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An optical watermarking scheme with two-layer framework based on computational ghost imaging
Optics and Lasers in Engineering 107 (2018) 38–45
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
An optical watermarking scheme with two-layer framework based on computational ghost imaging Sui Liansheng a,b,∗, Cheng Yin a, Tian Ailing c, Anand Krishna Asundi d a
School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China Shaanxi Key Laboratory for Network Computing and Security Technology, Xi’an 710048, China c Shaanxi Province Key Lab of Thin Film Technology and Optical Test, Xi’an Technological University, Xi’an 710048, China d School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore b
a r t i c l e
i n f o
Keywords: Computational ghost imaging Watermarking Nonlinear correlation algorithm
a b s t r a c t A two-layer watermarking scheme based on computational ghost imaging and singular value decomposition is proposed. In the first layer, the original watermark is encoded into a significantly small number of measured intensities in the process of computational ghost imaging to constitute a new watermark. In the second layer, the significant blocks chosen from the host image based on spatial frequency are combined to the reference image, which is used to embed the new watermark by using the singular value decomposition. Differing from other watermarking schemes, the information of original watermark can be verified without clear visualization via calculating the nonlinear correlation map between the original one and the reconstructed one. Besides optical parameters such as wavelength and propagation distance, a series of phase-only masks are used as security keys, which can enlarge the key space and enhance the level of security. The results illustrate the feasibility and effectiveness about the proposed watermarking mechanism, which provides an effective alternative for the related work. © 2018 Elsevier Ltd. All rights reserved.
1. Introduction Due to the rapid development of optical information processing technology and Internet, more and more researchers pay attention to the security of information storage and transmission using optical ways [15]. Since Refregier and Javidi [6] proposed the classic double random phase encoding (DRPE) in Fourier domain, lots of transform have been applied to image security techniques, such as fractional Fourier transform, Fresnel transform, fractional Mellin transform, gyrator transform and so on [7-17]. Due to intrinsic linearity of optical transform, most schemes are threatened with several common attacks [18-20]. Various kinds of information security cryptosystems based on different optical technologies such as polarized light, photon-counting, integral imaging, interference and diffractive imaging [21-28] have been reported, which have great potential to solve the issues on image encryption, information hiding, optical authentication, etc. Recently, ghost imaging known as single-pixel imaging is an intriguing optical technique [29,30], which provides a promising alternative in the field of information encryption due to its physical characteristics [31,32]. Zafari et al. [33] proposed an optical encryption based on selective computational ghost imaging to retrieve image with best qual-
∗
ity, where only one element of a random matrix attributes a different value in each realization. Zhang et al. [34] proposed a high-performance double cryptography to improve the security level, where the image is firstly encoded with fast Fourier transform, and then encrypted with the system of compressive ghost imaging. Chen [35] reported an optical data security system with high flexibility. In this system, a series of pre-generated random intensity patterns are used as security keys, where each pattern is encoded into two phase-only masks using noniterative interference-based phase extraction algorithm. During the process of encoding, each pair of phase-only masks are sequentially embedded into two spatial light modulators, and the measured intensity can be obtained with a single-pixel bucket detector. Although the affect of cross-talk cannot be eliminated in the scheme presented by Wu et al. [36], they demonstrated the validity of applying computational ghost imaging for optical multiple-image encryption. In the system suggested by Li et al. [37], the discrete cosine transformation distributions of multiple images are scrambled firstly, and then combined into an interim image using coordinate sampling. Finally, the interim image is placed in the object plane of compressive ghost imaging system, and the ciphertext is captured with a buck detector, from which the original information can be decoded with better quality.
Corresponding author at: School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China. E-mail address: [email protected] (S. Liansheng).
https://doi.org/10.1016/j.optlaseng.2018.03.005 Received 27 January 2018; Received in revised form 27 February 2018; Accepted 6 March 2018 0143-8166/© 2018 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 107 (2018) 38–45
As a promising way to protect private data from usurpation, the optical techniques about watermarking and information hiding have attracted more and more attentions [38-40]. Because the encoded results are real-valued measured intensities and the number of measurements used for object construction is significantly reduced, which lead to effective implementation, the watermarking and information hiding schemes based on ghost imaging have been continually reported in recent years. Chen and Chen [41] found that signals at reference and object beam arms can be converted into two quantization levels, and applied for object authentication along with reduction of data size. In the system reported by Chen [42], a series of phase-only masks are retrieved from pre-generated random intensity-only maps, and the corresponding propagation distances are axially varied in a random manner to enhance the security of scheme. Zhao et al. [43] researched the mechanism of optical encryption based on quick response code and computational ghost imaging, which can ensure the information not to access by an eavesdroppers even the eavesdropping ratio is up to 60%. Subsequently, they proposed a novel information hiding scheme with high security [44], where the watermark is firstly encrypted with the configuration of computational ghost imaging system. Then, the encrypted results are embedded into the least significant bits of pixels in the host image. To improve the quality of recovered watermark, total variation minimization by augmented Lagrangian and alternating direction algorithms is used for reconstruction. In this paper, an optical information hiding scheme is proposed based on computational ghost imaging, where both binary and gray-scale images can be considered as the watermarks. Initially, the original watermark is encoded into a series of measured intensities under the configuration of computation ghost imaging. Differing from the scheme presented in Ref. [44], the encoded results are embedded into the host image using singular value decomposition in the proposed scheme. Notably, it is not direct fusion between encoded information with host image. Some non-overlapping significant blocks are chosen from the host image based on spatial frequency coefficients to constitute an interim called as the reference image, which is used as a carrier to load the encoded information of original watermark. Compared with previous work, there are two main advantages to apply this kind of embedding mechanism. One is that an additional protection is afforded to improve the security, because the scheme will have camouflage property to some extent. Another is that it will have high robustness against common attacks such as Gaussian noise and occlusion attack due to excellent properties of singular value decomposition method. It is worth noting that the nonlinear correlation algorithm is applied to verify the presence of original information using the nonlinear correlation map. Although the watermark cannot be observed with clear visualization, the number of measured intensities obtained in the process of computational ghost imaging are considerably reduced. The rest of this paper is organized as follows. In Section 2, the proposed information hiding scheme is introduced in detail along with computational ghost imaging and singular value decomposition. Meanwhile, the verification of original information using nonlinear correlation algorithm is discussed. In Section 3, experimental results and security analysis are performed. Finally, a brief conclusion is described in Section 4.
Fig. 1. Schematic setup of computational ghost imaging encoded system: SLM, spatial light modulator; BD, bucket detector.
to embed the new watermark. Eventually, the reference image is inversely partitioned, and the resultant blocks are mapped into their original locations, with which the watermarked image is formulated in the second layer. The schematic arrangement of the computational ghost imaging adopted in the first layer of the proposed scheme is shown in Fig. 1. Differing from the conventional configuration where two spatially correlated beams pass through different optical paths, the rotating diffuser is substituted with the computer controlled spatial light modulator in the computational ghost imaging based encryption scheme, into which a series of random phase-only masks is sequentially embedded. Due to known phase-only masks, the intensity patterns at the reference beam arm can be virtually calculated by means of wave propagation in free space. The collimated laser beam is used for the illumination, and modulated by the beforehand phase-only masks to create random speckle patterns. A bucket detector without spatial resolution placed behind the object plane is used to measure the total intensity when each speckle pattern passes through the object, which can be described as 𝐵𝑖 =
∬
𝑑 𝜇𝑑 𝜐𝐼𝑖 (𝜇, 𝜐)𝑇 (𝜇, 𝜐),
(1)
where 𝑇 (𝜇, 𝜐) is the transmission function of the object and (𝜇, 𝜐) denotes the transversal coordinates in the object plane. The value of the measured intensity Bi is directly determined by the speckle patterns 𝐼𝑖 (𝜇, 𝜐) = |𝐸𝑖 (𝜇, 𝜐)|2 , where 𝐸𝑖 (𝜇, 𝜐) is the free-space propagation field for the phase-only mask exp(j𝜑i (x, y)). The propagation is a Fresnel diffraction process, which can be mathematically expressed as ( ) 𝐸𝑖 (𝜇, 𝜐) = exp 𝑗 𝜑𝑖 (𝑥, 𝑦) ∗ ℎ(𝑥, 𝑦, 𝑧). (2) Here, the symbol ∗ denotes the convolution operation and h(x, y, z) is the point pulse function of the Fresnel propagation at a distance z, which is defined as ) ( ) exp (𝑗2𝜋𝑧∕𝜆) 𝑗𝜋 ( 2 ℎ(𝑥, 𝑦, 𝑧) = (3) exp 𝑥 + 𝑦2 . 𝑗𝑧𝜆 𝑧𝜆 Here, 𝜆 is the wavelength of the laser beam. To reconstruct the object, the measured intensity values collected by the bucket detector are cross-correlated with the speckle patterns at the reference beam arm. Suppose the number of the measured intensities is K and ⟨ · ⟩ denotes the ensemble average computation, the decoded object can be mathematically expressed as
2. Proposed scheme
𝐺(𝜇, 𝜐) = ⟨𝐵𝐼 (𝜇, 𝜐)⟩−⟨𝐵 ⟩⟨𝐼 (𝜇, 𝜐)⟩ =
In this section, the details of the proposed optical image watermarking scheme along with the computational ghost imaging is presented, which includes two layers. Initially, the original watermark image is encoded into a series of intensity values by using the computational ghost imaging technology, and these intensity data are rearranged into a twodimensional interim image considered as the new watermark in the first layer. Subsequently, the host image is divided into smaller blocks, and some significant blocks are chosen to form the reference image, which has the same size as the new watermark. With the use of singular value decomposition, the singular values of the reference image are modified
𝐾 )( ) 1 ∑( 𝐵 −⟨𝐵𝑖 ⟩ 𝐼𝑖 (𝜇, 𝜐)−⟨𝐼𝑖 (𝜇, 𝜐)⟩ . 𝐾 𝑖=1 𝑖
(4) Let the original watermark image denoted as 𝑤(𝜇, 𝜐), it is encoded into a series of real-valued intensities via the process of computational ghost imaging. To embed them into the host image, these data are rearranged into an interim image as the new watermark 𝑤′ (𝜇, 𝜐) containing K pixels, which has m rows and n columns. It should be pointed out that the new watermark usually is not equal to the original one in the number of pixels. 39
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where 𝜎̂ 𝑓𝑗 ′ (𝑗 = 1, 2, ..., 𝑚) are the modified coefficients. The modulated reference image 𝑓̂′ (𝜇, 𝜐) can be obtained by performing an inverse singular value decomposition transform. Finally, the modulated image is inversely segmented into blocks, which are mapped into their original locations for constructing the watermarked image 𝑓̂(𝜇, 𝜐). In order to further illustrate the proposed scheme, a diagram of embedding the watermark into the host image is shown in Fig. 2. To retrieve the hidden watermark in the watermarked image, the extraction process should be performed, which is similar to aforementioned embedding process but in the reversed order. Initially, the watermarked image is partitioned into smaller blocks, where each block has the size p × q pixels. With the known of locations for the selected blocks, the modulated reference image is reconstructed again, on which the singular value decomposition transform is performed to obtain the modulated singular values. With the help of the singular values of original reference image calculated using Eq. (6), the information of new watermark can be recovered as
Suppose the host image denoted as 𝑓 (𝜇, 𝜐) containing M × N pixels, which satisfies the condition as M × N > K. Thus, the host image can be divided into enough non-overlapping smaller blocks, from which some significant blocks are chosen to constitute a reference image to carry the information of the watermark. Due to more information embedding capacity and more robustness against many kinds of common attacks, the mode of embedding the new watermark 𝑤′ (𝜇, 𝜐) by modulating the magnitude of coefficients in a transform of the reference image is applied. As we all know, the human visual system has less sensitivity to the modification of high-valued coefficients so that it can produce the watermarked image with high imperceptibility to embed watermark in them. However, it should be realized that the robustness of the produced watermark is fragile, which can be removed from the watermarked image using high frequency filter easily. If the watermark is embedded in the low-valued coefficients, the quality of the watermarked image will be degraded seriously. Because the most energies of an image are stored in low-valued coefficients, the human eyes can perceive the changes of these coefficients sensitively. To overcome the conflict of these requirements, a trade-off between imperceptibility and robustness is explored, where the blocks with middle-valued coefficients are chosen to form the reference image. As an effective measurement of the overall activity level in an image, spatial frequency can reflect the clarity of image [45]. So, a significant block can be identified by calculating its spatial frequency coefficient, which is mathematically defined as
𝑗 𝜎𝑤 ̂ 𝑓𝑗 ′ − 𝜎𝑓𝑗 ′ )∕𝛾. ′ = (𝜎
Subsequently, the new watermark 𝑤′ (𝜇, 𝜐) can be reconstructed by performing the inverse singular value decomposition with the matrices 𝑈𝑤′ (𝜇, 𝜐) and 𝑉𝑤′ (𝜇, 𝜐) calculated using Eq. (7). Furthermore, the new watermark is converted into a series of real-valued data, which actually are the measured intensities expressed in Eq. (1). Now, the original watermark 𝑤(𝜇, 𝜐) can be recovered as 𝐺(𝜇, 𝜐) by using the second-order correlation algorithm described as Eq. (4). As discussed in Ref. [30] that the ghost imaging measurement procedure is a vector projection of the object transmission function over a series of random vectors 𝐼𝑖 (𝜇, 𝜐), some effective reconstruction algorithms such as orthogonal matching pursuit [46] and smooth l0 (SL0 ) [47] based on compressive sensing can be applied to recover object from measured intensities, which can improve the image quality considerably. If there is no need for visual observation to the reconstructed object, the nonlinear correlation algorithm can be used to verify the presence of object [48]. In the proposed scheme, the recovered watermark 𝐺(𝜇, 𝜐) can be effectively authenticated as { }|2 | 𝑁 𝐶 (𝜇, 𝜐) = |𝐼 𝐹 𝑇 |𝑐 (𝜇, 𝜐)|𝜌−1 𝑐 (𝜇, 𝜐) | , (12) | |
√ √ 𝑝 𝑞 𝑝 𝑞 √ 1 ∑ ∑ 1 ∑∑ 𝑠𝑓 = √ (𝐵 𝑙𝑘(𝑖, 𝑗 )−𝐵 𝑙𝑘(𝑖, 𝑗 −1))2 + (𝐵 𝑙𝑘(𝑖, 𝑗 )−𝐵 𝑙𝑘(𝑖−1, 𝑗 ))2 . 𝑝𝑞 𝑖=1 𝑗=1 𝑝𝑞 𝑖=1 𝑗=1
(5) Here, Blk denotes a smaller block divided from the host image and has p × q pixels. After all blocks are evaluated, the spatial frequency coefficients are sorted in descending or ascending order, and the blocks with middle-valued coefficients are chosen. Notably, the selected blocks should be enough to constitute the reference image, which has the same size as the new watermark. For convenience, the combined reference image is denoted as 𝑓 ′ (𝜇, 𝜐), which also has m × n pixels. Currently, there are several advantages such as: the singular values of the image reflect energy characteristics as well as the singular vector represents intrinsic algebraic properties; the singular values have a very good stability, which indicates that these coefficients cannot change in large variation when a perturbation such as cropping, filtering and rotation is performed on the image; and there is no strict requirement about the size of an image in the process of singular value decomposition. Thus, the only condition on the size of reference image 𝑓 ′ (𝜇, 𝜐) is that the number of rows should be equal to the number of columns as soon as possible, i.e. m ≈ n. In the proposed scheme, the main idea based on singular value decomposition is to apply the transform to the reference image 𝑓 ′ (𝜇, 𝜐) and the new watermark 𝑤′ (𝜇, 𝜐), and then modify the singular value coefficients of reference image with those of watermark. Initially, two singular value decomposition transforms are performed on the reference image and watermark, respectively, which are described as 𝑓 ′ (𝜇, 𝜐) = 𝑈𝑓 ′ (𝜇, 𝜐)∗𝑆𝑓 ′ (𝜇, 𝜐)∗𝑉𝑓𝑇′ (𝜇, 𝜐),
(6)
𝑤′ (𝜇, 𝜐) = 𝑈𝑤′ (𝜇, 𝜐)∗𝑆𝑤′ (𝜇, 𝜐)∗𝑉𝑤𝑇′ (𝜇, 𝜐).
(7)
𝑐 (𝜇, 𝜐) = 𝐹 𝑇 {𝐺(𝜇, 𝜐)}𝑐𝑜𝑛𝑗 {𝐹 𝑇 {𝑤(𝜇, 𝜐)}}.
3. Experimental results and analyses To demonstrate the feasibility and effectiveness of the proposed scheme, the numerical experiment is conducted as shown in Fig. 1, where the plane wave from a He-Ne laser emitting at 632.8 nm is used for illumination. In the process of ghost imaging on the original watermark, a series of random phase-only masks exp(𝑗 𝜑𝑖 (𝑥, 𝑦)), 𝑖 = 1, 2, ..., 𝐾, are sequentially input into the spatial light modulator, which resolution is 64 × 64 pixels with 20 μm pixel pitch. The propagation distance between the spatial light modulator and the bucket detector plane is 7.4 cm, while the laser beam waist is 740 μm. By the van Cittert-Zernike theorem, the speckle size at the object plane can be calculated with 𝛿(𝑧) = 𝜆𝑧∕𝜆𝑧 and 𝜔 is the laser beam waist, which roughly leads to 20 μm.
Here, 𝜎𝑖𝑗 (𝑗 = 1, 2, ..., 𝑚) are the singular values of matrices. When the rank of the matrices is r, these coefficients satisfy the condition as (9)
Then, the singular values of reference image are modified with those of the watermark attenuated with a real weight factor 𝛾 as follows 𝑗 𝜎̂ 𝑓𝑗 ′ = 𝜎𝑓𝑗 ′ + 𝛾 ∗ 𝜎𝑤 ′,
(13)
Here, FT{ · } and IFT{ · } respectively represent the two-dimensional Fourier transform and inverse Fourier transform, conj{ · } computes the complex conjugation of the argument, 𝜌 is the strength of the applied nonlinearity, and 𝑤(𝜇, 𝜐) is the original watermark image. It is worthwhile to note that the nonlinear correlation algorithm can enable image authentication with far less measured intensities such as less than 5% of Nyquist limit. In addition, besides the phase distribution of random phase-only masks 𝜑𝑖 (𝑥, 𝑦), 𝑖 = 1, 2, ..., 𝐾, optical parameters such as wavelength 𝜆 and propagation distance z can be used as the secret keys to enhance the level of system security.
Here, the matrices 𝑈𝑖 (𝜇, 𝜐) and 𝑉𝑖 (𝜇, 𝜐)(𝑖 = 𝑓 ′ , 𝑤′ ) are orthogonal, and 𝑆𝑖 (𝜇, 𝜐) are diagonal which can be expressed as ( ) 𝑆𝑖 (𝜇, 𝜐) = 𝑑𝑖𝑎𝑔 𝜎𝑖1 , 𝜎𝑖2 , ..., 𝜎𝑖𝑚 . (8)
𝜎𝑖1 ≥ 𝜎𝑖2 ≥ ⋯ ≥ 𝜎𝑖𝑟 ≥ 𝜎𝑖𝑟+1 = 𝜎𝑖𝑟+2 = ⋯ = 𝜎𝑖𝑚 = 0.
(11)
(10) 40
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Fig. 2. Diagram of the watermark embedding process in the proposed information hiding system: CGI, computational ghost imaging; SVD, singular value decomposition.
Fig. 5. (a) Reconstructed watermark with less measured intensities using second-order correlation algorithm and (b) corresponding nonlinear correlation map.
Fig. 3. (a) Original host image “Peppers” and (b) original watermark “Flower”.
Fig. 3(a) shows a grayscale image “Peppers” with 128 × 128 pixels used as the host image, which is chosen from USC-SIPI image database [49]. Fig. 3(b) shows a binary image “Flower” with 64 × 64 pixels considered as the original watermark designed by oneself, where the pattern represents the meaning of flower in Chinese. The size of non-overlapping blocks divided from the host image is set to 4 × 4 pixels, i.e. 𝑝 = 4 and 𝑞 = 4. It should be pointed out that the size of reference image composed of significant blocks may vary depending on K measured intensities of original watermark in the process of computational ghost imaging. The real weight factor used for embedding the new watermark into the reference image based on singular value decomposition is set to 1.0𝑒 − 5.
The strength of the applied nonlinearity 𝜌 is set to 0.4. To evaluate the quality of the watermarked image, the peak signal noise ratio (PSNR) between it and the original host image is mathematically calculated as ( ) PSNR 𝑓 , 𝑓̂ = 10 × log
{
2552 ( ) MSE 𝑓 , 𝑓̂
} .
(14)
Here, f is the host image, 𝑓̂ is the watermarked image. For brevity, the coordinates are omitted. The mean squared error (MSE) between
Fig. 4. (a) Watermarked host image “Peppers”, (b) recovered watermark “Flower” using second-order correlation algorithm and (c) recovered watermark “Flower” using SL0 algorithm. 41
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Fig. 6. (a)–(d) Occluded watermarked host image from top, bottom, left and right side.
Fig. 7. (a)–(d) Nonlinear correlation maps respectively corresponding to Fig. 6(a)–(d).
them is expressed as ( ) MSE 𝑓 , 𝑓̂ =
𝑀 𝑁 1 ∑∑| |2 |𝑓 (𝜇, 𝜐) − 𝑓̂(𝜇, 𝜐)| . | 𝑀𝑁 𝑖=1 𝑗=1 |
point of human visual system. Notably, if the measured intensities are continually reduced, although the construction result can be enhanced by using compressive sensing methods, the watermark with high fidelity like Fig. 4(c) cannot be recovered. If the reconstructed watermark only needs to be authenticated, it can be implemented with far less measured intensities based on nonlinear correlation algorithm expressed by Eqs. (12) and (13). Fig. 5(a) shows the watermark reconstructed with 192 measured intensities (i.e., only 4.69% of Nyquist limit), which is noise-like and cannot clearly render information. However, there is a remarkable peak over the noisy back-ground in the corresponding nonlinear correlation map shown in Fig. 5(b), which means that the watermark can be effectively verified without clear visualization. As we all know, the watermark may not be recovered, when the watermarked image is contaminated with noise or destroyed severely such as pixel loss to a large percentage, namely the watermarked image is interfered by noise attack or occlusion attack. So, the robustness
(15)
In addition, the quality of the recovered watermark can be evaluated in a similar way. When 1760 measured intensities are used in the process of ghost imaging, the watermarked image with PSNR = 56.2114 dB is shown in Fig. 4(a), which indicates that the watermarked image has good performance of imperceptibility. The recovered watermark using the secondorder correlation algorithm is shown in Fig. 4(b). Although PSNR only reaches 6.1594 dB, the basic content of watermark can be discerned with naked eyes. When the construction algorithm based on compressive sensing is applied, the watermark with high PSNR can be obtained. With using SL0 , the recovered watermark with PSNR = 42.4962 dB is shown in Fig. 4(c), where there is no perceptual degradation observed from the 42
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Fig. 8. Nonlinear correlation map when (a) k = 0.4, (b) k = 0.6, (c) k = 0.8 and (d) k = 1.0.
Fig. 9. (a) and (b) Resultant nonlinear correlation maps respectively corresponding to wrong wavelength with error of ±40 nm, (c) and (d) calculated nonlinear correlation maps respectively corresponding to wrong propagation distance with error of ±5 mm.
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Fig. 10. (a) and (b) Resultant nonlinear correlation maps respectively corresponding to 50% and 60% of phase-only masks divulged in the process of reconstruction of watermark.
Fig. 11. (a) A gray-scale watermark, (b) reconstructed watermark and (c) nonlinear correlation map between (a) and (b).
against these attacks should be evaluated. Because the original watermark is embedded into the significant blocks with middle-valued spatial frequency coefficients, most blocks may be distributed in one region of the watermarked image. If this region is occluded, the watermark will not be retrieved. To verify the capacity of the proposed scheme, 50% pixels from the top, bottom, left and right side are cropped in the watermarked image as shown in Fig. 6(a)–(d), respectively. Using only 192 measured intensities, the corresponding nonlinear correlation maps are displayed in Fig. 7(a)–(d), respectively, from which it can be known that the retrieved results still contain useful information to generate good correlation signals to verify the presence of watermark. To evaluate the effect of noise attack, the watermarked image is supposed to be polluted with a Gaussian random noise 𝐺(𝜇, 𝜐) with zero-mean and identity standard deviation, which is mathematically expressed as 𝑓̂∗ (𝜇, 𝜐) = 𝑓̂(𝜇, 𝜐) × (1 + 𝑘𝐺(𝜇, 𝜐)).
ror of ±5 mm is used during the retrieved process, the resultant nonlinear correlation maps are depicted in Fig. 9(c) and (d), respectively. In these figures, there are multiple peaks generated and only the noisy backgrounds are obtained, from which it is impossible to verify the presence of watermark. Additionally, if a potential eavesdropper who knows the embedding mechanism of watermark and can access a fraction of phase-only masks illegally, it is possible to retrieve the hidden information about watermark. When 50% and 60% of masks are divulged, the resultant nonlinear correlation maps are depicted in Fig. 10(a) and (b), respectively. In fact, when 50% masks are known, the eavesdropper may obtain the map with a peak sometimes. With 60% masks known, it is assured that he can observe the remarkable peak at every turn, which means that the information only can be retrieved when the eavesdropper should intercept at least 60% of phase masks. Obviously, it can enlarge the key space when a series of phase-only masks is used as security key. From aforementioned analyses, it can be safe to say that these experimental parameters play an important role in the process of verifying the presence of original watermark and the proposed scheme has higher security. It is worth noting that the gray-scale image considered as the watermark can be effectively embedded into the host image as well as can be verified with far less measured intensities captured in the process of computational ghost imaging. However, the gray-scale watermark possesses larger spectrum range and more information than binary one, the number of measured intensities should be increased to some degree. As shown in Fig. 11(a), a gray-scale image with 64 × 64 pixels which is central part of the image “Lena” is considered as the watermark embedded into the host image “Peppers” shown in Fig. 3(a). When
(16)
Here, 𝑓̂∗ (𝜇, 𝜐) is the polluted watermarked image and k is noise strength. When k is set to 0.4, 0.6, 0.8 and 1.0, the corresponding nonlinear correlation maps are displayed in Fig. 8(a)–(d), respectively, where the sharp peaks are obviously observed. So, it can be concluded that the proposed scheme have better tolerance to these attacks. Similar to other schemes based on computational ghost imaging, a series of phase-only masks used to calculate the speckle patterns can be considered as security keys besides light wavelength and propagation distance. If one of security keys is wrong, the retrieved watermark will not contain sufficient information about original one. When the wrong wavelength with error of ±40 nm is used for reconstruction, the calculated nonlinear correlation maps are displayed in Fig. 9(a) and (b), respectively. Similarly, when the wrong propagation distance with er44
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320 measured intensities (i.e., 7.81% of Nyquist limit) are used, the reconstructed watermark using the second-order correlation algorithm is shown in Fig. 11(b) that is noise-like. The corresponding nonlinear correlation map is displayed in Fig. 11(c), where a sharp peak can be obtained to verify the presence of original watermark. Other analysis results similar to the binary watermark can be conducted.
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4. Conclusions In summary, a watermarking scheme based on computational ghost imaging is proposed. Differing from conventional approaches to verify the original watermark visually, it can be authenticated without clear observation by using the nonlinear correlation algorithm. There are two layers to enhance the security of watermark. Even if an eavesdropper cracks the second layer of embedding the new watermark into the reference image using singular value decomposition, the obtained result is a significantly small number of measured intensities, which is randomly distributed and captured in the process of computational ghost imaging. Due to optical parameters such as light wavelength, propagation distance and a large amount of phase-only masks considered as security keys, it is difficult to retrieve the original watermark even the eavesdropper knows the mechanism of the first layer. Meanwhile, the eavesdropper cannot easily destroy the presence of the presented watermark by analyzing common attacks such as noise and occlusion attack. It is believed that the work can provide a promising alternative for the research of watermark schemes. Acknowledgments This work was supported by Key Laboratory Science Research Plan of Education Department of Shaanxi Province under grant no. 16JS079. References [1] Alfalou A, Brosseau C. Optical image compression and encryption methods. Adv Opt Photonics 2009;1(November (3)):589–636. [2] Alfalou A, Brosseau C. Recent advances in optical image processing. Prog Opt 2015;60(April):119–262. [3] Chen W, Javidi B, Chen X. Advances in optical security systems. Adv Opt Photonics 2014;6(June (2)):120–55. [4] Javidi B, Carnicer A, Yamaguchi M, Nomura T, Pérez-Cabré E, Millán MS, Nishchal NK, Torroba R, Barrera JF, He W, Peng X, Stern A, Rivenson Y, Alfalou A, Brosseau C, Guo C, Sheridan JT, Situ G, Naruse M, Matsumoto T, Juvells I, Tajahuerce E, Lancis J, Chen W, Chen X, Pinkse PWH, Mosk AP, Markman A. Roadmap on optical security. J Opt 2016;18(August):083001. [5] Wang Q, Alfalou A, Brosseau C. New perspectives in face correlation research: a tutorial. Adv Opt Photonics 2017;9(March (1)):1–77. [6] Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 1995;20(April (7)):767–9. [7] Lang J, Zhang ZG. Blind digital watermarking method in the fractional Fourier transform domain. Opt Laser Eng 2014;53(February):112–21. [8] Liu Z, Guo C, Tan J, Liu W, Wu J, Wu Q, Pan L, Liu S. Securing color image by using phase-only encoding in Fresnel domains. Opt Lasers Eng 2015;68(May):87–92. [9] Chen W, Chen X, Stern A, Javidi B. Phase-modulated optical system with sparse representation for information encoding and authentication. IEEE Photon J 2013;5(April (2)):6900113. [10] Wang X, Chen W, Chen X. Optical encryption and authentication based on phase retrieval and sparsity constraints. IEEE Photon J 2015;7(April (2)):7800310. [11] Chen W. Single-shot imaging without reference wave using binary intensity pattern for optically-secured-based correlation. IEEE Photon J 2016;8(February (1)):6900209. [12] Chen W. Optical multiple-image encryption using three-dimensional space. IEEE Photon J 2016;8(April (2)):6900608. [13] Zhou N, Li H, Wang D, Pan S, Zhou Z. Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt Commun 2015;343(May):10–21. [14] Abuturab MR. Optical interference-based multiple-image encryption using spherical wave illumination and gyrator transform. Appl Opt 2014;53(October (29)):6719–28. [15] Liu Z, Guo C, Tan J, Wu Q, Pan L, Liu S. Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms. J Opt 2015;17(February (2)):025701. [16] Chen JX, Zhu ZL, Fu C, Zhang LB, Yu H. Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains. Opt Lasers Eng 2015;66(March):1–9.
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Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
An optical watermarking scheme with two-layer framework based on computational ghost imaging Sui Liansheng a,b,∗, Cheng Yin a, Tian Ailing c, Anand Krishna Asundi d a
School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China Shaanxi Key Laboratory for Network Computing and Security Technology, Xi’an 710048, China c Shaanxi Province Key Lab of Thin Film Technology and Optical Test, Xi’an Technological University, Xi’an 710048, China d School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore b
a r t i c l e
i n f o
Keywords: Computational ghost imaging Watermarking Nonlinear correlation algorithm
a b s t r a c t A two-layer watermarking scheme based on computational ghost imaging and singular value decomposition is proposed. In the first layer, the original watermark is encoded into a significantly small number of measured intensities in the process of computational ghost imaging to constitute a new watermark. In the second layer, the significant blocks chosen from the host image based on spatial frequency are combined to the reference image, which is used to embed the new watermark by using the singular value decomposition. Differing from other watermarking schemes, the information of original watermark can be verified without clear visualization via calculating the nonlinear correlation map between the original one and the reconstructed one. Besides optical parameters such as wavelength and propagation distance, a series of phase-only masks are used as security keys, which can enlarge the key space and enhance the level of security. The results illustrate the feasibility and effectiveness about the proposed watermarking mechanism, which provides an effective alternative for the related work. © 2018 Elsevier Ltd. All rights reserved.
1. Introduction Due to the rapid development of optical information processing technology and Internet, more and more researchers pay attention to the security of information storage and transmission using optical ways [15]. Since Refregier and Javidi [6] proposed the classic double random phase encoding (DRPE) in Fourier domain, lots of transform have been applied to image security techniques, such as fractional Fourier transform, Fresnel transform, fractional Mellin transform, gyrator transform and so on [7-17]. Due to intrinsic linearity of optical transform, most schemes are threatened with several common attacks [18-20]. Various kinds of information security cryptosystems based on different optical technologies such as polarized light, photon-counting, integral imaging, interference and diffractive imaging [21-28] have been reported, which have great potential to solve the issues on image encryption, information hiding, optical authentication, etc. Recently, ghost imaging known as single-pixel imaging is an intriguing optical technique [29,30], which provides a promising alternative in the field of information encryption due to its physical characteristics [31,32]. Zafari et al. [33] proposed an optical encryption based on selective computational ghost imaging to retrieve image with best qual-
∗
ity, where only one element of a random matrix attributes a different value in each realization. Zhang et al. [34] proposed a high-performance double cryptography to improve the security level, where the image is firstly encoded with fast Fourier transform, and then encrypted with the system of compressive ghost imaging. Chen [35] reported an optical data security system with high flexibility. In this system, a series of pre-generated random intensity patterns are used as security keys, where each pattern is encoded into two phase-only masks using noniterative interference-based phase extraction algorithm. During the process of encoding, each pair of phase-only masks are sequentially embedded into two spatial light modulators, and the measured intensity can be obtained with a single-pixel bucket detector. Although the affect of cross-talk cannot be eliminated in the scheme presented by Wu et al. [36], they demonstrated the validity of applying computational ghost imaging for optical multiple-image encryption. In the system suggested by Li et al. [37], the discrete cosine transformation distributions of multiple images are scrambled firstly, and then combined into an interim image using coordinate sampling. Finally, the interim image is placed in the object plane of compressive ghost imaging system, and the ciphertext is captured with a buck detector, from which the original information can be decoded with better quality.
Corresponding author at: School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China. E-mail address: [email protected] (S. Liansheng).
https://doi.org/10.1016/j.optlaseng.2018.03.005 Received 27 January 2018; Received in revised form 27 February 2018; Accepted 6 March 2018 0143-8166/© 2018 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 107 (2018) 38–45
As a promising way to protect private data from usurpation, the optical techniques about watermarking and information hiding have attracted more and more attentions [38-40]. Because the encoded results are real-valued measured intensities and the number of measurements used for object construction is significantly reduced, which lead to effective implementation, the watermarking and information hiding schemes based on ghost imaging have been continually reported in recent years. Chen and Chen [41] found that signals at reference and object beam arms can be converted into two quantization levels, and applied for object authentication along with reduction of data size. In the system reported by Chen [42], a series of phase-only masks are retrieved from pre-generated random intensity-only maps, and the corresponding propagation distances are axially varied in a random manner to enhance the security of scheme. Zhao et al. [43] researched the mechanism of optical encryption based on quick response code and computational ghost imaging, which can ensure the information not to access by an eavesdroppers even the eavesdropping ratio is up to 60%. Subsequently, they proposed a novel information hiding scheme with high security [44], where the watermark is firstly encrypted with the configuration of computational ghost imaging system. Then, the encrypted results are embedded into the least significant bits of pixels in the host image. To improve the quality of recovered watermark, total variation minimization by augmented Lagrangian and alternating direction algorithms is used for reconstruction. In this paper, an optical information hiding scheme is proposed based on computational ghost imaging, where both binary and gray-scale images can be considered as the watermarks. Initially, the original watermark is encoded into a series of measured intensities under the configuration of computation ghost imaging. Differing from the scheme presented in Ref. [44], the encoded results are embedded into the host image using singular value decomposition in the proposed scheme. Notably, it is not direct fusion between encoded information with host image. Some non-overlapping significant blocks are chosen from the host image based on spatial frequency coefficients to constitute an interim called as the reference image, which is used as a carrier to load the encoded information of original watermark. Compared with previous work, there are two main advantages to apply this kind of embedding mechanism. One is that an additional protection is afforded to improve the security, because the scheme will have camouflage property to some extent. Another is that it will have high robustness against common attacks such as Gaussian noise and occlusion attack due to excellent properties of singular value decomposition method. It is worth noting that the nonlinear correlation algorithm is applied to verify the presence of original information using the nonlinear correlation map. Although the watermark cannot be observed with clear visualization, the number of measured intensities obtained in the process of computational ghost imaging are considerably reduced. The rest of this paper is organized as follows. In Section 2, the proposed information hiding scheme is introduced in detail along with computational ghost imaging and singular value decomposition. Meanwhile, the verification of original information using nonlinear correlation algorithm is discussed. In Section 3, experimental results and security analysis are performed. Finally, a brief conclusion is described in Section 4.
Fig. 1. Schematic setup of computational ghost imaging encoded system: SLM, spatial light modulator; BD, bucket detector.
to embed the new watermark. Eventually, the reference image is inversely partitioned, and the resultant blocks are mapped into their original locations, with which the watermarked image is formulated in the second layer. The schematic arrangement of the computational ghost imaging adopted in the first layer of the proposed scheme is shown in Fig. 1. Differing from the conventional configuration where two spatially correlated beams pass through different optical paths, the rotating diffuser is substituted with the computer controlled spatial light modulator in the computational ghost imaging based encryption scheme, into which a series of random phase-only masks is sequentially embedded. Due to known phase-only masks, the intensity patterns at the reference beam arm can be virtually calculated by means of wave propagation in free space. The collimated laser beam is used for the illumination, and modulated by the beforehand phase-only masks to create random speckle patterns. A bucket detector without spatial resolution placed behind the object plane is used to measure the total intensity when each speckle pattern passes through the object, which can be described as 𝐵𝑖 =
∬
𝑑 𝜇𝑑 𝜐𝐼𝑖 (𝜇, 𝜐)𝑇 (𝜇, 𝜐),
(1)
where 𝑇 (𝜇, 𝜐) is the transmission function of the object and (𝜇, 𝜐) denotes the transversal coordinates in the object plane. The value of the measured intensity Bi is directly determined by the speckle patterns 𝐼𝑖 (𝜇, 𝜐) = |𝐸𝑖 (𝜇, 𝜐)|2 , where 𝐸𝑖 (𝜇, 𝜐) is the free-space propagation field for the phase-only mask exp(j𝜑i (x, y)). The propagation is a Fresnel diffraction process, which can be mathematically expressed as ( ) 𝐸𝑖 (𝜇, 𝜐) = exp 𝑗 𝜑𝑖 (𝑥, 𝑦) ∗ ℎ(𝑥, 𝑦, 𝑧). (2) Here, the symbol ∗ denotes the convolution operation and h(x, y, z) is the point pulse function of the Fresnel propagation at a distance z, which is defined as ) ( ) exp (𝑗2𝜋𝑧∕𝜆) 𝑗𝜋 ( 2 ℎ(𝑥, 𝑦, 𝑧) = (3) exp 𝑥 + 𝑦2 . 𝑗𝑧𝜆 𝑧𝜆 Here, 𝜆 is the wavelength of the laser beam. To reconstruct the object, the measured intensity values collected by the bucket detector are cross-correlated with the speckle patterns at the reference beam arm. Suppose the number of the measured intensities is K and ⟨ · ⟩ denotes the ensemble average computation, the decoded object can be mathematically expressed as
2. Proposed scheme
𝐺(𝜇, 𝜐) = ⟨𝐵𝐼 (𝜇, 𝜐)⟩−⟨𝐵 ⟩⟨𝐼 (𝜇, 𝜐)⟩ =
In this section, the details of the proposed optical image watermarking scheme along with the computational ghost imaging is presented, which includes two layers. Initially, the original watermark image is encoded into a series of intensity values by using the computational ghost imaging technology, and these intensity data are rearranged into a twodimensional interim image considered as the new watermark in the first layer. Subsequently, the host image is divided into smaller blocks, and some significant blocks are chosen to form the reference image, which has the same size as the new watermark. With the use of singular value decomposition, the singular values of the reference image are modified
𝐾 )( ) 1 ∑( 𝐵 −⟨𝐵𝑖 ⟩ 𝐼𝑖 (𝜇, 𝜐)−⟨𝐼𝑖 (𝜇, 𝜐)⟩ . 𝐾 𝑖=1 𝑖
(4) Let the original watermark image denoted as 𝑤(𝜇, 𝜐), it is encoded into a series of real-valued intensities via the process of computational ghost imaging. To embed them into the host image, these data are rearranged into an interim image as the new watermark 𝑤′ (𝜇, 𝜐) containing K pixels, which has m rows and n columns. It should be pointed out that the new watermark usually is not equal to the original one in the number of pixels. 39
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Optics and Lasers in Engineering 107 (2018) 38–45
where 𝜎̂ 𝑓𝑗 ′ (𝑗 = 1, 2, ..., 𝑚) are the modified coefficients. The modulated reference image 𝑓̂′ (𝜇, 𝜐) can be obtained by performing an inverse singular value decomposition transform. Finally, the modulated image is inversely segmented into blocks, which are mapped into their original locations for constructing the watermarked image 𝑓̂(𝜇, 𝜐). In order to further illustrate the proposed scheme, a diagram of embedding the watermark into the host image is shown in Fig. 2. To retrieve the hidden watermark in the watermarked image, the extraction process should be performed, which is similar to aforementioned embedding process but in the reversed order. Initially, the watermarked image is partitioned into smaller blocks, where each block has the size p × q pixels. With the known of locations for the selected blocks, the modulated reference image is reconstructed again, on which the singular value decomposition transform is performed to obtain the modulated singular values. With the help of the singular values of original reference image calculated using Eq. (6), the information of new watermark can be recovered as
Suppose the host image denoted as 𝑓 (𝜇, 𝜐) containing M × N pixels, which satisfies the condition as M × N > K. Thus, the host image can be divided into enough non-overlapping smaller blocks, from which some significant blocks are chosen to constitute a reference image to carry the information of the watermark. Due to more information embedding capacity and more robustness against many kinds of common attacks, the mode of embedding the new watermark 𝑤′ (𝜇, 𝜐) by modulating the magnitude of coefficients in a transform of the reference image is applied. As we all know, the human visual system has less sensitivity to the modification of high-valued coefficients so that it can produce the watermarked image with high imperceptibility to embed watermark in them. However, it should be realized that the robustness of the produced watermark is fragile, which can be removed from the watermarked image using high frequency filter easily. If the watermark is embedded in the low-valued coefficients, the quality of the watermarked image will be degraded seriously. Because the most energies of an image are stored in low-valued coefficients, the human eyes can perceive the changes of these coefficients sensitively. To overcome the conflict of these requirements, a trade-off between imperceptibility and robustness is explored, where the blocks with middle-valued coefficients are chosen to form the reference image. As an effective measurement of the overall activity level in an image, spatial frequency can reflect the clarity of image [45]. So, a significant block can be identified by calculating its spatial frequency coefficient, which is mathematically defined as
𝑗 𝜎𝑤 ̂ 𝑓𝑗 ′ − 𝜎𝑓𝑗 ′ )∕𝛾. ′ = (𝜎
Subsequently, the new watermark 𝑤′ (𝜇, 𝜐) can be reconstructed by performing the inverse singular value decomposition with the matrices 𝑈𝑤′ (𝜇, 𝜐) and 𝑉𝑤′ (𝜇, 𝜐) calculated using Eq. (7). Furthermore, the new watermark is converted into a series of real-valued data, which actually are the measured intensities expressed in Eq. (1). Now, the original watermark 𝑤(𝜇, 𝜐) can be recovered as 𝐺(𝜇, 𝜐) by using the second-order correlation algorithm described as Eq. (4). As discussed in Ref. [30] that the ghost imaging measurement procedure is a vector projection of the object transmission function over a series of random vectors 𝐼𝑖 (𝜇, 𝜐), some effective reconstruction algorithms such as orthogonal matching pursuit [46] and smooth l0 (SL0 ) [47] based on compressive sensing can be applied to recover object from measured intensities, which can improve the image quality considerably. If there is no need for visual observation to the reconstructed object, the nonlinear correlation algorithm can be used to verify the presence of object [48]. In the proposed scheme, the recovered watermark 𝐺(𝜇, 𝜐) can be effectively authenticated as { }|2 | 𝑁 𝐶 (𝜇, 𝜐) = |𝐼 𝐹 𝑇 |𝑐 (𝜇, 𝜐)|𝜌−1 𝑐 (𝜇, 𝜐) | , (12) | |
√ √ 𝑝 𝑞 𝑝 𝑞 √ 1 ∑ ∑ 1 ∑∑ 𝑠𝑓 = √ (𝐵 𝑙𝑘(𝑖, 𝑗 )−𝐵 𝑙𝑘(𝑖, 𝑗 −1))2 + (𝐵 𝑙𝑘(𝑖, 𝑗 )−𝐵 𝑙𝑘(𝑖−1, 𝑗 ))2 . 𝑝𝑞 𝑖=1 𝑗=1 𝑝𝑞 𝑖=1 𝑗=1
(5) Here, Blk denotes a smaller block divided from the host image and has p × q pixels. After all blocks are evaluated, the spatial frequency coefficients are sorted in descending or ascending order, and the blocks with middle-valued coefficients are chosen. Notably, the selected blocks should be enough to constitute the reference image, which has the same size as the new watermark. For convenience, the combined reference image is denoted as 𝑓 ′ (𝜇, 𝜐), which also has m × n pixels. Currently, there are several advantages such as: the singular values of the image reflect energy characteristics as well as the singular vector represents intrinsic algebraic properties; the singular values have a very good stability, which indicates that these coefficients cannot change in large variation when a perturbation such as cropping, filtering and rotation is performed on the image; and there is no strict requirement about the size of an image in the process of singular value decomposition. Thus, the only condition on the size of reference image 𝑓 ′ (𝜇, 𝜐) is that the number of rows should be equal to the number of columns as soon as possible, i.e. m ≈ n. In the proposed scheme, the main idea based on singular value decomposition is to apply the transform to the reference image 𝑓 ′ (𝜇, 𝜐) and the new watermark 𝑤′ (𝜇, 𝜐), and then modify the singular value coefficients of reference image with those of watermark. Initially, two singular value decomposition transforms are performed on the reference image and watermark, respectively, which are described as 𝑓 ′ (𝜇, 𝜐) = 𝑈𝑓 ′ (𝜇, 𝜐)∗𝑆𝑓 ′ (𝜇, 𝜐)∗𝑉𝑓𝑇′ (𝜇, 𝜐),
(6)
𝑤′ (𝜇, 𝜐) = 𝑈𝑤′ (𝜇, 𝜐)∗𝑆𝑤′ (𝜇, 𝜐)∗𝑉𝑤𝑇′ (𝜇, 𝜐).
(7)
𝑐 (𝜇, 𝜐) = 𝐹 𝑇 {𝐺(𝜇, 𝜐)}𝑐𝑜𝑛𝑗 {𝐹 𝑇 {𝑤(𝜇, 𝜐)}}.
3. Experimental results and analyses To demonstrate the feasibility and effectiveness of the proposed scheme, the numerical experiment is conducted as shown in Fig. 1, where the plane wave from a He-Ne laser emitting at 632.8 nm is used for illumination. In the process of ghost imaging on the original watermark, a series of random phase-only masks exp(𝑗 𝜑𝑖 (𝑥, 𝑦)), 𝑖 = 1, 2, ..., 𝐾, are sequentially input into the spatial light modulator, which resolution is 64 × 64 pixels with 20 μm pixel pitch. The propagation distance between the spatial light modulator and the bucket detector plane is 7.4 cm, while the laser beam waist is 740 μm. By the van Cittert-Zernike theorem, the speckle size at the object plane can be calculated with 𝛿(𝑧) = 𝜆𝑧∕𝜆𝑧 and 𝜔 is the laser beam waist, which roughly leads to 20 μm.
Here, 𝜎𝑖𝑗 (𝑗 = 1, 2, ..., 𝑚) are the singular values of matrices. When the rank of the matrices is r, these coefficients satisfy the condition as (9)
Then, the singular values of reference image are modified with those of the watermark attenuated with a real weight factor 𝛾 as follows 𝑗 𝜎̂ 𝑓𝑗 ′ = 𝜎𝑓𝑗 ′ + 𝛾 ∗ 𝜎𝑤 ′,
(13)
Here, FT{ · } and IFT{ · } respectively represent the two-dimensional Fourier transform and inverse Fourier transform, conj{ · } computes the complex conjugation of the argument, 𝜌 is the strength of the applied nonlinearity, and 𝑤(𝜇, 𝜐) is the original watermark image. It is worthwhile to note that the nonlinear correlation algorithm can enable image authentication with far less measured intensities such as less than 5% of Nyquist limit. In addition, besides the phase distribution of random phase-only masks 𝜑𝑖 (𝑥, 𝑦), 𝑖 = 1, 2, ..., 𝐾, optical parameters such as wavelength 𝜆 and propagation distance z can be used as the secret keys to enhance the level of system security.
Here, the matrices 𝑈𝑖 (𝜇, 𝜐) and 𝑉𝑖 (𝜇, 𝜐)(𝑖 = 𝑓 ′ , 𝑤′ ) are orthogonal, and 𝑆𝑖 (𝜇, 𝜐) are diagonal which can be expressed as ( ) 𝑆𝑖 (𝜇, 𝜐) = 𝑑𝑖𝑎𝑔 𝜎𝑖1 , 𝜎𝑖2 , ..., 𝜎𝑖𝑚 . (8)
𝜎𝑖1 ≥ 𝜎𝑖2 ≥ ⋯ ≥ 𝜎𝑖𝑟 ≥ 𝜎𝑖𝑟+1 = 𝜎𝑖𝑟+2 = ⋯ = 𝜎𝑖𝑚 = 0.
(11)
(10) 40
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Fig. 2. Diagram of the watermark embedding process in the proposed information hiding system: CGI, computational ghost imaging; SVD, singular value decomposition.
Fig. 5. (a) Reconstructed watermark with less measured intensities using second-order correlation algorithm and (b) corresponding nonlinear correlation map.
Fig. 3. (a) Original host image “Peppers” and (b) original watermark “Flower”.
Fig. 3(a) shows a grayscale image “Peppers” with 128 × 128 pixels used as the host image, which is chosen from USC-SIPI image database [49]. Fig. 3(b) shows a binary image “Flower” with 64 × 64 pixels considered as the original watermark designed by oneself, where the pattern represents the meaning of flower in Chinese. The size of non-overlapping blocks divided from the host image is set to 4 × 4 pixels, i.e. 𝑝 = 4 and 𝑞 = 4. It should be pointed out that the size of reference image composed of significant blocks may vary depending on K measured intensities of original watermark in the process of computational ghost imaging. The real weight factor used for embedding the new watermark into the reference image based on singular value decomposition is set to 1.0𝑒 − 5.
The strength of the applied nonlinearity 𝜌 is set to 0.4. To evaluate the quality of the watermarked image, the peak signal noise ratio (PSNR) between it and the original host image is mathematically calculated as ( ) PSNR 𝑓 , 𝑓̂ = 10 × log
{
2552 ( ) MSE 𝑓 , 𝑓̂
} .
(14)
Here, f is the host image, 𝑓̂ is the watermarked image. For brevity, the coordinates are omitted. The mean squared error (MSE) between
Fig. 4. (a) Watermarked host image “Peppers”, (b) recovered watermark “Flower” using second-order correlation algorithm and (c) recovered watermark “Flower” using SL0 algorithm. 41
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Fig. 6. (a)–(d) Occluded watermarked host image from top, bottom, left and right side.
Fig. 7. (a)–(d) Nonlinear correlation maps respectively corresponding to Fig. 6(a)–(d).
them is expressed as ( ) MSE 𝑓 , 𝑓̂ =
𝑀 𝑁 1 ∑∑| |2 |𝑓 (𝜇, 𝜐) − 𝑓̂(𝜇, 𝜐)| . | 𝑀𝑁 𝑖=1 𝑗=1 |
point of human visual system. Notably, if the measured intensities are continually reduced, although the construction result can be enhanced by using compressive sensing methods, the watermark with high fidelity like Fig. 4(c) cannot be recovered. If the reconstructed watermark only needs to be authenticated, it can be implemented with far less measured intensities based on nonlinear correlation algorithm expressed by Eqs. (12) and (13). Fig. 5(a) shows the watermark reconstructed with 192 measured intensities (i.e., only 4.69% of Nyquist limit), which is noise-like and cannot clearly render information. However, there is a remarkable peak over the noisy back-ground in the corresponding nonlinear correlation map shown in Fig. 5(b), which means that the watermark can be effectively verified without clear visualization. As we all know, the watermark may not be recovered, when the watermarked image is contaminated with noise or destroyed severely such as pixel loss to a large percentage, namely the watermarked image is interfered by noise attack or occlusion attack. So, the robustness
(15)
In addition, the quality of the recovered watermark can be evaluated in a similar way. When 1760 measured intensities are used in the process of ghost imaging, the watermarked image with PSNR = 56.2114 dB is shown in Fig. 4(a), which indicates that the watermarked image has good performance of imperceptibility. The recovered watermark using the secondorder correlation algorithm is shown in Fig. 4(b). Although PSNR only reaches 6.1594 dB, the basic content of watermark can be discerned with naked eyes. When the construction algorithm based on compressive sensing is applied, the watermark with high PSNR can be obtained. With using SL0 , the recovered watermark with PSNR = 42.4962 dB is shown in Fig. 4(c), where there is no perceptual degradation observed from the 42
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Fig. 8. Nonlinear correlation map when (a) k = 0.4, (b) k = 0.6, (c) k = 0.8 and (d) k = 1.0.
Fig. 9. (a) and (b) Resultant nonlinear correlation maps respectively corresponding to wrong wavelength with error of ±40 nm, (c) and (d) calculated nonlinear correlation maps respectively corresponding to wrong propagation distance with error of ±5 mm.
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Fig. 10. (a) and (b) Resultant nonlinear correlation maps respectively corresponding to 50% and 60% of phase-only masks divulged in the process of reconstruction of watermark.
Fig. 11. (a) A gray-scale watermark, (b) reconstructed watermark and (c) nonlinear correlation map between (a) and (b).
against these attacks should be evaluated. Because the original watermark is embedded into the significant blocks with middle-valued spatial frequency coefficients, most blocks may be distributed in one region of the watermarked image. If this region is occluded, the watermark will not be retrieved. To verify the capacity of the proposed scheme, 50% pixels from the top, bottom, left and right side are cropped in the watermarked image as shown in Fig. 6(a)–(d), respectively. Using only 192 measured intensities, the corresponding nonlinear correlation maps are displayed in Fig. 7(a)–(d), respectively, from which it can be known that the retrieved results still contain useful information to generate good correlation signals to verify the presence of watermark. To evaluate the effect of noise attack, the watermarked image is supposed to be polluted with a Gaussian random noise 𝐺(𝜇, 𝜐) with zero-mean and identity standard deviation, which is mathematically expressed as 𝑓̂∗ (𝜇, 𝜐) = 𝑓̂(𝜇, 𝜐) × (1 + 𝑘𝐺(𝜇, 𝜐)).
ror of ±5 mm is used during the retrieved process, the resultant nonlinear correlation maps are depicted in Fig. 9(c) and (d), respectively. In these figures, there are multiple peaks generated and only the noisy backgrounds are obtained, from which it is impossible to verify the presence of watermark. Additionally, if a potential eavesdropper who knows the embedding mechanism of watermark and can access a fraction of phase-only masks illegally, it is possible to retrieve the hidden information about watermark. When 50% and 60% of masks are divulged, the resultant nonlinear correlation maps are depicted in Fig. 10(a) and (b), respectively. In fact, when 50% masks are known, the eavesdropper may obtain the map with a peak sometimes. With 60% masks known, it is assured that he can observe the remarkable peak at every turn, which means that the information only can be retrieved when the eavesdropper should intercept at least 60% of phase masks. Obviously, it can enlarge the key space when a series of phase-only masks is used as security key. From aforementioned analyses, it can be safe to say that these experimental parameters play an important role in the process of verifying the presence of original watermark and the proposed scheme has higher security. It is worth noting that the gray-scale image considered as the watermark can be effectively embedded into the host image as well as can be verified with far less measured intensities captured in the process of computational ghost imaging. However, the gray-scale watermark possesses larger spectrum range and more information than binary one, the number of measured intensities should be increased to some degree. As shown in Fig. 11(a), a gray-scale image with 64 × 64 pixels which is central part of the image “Lena” is considered as the watermark embedded into the host image “Peppers” shown in Fig. 3(a). When
(16)
Here, 𝑓̂∗ (𝜇, 𝜐) is the polluted watermarked image and k is noise strength. When k is set to 0.4, 0.6, 0.8 and 1.0, the corresponding nonlinear correlation maps are displayed in Fig. 8(a)–(d), respectively, where the sharp peaks are obviously observed. So, it can be concluded that the proposed scheme have better tolerance to these attacks. Similar to other schemes based on computational ghost imaging, a series of phase-only masks used to calculate the speckle patterns can be considered as security keys besides light wavelength and propagation distance. If one of security keys is wrong, the retrieved watermark will not contain sufficient information about original one. When the wrong wavelength with error of ±40 nm is used for reconstruction, the calculated nonlinear correlation maps are displayed in Fig. 9(a) and (b), respectively. Similarly, when the wrong propagation distance with er44
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320 measured intensities (i.e., 7.81% of Nyquist limit) are used, the reconstructed watermark using the second-order correlation algorithm is shown in Fig. 11(b) that is noise-like. The corresponding nonlinear correlation map is displayed in Fig. 11(c), where a sharp peak can be obtained to verify the presence of original watermark. Other analysis results similar to the binary watermark can be conducted.
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4. Conclusions In summary, a watermarking scheme based on computational ghost imaging is proposed. Differing from conventional approaches to verify the original watermark visually, it can be authenticated without clear observation by using the nonlinear correlation algorithm. There are two layers to enhance the security of watermark. Even if an eavesdropper cracks the second layer of embedding the new watermark into the reference image using singular value decomposition, the obtained result is a significantly small number of measured intensities, which is randomly distributed and captured in the process of computational ghost imaging. Due to optical parameters such as light wavelength, propagation distance and a large amount of phase-only masks considered as security keys, it is difficult to retrieve the original watermark even the eavesdropper knows the mechanism of the first layer. Meanwhile, the eavesdropper cannot easily destroy the presence of the presented watermark by analyzing common attacks such as noise and occlusion attack. It is believed that the work can provide a promising alternative for the research of watermark schemes. Acknowledgments This work was supported by Key Laboratory Science Research Plan of Education Department of Shaanxi Province under grant no. 16JS079. References [1] Alfalou A, Brosseau C. Optical image compression and encryption methods. Adv Opt Photonics 2009;1(November (3)):589–636. [2] Alfalou A, Brosseau C. Recent advances in optical image processing. Prog Opt 2015;60(April):119–262. [3] Chen W, Javidi B, Chen X. Advances in optical security systems. Adv Opt Photonics 2014;6(June (2)):120–55. [4] Javidi B, Carnicer A, Yamaguchi M, Nomura T, Pérez-Cabré E, Millán MS, Nishchal NK, Torroba R, Barrera JF, He W, Peng X, Stern A, Rivenson Y, Alfalou A, Brosseau C, Guo C, Sheridan JT, Situ G, Naruse M, Matsumoto T, Juvells I, Tajahuerce E, Lancis J, Chen W, Chen X, Pinkse PWH, Mosk AP, Markman A. Roadmap on optical security. J Opt 2016;18(August):083001. [5] Wang Q, Alfalou A, Brosseau C. New perspectives in face correlation research: a tutorial. Adv Opt Photonics 2017;9(March (1)):1–77. [6] Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 1995;20(April (7)):767–9. [7] Lang J, Zhang ZG. Blind digital watermarking method in the fractional Fourier transform domain. Opt Laser Eng 2014;53(February):112–21. [8] Liu Z, Guo C, Tan J, Liu W, Wu J, Wu Q, Pan L, Liu S. Securing color image by using phase-only encoding in Fresnel domains. Opt Lasers Eng 2015;68(May):87–92. [9] Chen W, Chen X, Stern A, Javidi B. Phase-modulated optical system with sparse representation for information encoding and authentication. IEEE Photon J 2013;5(April (2)):6900113. [10] Wang X, Chen W, Chen X. Optical encryption and authentication based on phase retrieval and sparsity constraints. IEEE Photon J 2015;7(April (2)):7800310. [11] Chen W. Single-shot imaging without reference wave using binary intensity pattern for optically-secured-based correlation. IEEE Photon J 2016;8(February (1)):6900209. [12] Chen W. Optical multiple-image encryption using three-dimensional space. IEEE Photon J 2016;8(April (2)):6900608. [13] Zhou N, Li H, Wang D, Pan S, Zhou Z. Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt Commun 2015;343(May):10–21. [14] Abuturab MR. Optical interference-based multiple-image encryption using spherical wave illumination and gyrator transform. Appl Opt 2014;53(October (29)):6719–28. [15] Liu Z, Guo C, Tan J, Wu Q, Pan L, Liu S. Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms. J Opt 2015;17(February (2)):025701. [16] Chen JX, Zhu ZL, Fu C, Zhang LB, Yu H. Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains. Opt Lasers Eng 2015;66(March):1–9.
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