is organized as follows. SVD and the proposed Step 2: For each particular W , calculate the singular value vectorfeatures are explained in Section II. The image sets used in the experi- Sv of each subblock jments, the embedding processes related to the steganographic methods,and the experimental results are presented in Section III. Finally, theconclusions are drawn in Section IV. SVD(Subblockj ) 0 Svj = [1j ; 2j ; . . . ; Wj ]: ! (3) Step 3: Calculate the natural logarithm of the inverse power of each II. STEGANALYZER DESIGN singular value and add the singular values up with respect to the related subblock jA. Singular Value Decomposition W SVD is an essential matrix factorization method which is widely SvBj = 0 log ij 1 ; j = 1; 2; . . . ; TW ij 6= 0used in signal processing. It decomposes a matrix A 2 m2n into (4) i=1the product of two orthonormal matrices U 2 m2m , V 2 n2n anda diagonal matrix S 2 m2n as follows: where TW is the total number of subblocks sizes of W 2W . A = USV T : Step 4: Sum the ﬁnal results obtained in Step 3 and normalize them (1) with the number of total subblocks TThe diagonal elements of matrix S are non-negative and are sorted indecreasing order 1 2 1 1 1 min(m;n) , where m and n are the FW = T1 SvBj ; W = 3; . . . ; 27: (5) W j=1dimensions of A. These sorted elements produce a vector named as“singular value vector:” Using this algorithm, we obtain 25 dimensional (25D) features for each image. Sv = Diag(S): (2) One of the crucial obstacles for an efﬁcient steganalysis is the image content. To alleviate this obstacle, we drew an analogy between the de- tection problem for steganalysis and the classical dc signal detection inB. Feature Extraction additive white Gaussian noise (AWGN) channel [17, p. 67, Example The proposed method attacks steganographic content using the fea- 3.2]. According to the latter one, an increase in the noise variance re-tures derived from singular values. Let us assume a full rank matrix. sults in a decrease in the detection performance. For image steganal-If any two rows or columns of this matrix are modiﬁed so that they ysis, assuming that the embedding noise is the dc value which is aimedbecome linearly dependent, it can be observed that the lowest singular to be detected and AWGN as the image content, an increase in the dy-value vanishes. If this process is repeated using the next row or column, namic range corresponds to an increase in the variance of AWGN. Ac-the second lowest singular value becomes zero. This observation comes cordingly, any attempt to decrease the dynamic range can improve theup with two main ideas which are the pillars of the proposed method. detection performance. In respect of this analogy, we need to expectFirst, the reaction to the changes on the matrix content starts from the the pixel values of bitmap images to be in the interval of [0 f ], wherelowest singular value. Second, the lower valued singular values’ close- f 255 before the data embedding. This is obviously not possible.ness to zero indicates a group of vector’s closeness to the linear de- However, it is possible to estimate the cover image with a certain pre-pendency. This observation can be used to model the soft relationship cision. The difference image between the image under considerationbetween the image rows and columns which will be disturbed by the and the estimated image can be viewed as an estimation of the em-embedding process. bedding noise. This estimation provides diverse information from the Due to the aforementioned unequal effect of embedding noise on the original data. Therefore, we resort to extract other 25 features from thesingular values, it is necessary to adopt a function which can intensify difference image yielding 50 features in total. To estimate the originalthe lower valued singular values for a powerful steganalysis and can at- image, we use Wiener ﬁltering with a 3 2 3 window. In Section III-B,tenuate the higher valued ones to normalize the different energy levels we justify the use of this ﬁltering and we show that the merged 50 fea-of different images. For this purpose, a function comprising the loga- tures (WFLogSv) are superior to both 25D LogSv features  and 25D 0rithm of the inverse power of singular values log(x 1 ) is devised to Wiener ﬁltering process features (WF). These 50 features are used inderive features for the steganalysis. Since spatial domain represents a the classiﬁcation process to make a decision on the image under test,strong dependency between the pixels in the local neighborhoods the whether it is cover or stego.features are extracted from the subblocks representing the locality inthe spatial domain rather than the whole image. It is obvious that when III. EXPERIMENTAL RESULTSthe block size increases the number of examined blocks decreases. Thisresults in decreasing the dependencies which are considered. To alle- A. Image Setviate this problem, the subblocks are overlapped proportionally to the Greenspun’s image database consisting of 1800 natural color im-block size in order to be able to take into account the correlations within ages with the quality factor equals to 100 is used in the experimentsand among subblocks. Consequently, the feature extraction algorithm . These images are converted to grayscale and black borders around them are then cropped resulting in images of size 480 2 480 pixels. Weis described as follows. Step 1: Divide image I , into subblocks of size W 2 W , where W = 3; 4; . . . ; 27 according to the following overlapping rules: never compressed the images since it is harder to detect spatial-domain steganography in raw images than the preprocessed ones . All im- If W 8; no overlapping ages in the data set are embedded with relative payloads of 0.4, 0.2, If 8 W 13; 50% over lapping 0.1, and 0.05 bit per pixel (bpp) for spatial domain steganographic al- If W 13; 75% overlapping: gorithms or 0.4, 0.2, 0.1, and 0.05 bit per nonzero DCT coefﬁcient (bpc) for DCT domain ones in order to obtain the stego image set. Note that The methodology used in this overlapping strategy is ex- due to the limited capacity of the Outguess algorithm , the maximum plained with experiments in Section III-B. embedding rate is considered instead of 0.4 bpc.
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 5, NO. 2, JUNE 2010 351 TABLE I TABLE II DETECTION PERFORMANCES OF VARIOUS OVERLAPPING STRATEGIES DETECTION PERFORMANCES OF LogSv, WF AND WFLogSv For the PQ method, 1000 images from the last experiment of  arecombined with the Greenspun’s image set. There are 2603 images inthis combined set since PQ was not able to embed 0.4 bpc to 197 imagesin the Greenspun’s set. Only a 0.4-bpc rate is considered for PQ due toits very poor detectibility for lower embedding rates . JPEG qualityQ( ) factor is determined by the steganographic algorithms as 75 and C. Spatial Domain Steganalysis80 for Outguess and F5 methods, respectively. For these two methods, Besides the proposed approach, we have implemented the CNPCAthe same JPEG quality factor used to compress the stego images is classiﬁer as well as the high-dimensional features of Xuan et al. exploited to get the cover images. For PQ, because of the nature of the and BSM . The source code of Farid’s steganalysis method  ismethod, recompressed images are used as cover images via doubling obtained from the Internet  while that of WAM is provided by its Qthe ﬁrst quantization matrix ( 1 = 85) . authors . For a fair comparison, each steganalyzer is associated with a classiﬁer which provides the best performance on average. Three clas-B. The Overlapping Rule and the Content Independency Process siﬁers are considered: Support Vector Machine (SVM), Fisher Linear The design of the proportionally increasing overlapping rule relies Discriminator (FLD), and CNPCA. FLD for WAM and Farid, CNPCAon the trade-off between the accuracy of the steganalyzer and the time for Xuan and SVM for BSM, SVBS and WFLogSv have been chosennecessary to extract the features. The greater the number of overlap- empirically according to the best detection performance for the relatedpings, the higher the amount of collected statistics is. However, after staganalysis method, except for Xuan. Due to high feature dimension-exceeding a number of overlappings, in terms of detection performance ality CNPCA is adopted inevitably for the Xuan method. CNPCA andwe do not gain much. Therefore, our strategy was to achieve an ac- R C SVM have some free parameters, and ( , ), respectively. Optimumceptable detection performance within a considerable time slot. Ran- parameters for the steganalyzers are determined before the steganal-domly chosen 800 images from the Greenspun image set and the corre- ysis depending on solely the steganographic method by the use of asponding 0.05 rate embedded LSB images are used in the experiments. grid search algorithm having a step size of one for CNPCA and twoThe detection rates are calculated as the average of the maximum ac- with ﬁve fold cross validation for SVM. Pair of parameters ( C; ) arecuracy over 100 random trainings and tests using an SVM classiﬁer found as (217 2017 ), (215 21 ), and (215 203 ) for WFLogSv, BSM, ; ; ;with optimum parameters (see Section III-C for details). We compared and SVBS, respectively, for all steganographic methods. The param-the detection performance of the proposed overlapping algorithm to no R eter found for Xuan is = 523.overlapping, 50% and 75% overlappings. The detection performance Using the optimum parameters, the classiﬁers are trained by the ran-of 25D LogSv features for various training and testing sets and for the domly chosen 1200 cover and the corresponding 1200 stego imagesconsidered overlapping rules are listed in Table I. It is clear that using (300 images from each embedding rate) in the training phase. The restthis strategy we only reduce the computational time; the performance of images are used in the testing phase. These images intersect neitherloss compared to 75% overlapping is negligable. within nor among the training and testing sets (as it is true in all exper- The design parameter of a Wiener ﬁlter is the window size. Due to the iments). Note that in  the classiﬁers are trained only with the imagesstochastic nature of the distribution of the natural images, it is not pos- of a particular embedding rate according to Kerckhoffs’ principle (em-sible to provide a good window size by means of detection performance bedding rate is assumed to be known by the steganalyzer) whereas herewith theoretical analyses. Besides, ideally, an inﬁnite number of window we consider all embedding rates for the construction of the training set.sizes limits the number of practical experiments. We tested the window Because in the steganalysis community this principle has been foundsizes 2 2 2, 3 2 3, 4 2 4, and 5 2 5 with the same experimental setup. unrealistic by asserting that in a realistic scenario the embedding rateOut of 800 images, 500 images are used for training and the rest of the may not be known . Moreover, except for PQ, the experimentsimages for testing. With 25D features from the Wiener ﬁltering process, are iterated 100 times for all steganograpic methods in order to pro-we obtained detection performances; 86.7%, 87.1%, 86.6%, and 88.0% vide reliable results. For PQ, we iterated the training and the testingfor 2 2 2, 3 2 3, 4 2 4, and 5 2 5 window sizes, respectively. In case we phases for 10 times. The detection performances of the state-of-the-artconsider 50D features (25D LogSv and 25D Wiener ﬁltering features), steganalyzers are determined by averaging the maximum accuracy ofwe obtained 91.3%, 91.8%, 88.6%, and 89.3% detection performances : the classiﬁers, which is given as 1 0 0 5 2 (false alarm percentage +for 2 2 2, 3 2 3, 4 2 4, and 5 2 5 window sizes, respectively. Since the miss percentage), over all iterations. From Tables III–V, we give theﬁnal detection performance is of our interest, we decided for a Wiener ﬁl- detection performances of steganalyzers performing on spatial domaintering with a 3 2 3 window. In the next experiment, we investigated the steganography. It can be easily observed that the proposed method out-performance improvement with additional 3 2 3 Wiener ﬁltering fea- performs the prior arts for all spatial domain steganographic methodstures for all considered steganography algorithms. The detection per- with a signiﬁcant margin. Notice that for very low embedding rates thisformance of the proposed 50D WFLogSv features, 25D LogSv features divergence is more signiﬁcant., and 25D Wiener ﬁltering features are given in Table II. It can easilybe seen that WFLogSv leads to at least about 1% and at most about 7% D. DCT Domain Steganalysisperformance gain for all steganography algorithms. This clearly indi- In order to detect DCT domain steganography, there exist quite pow-cates one of the main contributions of this paper. erful DCT-based steganalysis algorithms, for example  and .
352 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 5, NO. 2, JUNE 2010 TABLE III TABLE VI DETECTION PERFORMANCES FOR LSB DETECTION PERFORMANCES FOR F5 TABLE IV TABLE VII DETECTION PERFORMANCES FOR LSB 6 DETECTION PERFORMANCES FOR JP HIDESEEK TABLE V TABLE VIII DETECTION PERFORMANCES FOR STEGHIDE DETECTION PERFORMANCES FOR OUTGUESS TABLE IXHowever, until recently, the performance of spatial domain steganal- DETECTION PERFORMANCES FOR MB1ysis algorithms to detect DCT domain steganography has not yet beeninvestigated. This kind of steganalytic attack can especially be usefulif the secret information is embedded in the DCT domain and the stegoimage is advertised as a bitmap image by adopting some error correc-tion codes and decompressing the image to the spatial domain. Actu-ally a similar scenario has been introduced recently  in the YASSmethod. YASS embeds information in the spatial domain but the stegoimage is advertised in the DCT domain (as a JPEG image) by em-ploying some error correcting codes. Our scenario considered in theDCT tests is the reverse version of the one provided in YASS. TABLE X Therefore, at one hand, DCT domain steganalysis algorithms should DETECTION PERFORMANCES FOR MB2have a good reason to attack bitmap images since it is always assumedthat if the image is represented in a particular domain, the embeddingshould have been performed on this domain as well , . On theother hand, DCT domain steganalysis algorithms can experience se-vere performance degradation due to the masking of decompressionon the embedding noise. Another reason for attacking DCT domainsteganography using spatial domain steganalysis is that, although de-tection can intuitively be estimated to be poor due to the decompres-sion, spatial domain features are likely to provide diverse informationfrom the DCT-based ones which is useful for some fusion schemes.From Tables VI–X, the detection performances of the state-of-the-art of the steganalysis methods over all DCT stegonagraphic methods, thespatial domain steganalysis methods on F5, JP HideSeek, Outguess, proposed method (WFLogSV) is the second best after WAM.MB1, and MB2 steganography methods are tabulated. The proposedmethod shows reasonable performance in the DCT domain. It is the E. Steganalysis of PQsecond best for JP HideSeek, MB1, and MB2 and the third best forF5 and Outguess on average. It is also the second best for F5 and Out- For the sake of completeness, we have investigated the potential ofguess for the lowest embedding rate (0.05). If we rank the performances the steganalyzers on PQ steganography. As a benchmark, we adopt the
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