A highly secure oblivious sparse coding-based

Expert Systems with Applications 42 (2015) 2224–2233

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A highly secure oblivious sparse coding-based watermarking system for ownership verification Afaf Tareef a,⇑, Ahmed Al-Ani b a b

School of Information Technologies, University of Sydney, NSW 2006, Australia Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW 2007, Australia

a r t i c l e

i n f o

Article history: Available online 25 October 2014 Keywords: False positive detection problem Multiple claims of ownership Sparse coding Watermarking security

a b s t r a c t In the last few decades, the watermarking security issue has become one of the main challenges facing the design of watermarking techniques. In this paper, a secure oblivious watermarking system, based on Sparse Coding (SC) is proposed in order to tackle the three most critical watermarking security problems, i.e., unauthorized reading, false positive detection, and multiple claims of ownership problems, as well as optimize the fidelity, imperceptibility, and robustness characteristics. The reason for incorporating SC in the proposed system is to encode the watermark image before embedding it in the host image. This process is implemented using the well-known Stagewise Orthogonal Matching Pursuit (StOMP) method and an orthogonal dictionary that is derived from the host image itself. The watermark embedding is implemented in the transform domain of the Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) of the host image. The proposed system is oblivious, as it does not need the original host image when extracting the embedded watermark. In addition, it is suitable for both bi-level and gray-level watermarks, and can accommodate large watermarks that are up to half the size of the host image. The proposed SC–DWT–SVD based watermarking scheme is tested for various malicious and un-malicious attacks and the experimental results show that it realizes the security requirement as it tackles the false positive detection and multiple claims of ownership problems on one hand and generates an encryption form of the watermark on the other hand. In addition, the added security does not compromise the imperceptibility and robustness aspects of the proposed technique and hence can be considered to be comparable or superior to other up-to-date watermarking techniques. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Digital watermarking can be defined as the process of hiding secrete imperceptible piece of information, called watermark, into the multimedia data (i.e., images, videos and audios), called host or cover signal. For different purposes, digital watermarking is categorized into two classes based on the watermarks’ resistance to attacks: robust watermarking and fragile watermarking. The main purpose of the robust watermarking is protecting ownership of the digital media, whereas the fragile watermarking is used to ensure the integrity of the digital media (Bianchi & Piva, 2013). In the last decade, robust digital watermarking has received a great attention. In general, watermarking techniques have been evaluated according to the robustness, invisibility and capacity measures. ⇑ Corresponding author. E-mail addresses: [email protected] (A. Tareef), [email protected]. au (A. Al-Ani). http://dx.doi.org/10.1016/j.eswa.2014.09.055 0957-4174/Ó 2014 Elsevier Ltd. All rights reserved.

The watermarking security has not been properly considered in most of the current literature despite of being an essential issue in many critical watermarking applications, such as those related to legal environments (e.g., authentication of legal documents, data monitoring, fingerprinting and medical image watermarking). In such applications, accepting fake information as legal is more detrimental than rejecting a legal one (Pérez-Freire, Comesana, Troncoso-Pastoriza, & Pérez-González, 2006). One of the most important problems related to the security issue of watermarking technology is the false positive detection problem, which is referred to as the ability to extract an un-embedded watermark from the digital host image. Many of the existing watermarking techniques, especially SVD-based watermarking ones, suffer from this problem. Fig. 1 illustrates the problem of false positive detection. Another critical problem related to the security issue of watermarking technology is the problem of multiple claims of ownership. As known, protecting ownership rights is one of the earliest purposes of digital watermarking. However, extracting the embedded watermark from the watermarked multimedia is

A. Tareef, A. Al-Ani / Expert Systems with Applications 42 (2015) 2224–2233

not enough to confirm ownership unless certain requirements are imposed (Al-Nu’aimi and Qahwaji, 2009; Mohammad, Alhaj, & Shaltaf, 2008). If an attacker embeds another un-legal watermark to the already watermarked image, proofing the ownership becomes a serious problem. According to Craver, Memon, Yeo, & Yeung, (1998), rightful ownership cannot be resolved by most of the existing watermarking schemes. The false positive detection problem is largely arisen in the SVD-based watermarking techniques (Ali, Ahn, & Pant, 2014; Aslantas, 2009; Bhatnagar & Raman, 2009; Ganic & Eskicioglu, 2004; Huang & Guan, 2004; Lai, 2011; Lai & Tsai, 2010; Liu & Tan, 2002; Makbol & Khoo, 2013; Mishra, Agarwal, Sharma, & Bedi, 2014; Ouhsain & Hamza, 2009; Rastegar, Namazi, Yaghmaie, & Aliabadian, 2011; Shieh, Lou, & Chang, 2006). As a solution, (Mohammad et al., 2008) suggested dealing with this problem by ensuring to reach the maximum allowable amount of embedded information to prevent the attacker from adding any extra information to the image. However, this solution discourages some of the applications in watermarking technology that require embedding more than one watermark. The false positive detection in SVD-based watermarking techniques is still an open problem. In this paper, an effective solution for this challenging problem is proposed and evaluated using bi-level and gray-level watermarks. The false positive detection problem is tackled by using the host image itself as an evidence to prove the right watermark through the utilization of sparse coding, at the same time, the proposed approach can embed multiple high quality watermarks. Another common security challenge that face watermarking techniques is keeping the secrete message unreadable and un-understood for unauthorized persons. Many algorithms deal with this challenge by using cryptography techniques, such as the Arnold transformation (Zhang, Wang, & Wang, 2008; Lu, Sun, & Cai, 2010; Ali, Ahn, & Pant, 2014) and chaotic encryption (Keyvanpour & Bayat, 2013; Song, Hou, Li, & Huang, 2011). This paper introduces a new version of encryption using the sparse coding theory. An important issue related to the efficiency and practicability of watermarking schemes is blind watermarking. Based on whether or not the original image/signal is needed in the time of extraction, digital watermarking algorithms are divided into two main categories; blind and non-blind. Non-blind techniques are those that require the original image/signal for watermark extraction, which is not the case with the blind techniques. Blind watermarking (so-called oblivious or public watermarking) has a great significance and practical value in many applications where keeping a copy of the original signal without security is not practical. All these issues, along with high robustness, invisibility and payload are maintained in our proposed watermarking system. Our SC–DWT–SVD based watermarking technique enables the legal owner to prove his/her ownership of the digital image even if an attacker embeds a fake watermark in it. To the best of our knowledge, this research represents the first attempt to encode the watermark as a function of its carrier using sparse coding. The incorporation of sparse coding in our proposed technique is

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based on generating a private dictionary from the host image itself to encode and decode the watermark image, which will inherently solve the watermarking security problems, as well as, enhance the robustness and imperceptibility. We believe this research will open the door for further researches in this area. The rest of this paper is organized as follows: in Section 2, a brief background about watermarking is given. Section 3 presents the basic theoretical concepts of the sparse coding. Section 4 describes the details of the proposed watermarking system. Simulations and analysis of the performance of the algorithm are presented in Section 5. The conclusion is drawn in Section 6. 2. Background Digital image watermarking techniques can be categorized based on their applications, embedding domain and characteristics. With respect to the embedding domain, watermarking methods are divided into spatial domain techniques and frequency domain techniques. In the spatial domain watermarking algorithms, the watermark is embedded directly into image pixels while transform domain watermarking algorithms embed the watermark by altering the transformed coefficients after applying one or more transforms e.g., Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), Singular Value Decomposing (SVD), Discrete Walsh Hadmard Transform (WHT), Discrete Fourier Transform (DFT) (Cox, Miller, Bloom, & Honsinger, 2002), or moment-based transformation, such as Tchebichef, Wavelet, Krawtchouk, and Zernike moments (Tsougenis, Papakostas, Koulouriotis, & Tourassis, 2012). Generally, embedding the watermark into the transform domain makes it more robust and invisible than embedding in the spatial domain, and the performance of frequency domain techniques can be further improved by combining two or more transforms. In this section, the concepts of Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) are briefly described. 2.1. Discrete Wavelet Transform (DWT) One of the most common used transforms is the Discrete Wavelet Transform (DWT). The idea behind DWT is dividing an image into four sub-bands in a single level: Low–Low (LL). Low–High (LH), High–Low (HL) and High–High (HH) frequency sub-bands. This process can be iterated many times to compute multiple scale wavelet decomposition as shown in Fig. 2. DWT is widely used in watermarking as it has found to enhance imperceptibility in the watermarked image. Some examples of DWT based watermarking techniques can be found in (Barni, Bartolini, & Piva, 2001; Lin, Wang, Horng, Kao, & Pan, 2009; Ouhsain & Hamza, 2009; Run et al., 2011). One of the blind watermarking algorithms that utilized DWT was proposed by Lin et al. (2009) using maximum wavelet coefficient quantization. For embedding the watermark bits, the local maximum coefficients of various sized blocks, which are randomly selected from two sub-bands, are quantized. Another blind wavelet-tree based watermarking algorithm based on quantizing the maximum wavelet coefficient in a wavelet tree is proposed in Run et al. (2011). However, the two main limitations of the algorithm are its sensitivity to the rotating and cropping attacks and its inability to resolve the rightful ownership of an image when embedded with multiple signatures (Run et al., 2011). 2.2. Singular Value Decomposition (SVD)

Fig. 1. Illustrates the problem of false positive detection.

Singular Value Decomposing (SVD) is an effective mathematical tool for extracting algebraic features from images. It has been used in signal processing for multiple purposes, such as image

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Fig. 2. Discrete Wavelet Transform.

compression and noise reduction. It decomposes a matrix into three matrices of the same size, two unitary matrices and one diagonal matrix which is usually chosen as a host part since it contains the largest values of all the elements when compared to the other two matrices. To illustrate, assume M  N matrix A with rank r 6 min (M, N). SVD is presented as following:

2

k1 6 . T 6 A ¼ U KV ¼ ½u1 ;u2 ;...;un 4 .. 0

3  0 r X . . .. 7 T 7 ki ui v Ti . . 5½v 1 ; v 2 ;... v n  ¼ i¼1  kn ð1Þ

¼ k1 u1 v T1 þ k2 u2 v T2 þ    þ kr ur v Tr

ð2Þ

where U and V are the left and right eigenvectors, respectively, satisfying U  UT = I, V  VT = I. S is a diagonal matrix with nonnegative real numbers, satisfying k1  k2      kr > krþ1 ¼    ¼ kn . SVD has been widely-used in watermarking due to the stability of the singular value matrix and its ability to resist geometric attacks. Despite of the high robustness of SVD-based watermarking, most of the existing methods cannot resolve the rightful ownership problem due to their high false positive rates (Aslantas, 2009; Ganic & Eskicioglu, 2004; Huang & Guan, 2004; Liu & Tan, 2002; Rastegar et al., 2011). Many of the existing SVD-based watermarking methods embed only the singular value matrix of the watermark into the host image, which makes it possible for the attacker to claim ownership of the watermarked image through the reconstruction of an illegal watermark by utilizing its eigenvectors. To resolve this issue, (Jain, Arora, & Panigrahi, 2008) proposed an SVD-based watermarking technique that embeds the principal components of the watermark in the host image instead of the singular value matrix. However, the false positive detection problem can still occur when using fake watermarked eigenvectors. The authors of Mohammad et al. (2008) introduced another watermarking method that treats the false positive problem and multiple claims of ownership, but at the expense of robustness. The resistance of this method to image processing operations is not satisfactory. There are many hybrid watermarking schemes that used more than one transformation to improve the watermarking properties in the literature (Al-Haj, 2007; Ali & Ahn, 2014; Bhatnagar & Raman, 2009; Huang & Guan, 2004; Lai & Tsai, 2010; Run et al., 2012). In Run et al. (2012), two hybrid watermarking techniques are proposed based on Particle Swarm Optimization (PSO) to achieve the security and robustness. The principal components of the watermark are embedded into both the discrete cosine and wavelet transformations. In Lai and Tsai (2010), a DWT-SVD watermarking technique is proposed that divides the watermark into two parts that are embedded into the singular values of HL and LH sub-bands of the DWT. The robustness and imperceptibility for this technique are satisfactory, however, it is not secure and

cannot prove the ownership as it has a high false positive rate. It also cannot solve the problem of multiple claims of ownership. Recently, many watermarking techniques have used population based optimization techniques to achieve good balance between the conflicting watermarking properties. The swarm optimization (Mishra et al., 2014; Rao, Shekhawat, & Srivastava, 2012; Run et al., 2012), and differential evolution (Ali & Ahn, 2014; Ali et al., 2014; Aslantas, 2009) were used to find an optimal scaling factor for watermark embedding that gives a good robustness without affecting the imperceptivity. However, using optimization techniques will increase the computational cost of the watermarking techniques. One of such recent techniques is proposed in Ali and Ahn (2014). A self-adaptive differential evolution is used to determine the threshold, which is used in embedding the principal components of the watermark in all DWT sub-bands. Although this technique produces promising results and tackles the false positive detection problem, it does not deal with multiple claims of ownership problem. In contrary to Ali and Ahn (2014), Lai and Tsai (2010), our proposed technique only uses one sub-band for embedding the watermark due to the incorporation of sparse coding, and hence improves the imperceptibility. Moreover, as the entire watermark is embedded in the host image instead of only embedding the principal components, the number of keys used in the extraction stage is decreased. Another advantage of the proposed approach is that it is not affected by the increase of the scaling factor, which is not the case for other watermarking techniques (e.g., Ali and Ahn (2014), Lai and Tsai (2010)). The utilization of a sparse representation to encode the watermark will only cause a very small number of the host image significant coefficients to be changed. Thus, a large scaling factor enhancing the robustness can be used without affecting the quality of the watermarked image. The major advantage of the proposed system is solving the problem of multiple claims of ownership, as well as other security problems. The experimental results show that while meeting the security requirement, the fidelity, imperceptibility, and robustness achieved by our proposed approach are largely improved. 3. Sparse coding (SC) Recently, there have been stupendous breakthroughs in the study of sparse coding and its applications. Sparse coding (SC) is the process of computing and modeling signal vectors as linear combinations of relatively few atoms in a dictionary. SC has been used in many applications such as signal processing (i.e., denoising, blind source separation, inpainting), machine learning, and statistics (Mairal, Bach, Ponce, & Sapiro, 2009). To illustrate the principles of sparse coding, let’s consider the signal X ¼ ½x1 ; x2 ; x3 ; . . . ; xn  2 Rmn and let / ¼ ½/1 ; /2 ; /3 ; . . . ; /k  2 Rmk be the basis matrix, and s be the basis size. Let a ¼ ½a1 ; a2 ; a3 ; . . . ; an  2 Rkn be the coefficient matrix, where each

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column is a sparse representation for a corresponding vector in X. The goal of sparse coding is to represent xi as a sparse linear combination of the basis vectors of /. This can be summarized in the following equation.

x ¼ /a

ð3Þ

It is usually the case that the dictionary / is over-completed (m < k); i.e., there are fewer rows than columns. The above problem is called an underdetermined linear equation system and it has infinite number of solutions. However, the goal of sparse coding is to find the sparsest solution, which is the solution with as few non-zero coefficients as possible. To count the number of nonzero coefficients in the solution, ‘0 quasi-norm is used which reflects the signal sparsity. ‘0 quasi-norm can be presented as following:

kak0 ¼ #fjjaj – 0g

ð4Þ

If the number of nonzero elements in a is less than the total number of its elements, then we say that a is sparse. A sparsest solution can be found by solving the following non-convex optimization problem:

ðP 0 Þ :

min kak0

S:t: x ¼ /a

ð5Þ

The above problem can be approximated as a l1-norm minimization problem, and hence solved via linear programming. The ‘1norm minimization problem is

ðP 1 Þ :

min kak1

S:t: x ¼ /a

ð6Þ

There are many effective algorithms based on convex optimization or greedy pursuit that quite effectively solve such problems in the literature. An effective greedy method for sparse approximation called Stagewise Orthogonal Matching Pursuit (StOMP) has been presented in Donoho, Tsaig, Drori, & Starck (2006, 2012). StOMP is a rapid iterative technique that constructs a solution by going through a small number of iterations. In each iteration, residualization, thresholding, and projection are performed. In our proposed algorithm, StOMP is used to sparse represent the watermark due to three reasons; (i) it can work with most types of dictionaries, (ii) It gives a good approximation, and (iii) takes less computational time than many of other competing techniques (Pope, 2009). StOMP solves the under-determined equation by solving the following convex optimization problem (LP):

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explained later, this will be the key for dealing with the watermarking security problems. Despite of the wide use of Sparse Coding in many applications and realizing very promising results from using it in many fields, its use in digital watermarking is still rare. In Fakhr (2013), sparse coding and compressed sensing are used for audio watermarking. The watermark is a sparse vector adaptively selected from Gaussian random matrix by searching for the best vector that is robust to MP3 attacks. The dictionary used in this technique is a combined dictionary with one part containing DCT, WHT, and KLT, and the other part is Gaussian random dictionary. The extraction of the watermark is formulated as basis pursuit denoising problem solved to estimate the watermark. The drawbacks of this technique that it is used random selected watermark, whereas, a meaningful message need to be embed in image watermarking. Moreover, this technique uses common convolutional dictionary which cannot guarantee a solution for the security issues. In our proposed work, the dictionary is generated from the host image to encode the watermark as a function of its carrier in order to provide a robust solution to the security problems. In addition, a bi-level and graylevel meaningful image chosen by the owner can be embedded. This work demonstrates that sparse coding the watermark using the host image will provide an effective solution to the false positive detection and multiple claims of ownership problems, as well as provide a strong encryption of the watermark, and hence meet the security requirement of watermarking. It also helps in improving the imperceptibility by performing a high level of compression and reducing the number of elements needed to represent the watermark. Finally, it contributes to achieving the required robustness against noise due to the fact that noise cannot be sparse represented. 4. The proposed watermarking system The proposed SC–DWT–SVD-based watermarking system assumes the original host image to be a gray-scale image of size m  n, and the watermark is either gray or bi-level image of size r  c. The proposed watermarking system passes through three basic stages. The detailed procedure is described in the following three subsections. 4.1. Watermark modeling stage

ðLPÞ :

mins jj/a  xjj22

S:t: xi ¼ 0; 8i R C

ð7Þ

where C is a subset of the indices {1, 2, 3, . . ., n} which is updated iteratively. The StOMP algorithm is outlined in Table 1 (Breen, 2009). Another crucial issue in sparse coding is choosing a suitable dictionary for representing the signal, as different dictionaries yield to different representations for the same signal (Rubinstein, Bruckstein, & Elad, 2010). In the proposed algorithm, we build an orthogonal dictionary from the host image itself. As will be

Table 1 The StOMP pseudo code. StOMP sparse coding algorithm Input: Matrix /, vector xi, and threshold n Output: Approximation vector a or index set V 1. Start by setting the residual R0 = xi, the iteration count t = 0 and index set V = ‘‘ ’’; 2. Create a set K consisting of the index of all entries in the vector U = /0 * Rt above a threshold n. kx  /ak2 3. Update the index set V = V [ K and residual by X ¼ min v c2R

Rtþ1 ¼ x  /a: 4. Check the stopping criterion. Return to step 2 if it has not been satisfied.

In this stage, sparse coding is used to represent the watermark in term of few number of dictionary elements. This stage can be summarized in the following steps: Step 1. Building the dictionary. The dictionary will be derived from the host image by applying k level DWT on the host gray-level image. k depends on the size of the host image and the watermark. It can be calculated by the following equation:

k ¼ min

h

log2

mi h ni ; log2 c c

ð8Þ

where bc is the floor function. The proposed algorithm stipulate a condition on the number of watermark rows as r 6 c and r 6 m=2. In our algorithm, we assume that r can be equal to c (i.e., the number of sparse elements in each vector ai can be equal to the number of elements in xi ; i 6 nÞ; which is not generally the case, but possible. After applying k level DWT, we will get four sub-band [LLk, HLk, LHk, HHk]. The low frequency sub-band will be chosen to generate the dictionary due to its high energy. To add an extra level of security, a permutation can be performed on the host sub-band. Then, SVD is applied to get two orthogonal matrices Uk and Vk and singular value matrix Sk which is used to carry the sparse watermark in the next stage.

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Fig. 3. 512  512 test images.

Table 2 General comparison between the proposed technique and Ali and Ahn (2014), Lai and Tsai (2010), and Mohammad et al. (2008) techniques.

Watermark type Type of transform Embedding DWT sub-bands Type of watermark representation Type of scheme Watermark encryption

LLk ¼ U k Sk V Tk

Mohammad et al.

Lai and Tsai

Ali and Ahn

Proposed technique

Binary SVD – – Non-blind No

Gray DWT + SVD HL, LH – Non-blind No

Gray DWT + SVD All SVD Non-blind No

Gray/binary DWT + SVD LL SR Blind Yes

ð9Þ

Finally, the dictionary / is generated by sampling r rows of a (m/2k  n/2k) orthogonal matrix Vk. Step 2. Finding the sparse coding. Assume X is a watermark consisting a sequence of ownership labels, X = [x1, x2, x3, . . ., xn]. To get the corresponding sparse vectors a = [a1, a2, a3, . . ., an], StOMP is repeated c times. As the watermark is presented as a function of dictionary and sparse coefficients with very small values, it will be very easy to change the sparse coefficient values under various attacks. This will cause a perceptual degradation in the reconstructed watermark quality. This flaw can be considered the main reason behind the absence of serious employment of SC in image watermarking. In this paper, this flaw is solved by choosing the singular values of the host image for embedding as they have very good stability. Even if the image is seriously corrupted, the singular values will still be stable.

4.2. Encoding stage Step 1. To embed the watermark, the singular value matrix Sk of the low frequency sub-band used to generate the dictionary is used as a host. By embedding the watermark in the low-frequency subband using a well-chosen threshold, the attacker cannot modify this sub-band significantly without spoiling the quality of the watermarked image, and so, the dictionary will still be extractable as long as the image quality is not affected. In other words, if the attacker want to embed his/her own watermark in this sub-band without damaging the image or degrade its quality, the strength of the new watermark should not be very high, and in this case, the owner can still extract the dictionary to prove his/her rightful ownership, otherwise, if the attacker tries to increase the watermark strength, the quality of the image will be degraded. Whereas,

embedding robustly in other sub-bands degrades the quality of the watermarked image. As explained earlier, our system is able to embed multiple watermarks without damaging the evidence of rightful ownership. Step 2. Embedding the watermark. The embedding process is achieved by an encoding function l where WSk is the watermarked singular value matrix and k is the scaling factor that determines the strength of the watermark.

WSk ¼ lðSk ; aÞ ¼ Sk  k  a

ð10Þ

where k is the scaling factor that determines the strength of the watermark. In this embedding process, only a few number of the host image coefficients will be modified. So, the scaling factor can be increased to achieve the best robustness without causing a noticeable degradation in the quality of host image. The results presented in the next section show that the proposed system can successfully achieve a good compromise between the watermark strength, robustness and imperceptibility. Step 3. Reconstructing the watermarked low frequency subband is achieved by combining the orthogonal matrices of the original host part Uk and Vk with the singular values of the watermarked part Sw obtained by applying SVD on WSk.

WSk ¼ U w Sw V w

ð11Þ

wLLk ¼ U k Sw V Tk

ð12Þ

Step 4. Inverse DWT. IDWT is applied to the watermarked subband wLLk and the original high sub-bands LHk, HLk, and HHk to get the watermarked image g. 4.3. Decoding stage Decoding consists of the same first two steps that are carried out at the time of encoding. The details as following:

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Fig. 4. (a) The original watermark, (b) the sparse representation, (c) the reconstructed watermark, (d) decrypted watermark using incorrect dictionary.

Fig. 5. Treatment rightful ownership problem.

Step 1. Extraction of the watermarked singular value. After performing DWT, permutation, and SVD on the watermarked image as described in steps 1 and 2 in the embedding stage, the extracted singular value ex_Sw will be combined with the principal components of the watermarked part obtained in the previous stage (Uw and Vw) as following:

wSw ¼ U w ex Sw V Tw

ð13Þ

Step 2. Extract the sparse representation of the watermark by the decoding function E.

Ex a ¼ EðwSw ; ex Sw Þ ¼ ðwSw € ex Sw Þ=k

ð14Þ

Step 3. Reconstruction stage. In this stage the dictionary / that used in encoding is needed. The sparse coded watermark is reconstructed as following:

Ex W ¼ /  Ex a

ð15Þ

The Ex_a extracted from the previous step, is an encrypted form of the original watermark. In the proposed algorithm, only authorized users can read and understand the message. For the applications that need more security, complex procedures for generating the dictionary / using cryptographic key can be applied. Ex_W is the extracted decrypted watermark.

Fig. 7. Multiple claims of ownership.

Table 3 The PSNR values of the proposed system using different capacity. No.

Capacity

Our system (dB)

1 2 3

64  64 128  128 256  256

65.3938 62.5321 60.5276

5. Experimental results In this section, we present the results of applying the proposed method to 512  512 gray-scale test images from the USC-SIPI database, including some commonly used images (i.e., Man, Sailboat, Lena, Elaine, House and Boat). The tested images are illustrated in Fig. 3. The sparse representation is obtained using an implementation of StOMP from the SparseLab software package (Donoho, Stodden, & Tsaig, 2007). The basic properties of our proposed system and some of the existing SVD-based and DWT-SVD based watermarking techniques introduced in Ali and Ahn (2014), Lai and Tsai (2010), Mohammad et al. (2008) are listed in Table 2. As mentioned earlier, our

Fig. 6. False positive detection problem.

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Table 4 PSNR values using different images. Images

Lai and Tsai

Ali and Ahn

Our system

Man Sailboat Lena

51.0715 50.4954 48.6745

33.2837 34.8741 –

60.5276 60.8093 59.6646

proposed algorithm can be used for both bi-level and gray-level watermarks, and it embeds the watermark in only one sub-band, which can enhance the imperceptibility while other algorithms use two (Lai & Tsai, 2010) and four sub-bands (Ali & Ahn, 2014) for embedding. Unlike existing techniques, our technique incorporates an encryption mechanism to protect the watermark. Regarding the number of keys needed for extraction, the SVD components of the original image (or the original image itself with size m  n) are needed in Mohammad et al. (2008) to extract the watermark. In Lai and Tsai (2010), the original HL and LH frequency sub-bands along with their watermarked principal components (i.e., 6 matrices, each of size m2  n2) are needed, whereas the orthogonal matrices V of the watermark sub-bands (4 matrices) along with the original image are needed in Ali and Ahn (2014) to extract the embedded watermark. In our approach, we only need the orthogonal matrices of LL (each of size m2  n2) along with the dictionary (with size 2mk  2nk ), which can be also extracted from the watermarked image. The Peak Signal-to-Noise Ratio (PSNR) and Normalized Correlation (NC) will be used to evaluate the performance of the watermarking algorithms. The Peak Signal-to-Noise Ratio (PSNR) between the original and watermarked image has been widely used to evaluate imperceptibility, and is calculated using Eq. (16):

2552  m  n PSNR ¼ 10  log10 Pm Pn 2 i¼1 j¼1 ðf ði; jÞ  gði; jÞÞ Þ

ð16Þ

where f is the original host image, and g is the watermarked image. m and n are the width and height of the original image. For robustness evaluation, Normalized Correlation (NC) between the original and recovered watermark under several attacks is used. NC is calculated using the following equations.

PP 0 i jW  W NC ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P 2 P P 02 i jW  i jW

ð17Þ

W and W0 are the original and extracted watermark, respectively. NC takes values between 1 (optimal case) and 1 (no similarity). The experimental results consist of two main tests, a security test, and a robustness and imperceptibility test. 5.1. Security test In this section, the security issues are tested, which are: (i) unauthorized reading of the secrete message, (ii) the problem of false positive detection, and (iii) the problem of multiple claims of ownership. Fig. 4 shows (a) the original watermark, (b) its sparse representation, and the reconstructed watermark using (c) correct dictionary and (d) incorrect dictionary, derived using DCT instead of DWT. As shown, the sparse coding of the watermark is unreadable. Only the authorized user can reconstruct the watermark using the dictionary chosen in an earlier stage. Even if the attacker knew that the dictionary can be derived from the watermarked image, it is difficult to know the level of decomposition as it depends on the owner’s watermark, the used sub-band, how the watermarked sub-band was permutated, and the way used to generate the dictionary. All these four security keys are second line defense in case of knowing the dictionary which is highly unlikely.

The false positive detection problem is the main drawback of most of the current SVD-based watermarking techniques. This is due to the need of providing some information during extraction which may give a faked watermark with an acceptable quality. The proposed approach succeeds in tackling the false positive detection problem by encoding the original watermark using a part of the original host image (i.e., dictionary), so the right watermark will be kept in a relationship with the host image. Only the right information can provide a meaningful message. Assume we have a rightful owner and an attacker. The information of both claimers will be entered into our watermarking system, which will extract the dictionary from the given watermarked images, and hence will be the judge in this situation. Fig. 5 demonstrates this issue. The rightful information (watermarked eigenvectors) enables the extraction of the owner watermark image shown in (a), whereas, providing fake information gives an unrecognized image, shown in (b). Since the dictionary is generated from the highest-energy part of the transformed image and the nonzero coefficients of the sparse watermark are mysteriously distributed within this part, the dictionary survives as long as the quality of the watermarked image is not affected. Let us consider the worst case scenario where the attacker knows that the dictionary is derived from the watermarked image. If the attacker tries to obstruct generating the dictionary, then he/she has one of two choices; affecting the quality of the watermarked image, and in this case, the attack will be discovered, or preserving it, and in this case, the ownership evidence can be displayed. Fig. 6 shows the extracted watermarks and the normalized correlation (NC) values between the extracted watermarks and the original and counterfeit watermarks using six images from Fig. 3 as a watermark. Fake eigenvectors are obtained by embedding Cameraman image in the same host image used to carry the original watermark. The NC values show that there are no similarities between the extracted and counterfeit watermarks, and hence gives a clear indication that our proposed technique is able to overcome the false positive detection problem. Fig. 7 proves the efficiency of the proposed system in resolving the rightful ownership of a double watermarked image. It displays double watermarked images, and the extracted watermarks using the authentic information. As seen, as long as the watermarked image has an acceptable Peak Signal-to-Noise Ratio (PSNR), the embedded watermark can be extracted. 5.2. Imperceptibility and robustness test In addition to achieving a high degree of security and tackling critical problems, our SC–DWT–SVD-based watermarking system improves the robustness and imperceptibility characteristics of DWT–SVD based watermarking. Table 3 presents the PSNR values of the proposed approach using the ‘Man’ host image (shown in Fig. 3(a)) and different sizes of the ‘Peppers’ watermark image (shown in Fig. 3(g)). The results show that for the three different watermark sizes, the PSNR values are still above 56 dB, which means that the quality of the watermarked image is very high even when embedding a large watermark. In the remaining experiments, 256  256 ‘Peppers’ image is used as a watermark. Table 4 represents the PSNR for different images for our technique and other DWT–SVD watermarking techniques introduced in Ali and Ahn (2014), Lai and Tsai (2010). As noticed, the PSNR values of our algorithm are noticeably higher than other algorithms because only a few numbers of coefficients that represent the watermark are embedded instead of using all coefficients. Table 5 shows the NC results under several image processing operations and geometric distortions after embedding the ‘‘Peppers’’ watermark in the ‘‘Man’’ cover image. The NC values of

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the proposed technique are always above 0.84, which reflects the high quality of the extracted watermark. It is clear that the proposed algorithm shows good robustness even when the attack is very strong. A comparison between the proposed algorithm and the algorithm described in Ali and Ahn (2014), Lai and Tsai (2010) is displayed in Table 6 using the results reported in Ali and Ahn (2014) and results obtained by implementing the algorithm of Lai and Tsai (2010) on the same data to achieve a fair comparison.

The listed results indicate that the proposed SC–DWT–SVD algorithm is more robust than the other two DWT–SVD based algorithms especially against RST (rotation, scaling, and translation). The reason behind the high performance of the proposed approach under RST is due to three factors: using sparse coding of the watermark, so just a few numbers of coefficients affect the quality of the reconstructed watermark, and at the same time, it allows us to use a high embedding factor which enhances the robustness.

Table 5 NC values of the proposed system under various attacks.

Table 6 Robustness comparison using Man and Sailboat images. Attacks

Average filter [3  3] Median filter [3  3] Gaussian low pass filter Gaussian noise (0.01) Gaussian noise (0.1) Salt & pepper (0.01) Salt & pepper (0.1) Speckle noise (0.01) Speckle noise (0.1) Sharpening Blurring Contrast adjustment Histogram equalization Gamma correction (0.8) Soft threshold (0.4) Hard threshold (0.4) JPEG compression (QF = 50) Rescaling (512-256-512) Rotation 45° Rotation 270° Cropping (25%) Cropping (50%)

Lai and Tsai (2010)

Ali and Ahn (2014)

Our proposed system

Man

Sailboat

Man

Sailboat

Man

Sailboat

0.9402 0.9702 0.9708 0.8736 0.8000 0.9470 0.7978 0.9762 0.8219 0.9663 0.6535 0.9825 0.9755 0.9831 0.9491 0.9450 0.9841 0.8991 0.8717 0.9727 0.9705 0.8795

0.9196 0.9409 0.9373 0.8668 0.7782 0.9581 0.7982 0.9554 0.8171 0.9591 0.6287 0.9791 0.9803 0.9856 0.9526 0.9461 0.9857 0.8776 0.8276 0.9046 0.9625 0.8636

0.9191 0.9495 0.9630 0.8589 – – – – – 0.8893 – 0.9490 0.9279 0.9639 – – 0.9607 0.9445 – – – –

0.9435 0.9753 0.9906 0.8894 – – – – – 0.9073 – 0.9224 0.9654 0.9625 – – 0.9892 0.9731 – – – –

0.9757 0.9817 0.9785 0.9681 0.8619 0.9823 0.9113 0.9838 0.9541 0.9769 0.8415 0.9865 0.9817 0.9889 0.9297 0.9490 0.9852 0.9652 0.9763 0.9867 0.9757 0.9285

0.9790 0.9809 0.9788 0.9565 0.8274 0.9791 0.8982 0.9786 0.9140 0.9754 0.7921 0.9794 0.9811 0.9791 0.9355 0.9488 0.9846 0.9662 0.9171 0.9852 0.9484 0.9249

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The second factor is using the provided principal components in the extraction stage to decode the sparse coding coefficients (based on Eq. (13)). The third parameter contributing in reconstructing the watermark is the dictionary as shown in Eq. (14). The principal components and the dictionary, used to retrieve the sparse coding coefficients and reconstruct the watermark, are not affected by the attacks, and at the same time, no one can get any useful information about the watermark from the dictionary itself as each image has a unique combination of the dictionary’s columns. Even though that the principal components are used as a part of the extraction stage in the majority of SVD-based watermarking techniques; however, these techniques have a high false positive detection rate. Our approach successes in overcoming this drawback and using the principal components with guaranteeing a high security level, as proved in Section 5.1. At the same time, the number of keys needed for extraction in our technique is still smaller than others. The superiority of our proposed algorithm is clearly illustrated Fig. 8, which graphically represent the results listed in Table 6 using the ‘‘Man’’ cover image and the ten attacks considered in Ali and Ahn (2014). These attacks are: Average Filter with 3  3 window (AF), Median Filter with 3  3 window (MF), Gaussian Low pass Filter (GL), Gaussian Noise with variance 0.01 (GN), Sharpening (SH), Contrast adjustment (CA), Histogram equalization (HE), Gamma Correlation 0.8 (GC), JPEG Compression with QF = 50 (JPEG), Rescaling 512 ? 256 ? 512 (RS). The proposed technique also outperforms some of binary image watermarking techniques. In order to demonstrate that, a comparison between our algorithm and the pure SVD-based watermarking algorithm introduced in (Mohammad et al., 2008) under some attacks (Average Filter (AV), Median Filter (MF), Gaussian Noise (GN), Sharpening (SH), JPEG Compression (JPEG), Gamma Correction (GC), Histogram Equalization (HE), and Rotation (RT)) is summarized in Fig. 9. The figure clearly shows the superiority of our algorithm. Although the robustness of the algorithm of Mohammad et al. is not satisfactory, it is considered as one of the leading research algorithms in tackling the false positive detection problem in SVD-based watermarking. Accordingly, the above experimental results show that the proposed algorithm can achieve the security requirement while maintaining robustness against image operations and geometric attacks.

6. Conclusion and future work There has been an increased need for the development of secure watermarking algorithms that maintain high level of robustness and imperceptibility. We presented in this paper a novel secure watermarking system based on sparse coding, Discrete Wavelet Transform and Singular Value Decomposition. The main contribution of the proposed approach is performing sparse coding with a private dictionary generated from the host image to encode the watermark as a function of its carrier. The incorporation of sparse coding facilitates a high level of compression, reduces the number of elements needed to effectively represent the watermark, and meets the security requirement. Such measures proved to be successful in dealing with the unauthorized reading problem and the problems of false positive detection and multiple claims of ownership. Moreover, the imperceptibility and robustness aspects of the proposed algorithm are found to be superior to that of other up-to-date algorithms due to its high capability in compressing the watermark. The experimental results show that the proposed approach manages to deal efficiently with various watermarking requirements. Despite of the high performance of the proposed approach in term of robustness, imperceptibility, and security requirement, the complexity requirement is sacrificed as the use of sparse coding adds extra complexity to the watermarking technique. Although the proposed approach uses StOMP sparse coding algorithm, which is relatively fast when compared with many other techniques, there is still a need for faster implementation. It should be noted also that the security of the proposed approach is evaluated using only two attacking techniques. The proposed approach may need to be further examined in the future using different attacking approaches. As a future work, a totally blind sparse coding-based watermarking framework able to extract the watermark with zero-side information will be considered. Moreover, the time complexity and computation cost will need to be enhanced to present a more reliable scheme. The proposed approach proves its reliability for image watermarking, and it will be extended to the video watermarking in the future. It is believed that this research will open the door for serious exploitation of sparse coding in digital watermarking. Future watermarking algorithms may adapt this approach and benefit from its promising behavior for many applications, such as fingerprinting and medical image watermarking.

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Fig. 8. Robustness comparison for the ‘‘Man’’ cover image.

Fig. 9. Comparison between our algorithm and Mohammad et al. (2008).

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