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Security and Communication Networks
Volume 2018, Article ID 1254081, 16 pages
Research Article

A Robust Watermarking Scheme Based on the Mean Modulation of DWT Coefficients

1National School of Engineers of Sousse, University of Sousse, Erriadh City, 4023, Tunisia
2CSR Group with the Electronic and Microelectronic Lab, National School of Engineers of Monastir, University of Monastir, Ibn El Jazzar Avenue, 5035, Tunisia
3LATIS Lab, National School of Engineers of Sousse, University of Sousse, Erriadh City, 4023, Tunisia
4National School of Engineers of Monastir, University of Monastir, Ibn El Jazzar Avenue, 5035, Tunisia
5ESIR Research Unit, National School of Engineers of Monastir, University of Monastir, Ibn El Jazzar Avenue, 5035, Tunisia

Correspondence should be addressed to Zied Kricha; moc.liamg@deiz.ahcirk

Received 4 May 2018; Revised 29 October 2018; Accepted 21 November 2018; Published 6 December 2018

Academic Editor: Emanuele Maiorana

Copyright © 2018 Zied Kricha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In an endeavor to deal with image copyright infringement, robust watermarking approaches are commonly used. However, most of the existing approaches either present a limited robustness or rely on highly computational algorithms, thereby limiting the efficiency of these solutions. In this paper, a novel blind and robust watermarking method is presented. First, the vertical and horizontal subbands coefficients, resulting from the wavelet transformation, are scrambled using a chaotic sequence and then gathered into individual blocks. Next, the mean value of each block is modulated according to watermark bit. At the extraction stage, based on the sign of the blocks’ mean, a blind watermark extractor is suggested. The imperceptibility, security, complexity, and robustness of the proposed approach have been evaluated and compared with state of the art solutions. Experimental results prove that the proposed approach successfully satisfies the watermarking requirement and outperforms existing methods against both geometric and signal processing attacks.

1. Introduction

We all remember directing a banknote toward a source of light to verify its authenticity. The presence of a predefined pattern, number, or portrait, technically called watermark, determines whether the banknote is fake or not. Watermarking is an old technique used to prevent counterfeiting of several official paper documents. Nowadays, physical form of paper is not the only valuable thing worth securing, whereas images, audio tracks, and video sequences present a new form of money, that is vulnerable to unauthorized distribution and modification. In an effort to address these issues, watermarking concept was again adopted, but this time with the prefix “digital" for referring to digital objects. Digital watermarking is the act of incorporating supplemental information into multimedia material (still images, audio, or video) in such a manner that it does not alter the delivered material and yet still readily exploited by the watermark detector, even after some undesirable operations. An overview of the literature reveals a broad range of application domains including encryption [1], copyright protection [2], integrity verification [3], content restoration [4], and documentation [5].

The main focus of this paper is to design a robust watermarking scheme for image copyright protection. The first watermarking schemes in this regard targeted the least significant bit (LSB) of pixels’ brightness [6]. Despite their simplicity of realization, LSB based schemes suffer from a high sensitivity to noise, which prompted researchers to look for new alternatives. In fact, researchers have targeted different parts of the watermarking process; the generation of carrier elements from the raw representation (e.g., pixels values) [7, 8], the choice of an embedding method, summarized by the embedding equation that describes how the watermarked elements are generated from the original coefficients [9, 10], and finally the choice of a suitable watermark detector [11].

The two main used techniques for watermark embedding are the spread spectrum (SS) [12] and the quantization (QIM) [10] based techniques. These techniques have been subject to much amelioration such as the spread transform dither modulation [13] and the progressive quantization [14] for QIM-based-techniques; and the improved SS [9], the multiplicative SS (MSS) [15], and the improved MSS for SS-based-techniques [16].

The digital watermark may be inserted either in the raw representation of the image, where each watermark bit is inserted straight into pixel’s brightness, or after a preprocessing phase involving the generation of a new domain or/and the selection of an appropriate component on which the embedding algorithm will be applied.

The straightforward option, though it is not the robuster, is to insert the watermark in the spatial domain. A preliminary work in this trend is presented in [17], where the watermark is repeatedly inserted in a subtractive or additive way depending on the pixels’ characteristics. To consolidate the robustness of the DC coefficients with the rapidity of direct pixels manipulation, Su et al. [18] proposed to compute the DC without going through the DCT transformation. Although this method is computationally lighter than the conventional insertion in transform domain, it provides fewer choices, and it is limited, so far, to the DC coefficients.

In contrast to the spatial domain, transform ones offer more flexibility. For instance, in the DCT domain, the watermark has been embedded into different positions, such as the DC [19] or the AC frequency [20]. Similarly, in the Discrete Wavelet Transform (DWT), researchers opted for different subbands and different wavelet families. In [21], the watermark is embedded into the subband of the Haar wavelet decomposition and into the subband of the integer DWT in [22]. Other employed transformations include the gyrator domain [1], the contourlet [23], and the Hessenberg [24] transforms.

When most of schemes have been designed to embed the watermark into the amplitude of coefficients, either in the spatial or frequency domain, some academics have chosen to create or form a new carrier using various representations of these coefficients. Inspired by the works realized in communication theory, specifically the modulation of the phase instead of the amplitude, Ourique et al. [25] proposed to watermark the angle constituted by the host vector with respect to a hyperspherical coordinate system.

Recently, many researchers have tended to embed the watermark into a robust feature obtained from a set of coefficients, such as the coefficient difference computed between the two largest wavelet coefficients belonging to the same group [7], or the difference between adjacent coefficients of the same DWT subbands [8]. In [26, 27], the watermark is embedded into the image’s significant elements. In [27], the nonsubsampled Shearlet transform of images significant region is calculated, and then the watermark is embedded in the high-pass subband with the highest energy. The human visual system can barely notice the modifications of high edge concentration zones. To benefit from this weakness, the authors of [26] proposed to adjust the watermark strength according to the blocks complexity. The embedding stage consists in the modification of two DCT coefficients from each block. At the extraction phase, the difference between these coefficients specifies the value of the watermark bit. In [28], Lilu et al. took advantage of the LL subband’s robustness to provide blindness to the additive SS algorithm, where the HH subband is replaced by the quantized and watermarked LL subband.

The bottom line of the literature review reveals that the watermarking problem persists and the dilemma remains unsolved. Most of the existing schemes either manifest a weak robustness or make recourse to overcomputational schemes through a cascade of transformations [14, 29, 30], metaheuristic algorithms [31], or both [32, 33].

The main objective of this paper is to investigate and implement an efficient watermarking scheme for grayscale images. This objective is achieved by using a single transformation (DWT) to localize the appropriate frequencies, a block mean as a representation of the watermark carrier, a chaotic encryption for security, and a mean modulation for embedding.

To the best of our knowledge, the closest work to ours is perhaps that of [34], in which the authors embedded the watermark in the mean value of DWT coefficients. However the difference between the two approaches is threefold. Firstly, the two papers are dealing with different cover media; in [34] the host signal is an auditory signal while this paper addresses robust image watermarking problem. Secondly, the mean value in [34] is computed between adjacent coefficients obtained from the same subband, while in our work it is computed from gathered coefficients from different subbands. Thirdly, the embedding method is different, where in [34] the mean value is moved to the nearest integer multiple of the used quantization step. However, in this work the watermark is embedded by changing the sign of the mean value.

The rest of this paper is organized as follows. In Section 2, we introduced the advantages of the used watermark carrier. Section 3 describes how the watermark is inserted and detected. The performances of our scheme are evaluated and discussed in Section 4. Finally, the conclusions are stated in Section 5.

2. Watermark Carrier Selection

As discussed in the previous section, the selection of a watermark carrier involves the choice of a transform domain alongside with an adequate representation.

2.1. Transform Domain

The wavelet transformation (WT) is a mathematical tool used to analyze a discrete or continuous signal by extracting its frequency components and localize them in time. Hence, it allows access to important information unattainable in the original representation. The WT is widely used in multidisciplinary fields such as astronomy, economy, earthquake prediction, signal processing, and watermarking. Although developed on the basis of the Fourier transform, the WT is more effective in terms of computational complexity and frequency localization.

In order to prove the complexity advantage of the DWT over other transformations, the computational time of the DWT (1 level), DCT (8 × 8 blocks), and the Shearlet transform are examined using different image sizes (Figure 1). These transformations are employed in [7, 28, 35], [13, 20, 36], and [27] respectively. The advantage of the DWT over other transformations is clear for large image sizes and especially over the DCT, which is the most time consuming among the three evaluated transformations.

Figure 1: Computational time evolution with respect to the image dimension of some 2D transformations.

Due to the above advantages, we adopted the DWT transformation in our scheme. When applied to an image, the DWT is achieved by filtering separately the rows and columns of the image. Each individual image transformation produces four separable subbands: one coarse subimage locating the low frequencies (), and three locating the horizontal (), vertical (), and diagonal () details (high frequencies). The WT may be repeated, as appropriate, by filtering again the low frequency subband. Each individual operation stage produce a resolution level, and each higher level yields to a better frequency localization, but a shrinkage in the subband size. From the perspective of imperceptibility, the subband is inappropriate for watermark insertion. The approximation coefficients represent the low frequencies that reflect significant information about an image. Thus, the manipulation of these coefficients provokes quality degradation. On the other hand, the modification of the coefficients may go unnoticed, but the watermark may be easily removed by image processing tasks such as lossy compression. The remaining subbands ( and ) serve as a good candidate for watermark embedding. They are midfrequency subbands; thus they are less noticeable and more robust than the and subbands, respectively.

2.2. Carrier Selection

Regardless of the insertion method, there are always two ways to embed a watermark; either to insert one bit in a single coefficient or one bit in multiple coefficients. The latter solution leads to some important advantages of both robustness and imperceptibility [36]. In fact, a good watermark carrier has to guarantee two main properties: a high robustness combined with a low perceptibility. From a carrier’s point of view, these properties are manifested by a low distortion after attacks and an imperceptible change after embedding the watermark. The blocks’ mean values (BMV) of and subbands satisfy the above requirements; it is computed from multiple coefficients, and it manifests a high robustness and imperceptibility. To prove this claim, we analyze the variation of BMVs through the cumulative distribution function (CDF), where each block is constructed by gathering eight coefficients from unrepeated random positions. The insertion of a watermark bit into a BMV can only be accomplished through the modification of its block-coefficients. Hence, to emulate the insertion, we propose to modify all the coefficients of each block by a fixed value (negative or positive).

First, we investigate the quality of the resulting image. The CDF in Figure 3(b) shows the large variations of the BMVs expressed in terms of percentage; the variation reaches up to 2 000%, where 58% of the BMVs are modified between 100% and 950% from their original values. Despite this large variation, the modified image (Figure 2(b)) remains highly similar to the original one (Figure 2(a)).

Figure 2: Lena image (a) original and (b) after modification of all the and coefficients.
Figure 3: Absolute value of Cumulative histogram of (a) original BMVs, (b) difference between the original BMVs and the altered ones ((a) and (b)), (c) difference after JPEG(30) compression, and (d) difference after median filtering (3 × 3).

Concerning the robustness, Figures 3(c) and 3(d) depict the variation of BMVs, always in terms of percentage, after JPEG compression and median filtering, respectively. Here, we can observe the limited variation, which implies a high robustness. In fact, in 72% of the cases, the variation is less than 10% after compression and less than 20% in 73% of the times after filtering operations. In both cases the variation is less than 30% in 83% of the BMVs.

It is worth noting that despite the robustness and imperceptibility of the BMVs, the final results will also depend on the insertion and detection method described in the next section.

3. The Proposed Scheme

This section describes the insertion and extraction processes of a binary watermark , in a grayscale image with height and width. At this point, the embedding parameters are not specified but kept generalized to point out the flexibility of the scheme. At first, the original image goes through levels of DWT in order to manifest the different frequencies of the image. For the reasons presented in Section 2, the and the subbands are selected for embedding. Let and , be the full set of carrier coefficients, where , and . The coefficients of the two subbands are then concatenated into a single vector , where and . Next, the carrier vector is shuffled using a chaotic sequence generated using the logistic map, and each watermark bit is embedded by modulating the mean value of a set of coefficients. The complete block diagram of the embedding process is given in Figure 4. The three main stages involved in the watermarking process (chaotic sequence generation, coefficients shuffling, and mean block modulation) are detailed in the rest of this section.

Figure 4: Block diagram of the watermark embedding scheme.
3.1. Chaotic Sequence Generation

Chaotic maps are dynamic systems defined by a mathematical function () that model a chaotic behavior. In practice, a variety of chaotic systems may be utilized (e.g. Baker’s map, circle map, duffing map, logistic map, etc.). The implementation of the latter is one of the simplest thanks to its polynomial mapping degree, though it’s high dynamic complexity. These features allowed the logistic map to attract a lot of attention in the information security disciplines such as cryptography and watermarking.

The logistic map may be described by the following recurrence relation:The chaotic sequence generated by the function after iterations is determined by its input parameters and , where is the initial value of the sequence and is the control parameters. In practice is choosing between and lies between 3.569955672 and 4. These ranges guarantee a chaotic sequence with a high randomness in the output, where the slightest difference in the initial parameters ( and ) will lead to uncorrelated sequences over time.

3.2. Shuffling

In the shuffling phase, the elements of the vector are assigned to new positions according the generated chaotic sequence. The objective of this shuffling is double-fold. Firstly, it aims to improve the security of the scheme; the coefficients forming each block () are randomly selected, thereby making it difficult for a third party to extract the watermark or selectively attack the host coefficients to destroy the watermark without the permutation sequence. Secondly, the shuffling dispels the correlation between adjacent coefficients. In fact, adjacent coefficients tend to be of the same sign, leading to MVBs distant from zero. In contrast, the MVBs of scattered coefficients are gathered around the zero value, which will serve us to minimize the embedding strength and hence the perceptibility of the watermark.

The logistic map defined by (1) is employed to produce a pseudo-random key containing the new positions for each coefficient.

Let be the chaotic sequence generated by means of the logistic map using the secret key , where is the number of iterations that is equal to the total number of coefficients in and . The coefficients are then sorted in a ascending order (), and so the permutation sequence () is obtained.

The example shown in Figure 5 illustrates a concrete example for the shuffling operation. In this example, is equal to eight, the vector is the concatenation of the diagonal DWT coefficients, and is the shuffled version of .

Figure 5: Shuffling of DWT diagonal subbands using a chaotic sequence of eight real numbers.
3.3. Block Mean Modulation

The first step in the block modulation phase is the partitioning of the confused host coefficients into independent blocks. This operation is realized by gathering each adjacent coefficients into a single block as given by (2), where is the index of the block and is the concatenation symbol. The total number of generated blocks should be larger or equal than the binary watermark message length. In other words, such as .To embed a robust watermark, we consider the quantization technique, which modulates the carrier hosts to nonoverlapping sets, where represents the possible embedded words. In this work, the watermark is a binary message, hence the carrier will be modulated to two different sets (), each associated to a watermark bit. The robustness of the quantization-based insertion method depends on the distance between the two sets. On the other hand, widening the gap will lead to mediocre results in terms of visual quality. To work around this issue, Chen et al. [10] proposed to increase the element of each set, and it is up to the embedding algorithm to choose the appropriate quantizer among the available ones. However, as illustrated in Figure 3(a), most of the BMV are concentrated around the zero, where in 80% of the BMVs are in the range . Thus, we propose to modulate the blocks’ mean values by a positive or negative number according to the embedded bit. Let be the mean value of the block defined byThe modulation of goes by firstly nullifying the mean value by spreading its value equally to all block’s coefficients, then adding or subtracting a threshold according to the embedded bit . The equation of modulation is given by (4), where is a coefficient belonging to the block (). Once all the watermark bits are inserted, the watermarked coefficients are rearranged into their initial positions using the same key SK. Finally, the inverse DWT is performed to obtain the watermarked image.

3.4. Watermark Extraction

In the watermark extraction phase, the watermarked image is firstly transformed in the frequency domain, as in the embedding, and the same key SK is used to constitute different blocks. The decision upon the embedded bit is judged according to the block’s mean value of the attacked watermarked block

4. Experimental Results

This section is dedicated to evaluate the performance of the suggested watermarking framework. A variety of 8-bit depth () grayscale standard benchmark images, with a resolution of pixels (), have been subjects of assessment. The used image database includes Lena, Baboon, Peppers, and Tank. These images present a variety of image properties (e.g., mixture of dark and light area, alongside with highly textures regions (hair) in the Lena image), which refutes the idea of tying the performance of the scheme to some image properties.

The performance of the suggested method is experimentally examined from different aspects. Firstly, the relation between the capacity and the imperceptibility is evaluated using different insertion parameters. Next, the evolution of complexity according to the host image size is monitored. Afterwards, the robustness is validated in two ways: initially the robustness against different levels of attacks is examined and then a comparative study with similar works is presented. Finally, the security of the scheme is verified.

4.1. Imperceptibility

The imperceptibility feature reflects the fidelity of the watermarked image toward the original one. Several metrics can be used to quantify the noticeable difference between two images, involving subjective and objective metrics. In this work we employed the Peek Signal to Noise Ratio (PSNR) and the Structural Similarity Index Measure (SSIM) given by (6) and (7), respectively.where and are, respectively, the mean intensity and the standard deviation of the original image and is the sample cross-correlation between and . The constants and are defined as and , where .

4.2. Capacity

The maximum capacity of the proposed scheme depends on three variables: the image dimension ( and ), the wavelet level (), and the block length (). Hence we can express the maximum capacity usingFor a better understanding of the relation between the capacity and imperceptibility, we embedded a variable message size () at different levels of decomposition () into three different images namely Lena, Couple, and Baboon. For each watermarking operation, the blocks’ size is maximized so that all coefficients are involved in the watermarking process (e.g., and for ). The threshold is manually chosen to reach a PSNR value of 38, 41, and 45 dB. The parameters of insertion (), the objective measurements (PSNR and SSIM), and the watermarked images are all listed in Table 1.

Table 1: Quality of watermarked images using different insertion parameters ().

The first observation that we draw from Table 1 is that for a given PSNR, the threshold is converging toward the same value regardless the host image or the watermark size. This amounts to saying that we can anticipate the value according to the level of transformation and the targeted PSNR. Figure 6 illustrates the relation between these parameters, where is obtained by averaging all the values for a specific level and PSNR. Secondly, it is shown from Table 1 that at 45 dB, the distortion due to the watermark insertion is invisible whatever the size of the message and the level of decomposition. However, for watermarked images with a PSNR of 38 and 41 dB, the imperceptibility is conditioned upon the level ; the higher is, the lower the quality is going to be.

Figure 6: Relation of threshold value (T) and the PSNR at different DWT levels.
4.3. Complexity

The computational cost of the watermark embedding and extraction is an important aspect that may restrict or expand the use of a given watermarking scheme. In the literature, most of schemes are evaluated in a standard image with a size of 512 × 512 pixels, and there is no perspective of the computational cost trend when the image goes bigger, which is more realistic. Hence, we propose to vary the size of the image beginning with pixels and ending with pixels, by doubling the height and width after each insertion. For the sake of simplicity, the watermark was embedded after one level of DWT (), with a fixed block size () and a maximum watermark size as defined by (8).

Figure 7(a) depicts the execution time evolution of the overall embedding and detection, alongside with the variation of the watermark size (red), as a function of the image size. The details of the embedding phase are shown in Figure 7(b). The most important remark to be made from Figure 7 is that the computational time evolves broadly in line with the watermark size (red curve), to find out the complexity of our scheme in comparison with other state-of the-art methods.

Figure 7: Computational time of (a) overall insertion and detection and (b) details of the embedding stage.
4.4. Robustness

In the following, we investigate the robustness of the suggested watermarking approach under several types of attacks. The robustness is quantified using the Bit Error Rate (BER) and the Normalized Correlation (NC) metrics.

4.4.1. Evaluated Attacks

Since the proposed scheme is designed to be robust, the embedded message should last, or at list a significant part of it, after image processing operations. From watermark perspective all image processing operations, whatever performed on goodwill or not is considered as attacks. The involved attacks in the evaluation tests are classified into three groups:(i)Compression attacks: usually images are not stored in a raw format, but after a compression operation that aims to reduce the required storage space. JPEG algorithm is one of the most used compression algorithms. However, JPEG is a lossy algorithm that causes some quality degradation, inversely commensurate with the compression quality factor. Hence, we tested the robustness of our algorithm under different JPEG quality factors ranging from 10 to 90.(ii)Image processing attacks: used to imitate a noise contaminating the image during transmission such as salt and peppers, or to improve the image’s quality by eliminating a noise or enhancing some properties. The used attacks are listed as follows: scaling, median filtering, sharpening, Gaussian filtering, average filtering, Gaussian noise, salt and pepper noise contamination, histogram equalization, and additive white Gaussian noise (AWGN).(iii)Geometric attacks: used to correct geometric distortions such camera orientation (rotation), or images’ alignment (cropping). The used attacks are listed as follows: image cropping and resizing and rotation.

Since the DWT coefficients are not geometrically invariant, a manual synchronization of the image’s dimension and orientation was realized prior to the extraction.

4.4.2. Performance Evaluation

Here we test the robustness of our scheme on three different images: Boat, Peppers and Barbara. Each time, we varied the embedded message between 128 bits and 2048 bits. The embedding threshold is manually tuned to provide a watermarked image with a PSNR value of 40 dB and 45 dB. The robustness is expressed in terms of BER (%) after mean filter (Figure 8), JPEG compression (Figure 9), median filter (Figure 10) and gamma correction, Poisson noise, histogram equalization, and image unsharpening (Figure 11). Figures 811 show that the robustness performance slightly differs between images. For a small message length (between 128 and 256 bits) and a PSNR value of 40 dB, the BER does not exceed for most of attacks. However the larger the message size is or the stronger the attack is, the higher the BER will be.

Figure 8: BER(%) after mean filter attacks using different message lengths at different PSNR values (a) 40 dB and (b) 45 dB.
Figure 9: BER(%) after JPEG compression using different message lengths at different PSNR values (a) 40 dB and (b) 45 dB.
Figure 10: BER(%) after median filter attacks using different message lengths at different PSNR values (a) 40 dB and (b) 45 dB.
Figure 11: BER(%) after various attacks using different message lengths at different PSNR values (a) 40 dB and (b) 45 dB.
4.4.3. Comparative Study

To prove the superiority and the robustness advantages of our scheme a comparative study with state of the art works is indispensable. In fact, we compared the robustness of our scheme with six robust watermarking schemes [26, 27, 35, 3739]. In order to carry out a fair comparison, the same insertion parameters (PSNR, watermark size) and attacks are used in this comparison. The PSNRs value of different images and their corresponding values in the comparative schemes are illustrated in Figure 12. It is worth mentioning that the insertion parameters () were empirically chosen to produce the same PSNR alongside with an acceptable visual quality.

Figure 12: PSNR values of different experimentations: (a) Table 3, (b) Table 2, (c) Table 4, and (d) Table 5.
Table 2: BER comparison with [27] and [37] using a message length of 128 bits.
Table 3: NC comparison with [38] using a message length of 512 bits.
Table 4: NC comparison with [35] and [39] using a message length of 512 bits.
Table 5: BER(%) comparison with [26] using a message length of 128 bits.

The robustness results are presented in Tables 25, in terms of either BER or NC depending on how they appear in the reference papers, and the superior results are marked in bold number.

Based on the simulation results given in Tables 25, it can be found that our approach outperforms similar schemes on 71.94% of the time. Equal results are obtained on 23.43% of the time, and our scheme underperforms on 4.62% of the cases.

4.5. Security

The robustness of a watermarking scheme is not sufficient to judge a scheme as reliable. As discussed in the first section, robust watermarking is used to secure images. Hence, the security is necessary. First, the watermark should be immune against illegal extraction, even when the embedding procedure is exposed. Second, the watermark detector should not report the existence of the watermark when none is embedded. To evaluate these two risks, we extract the watermark from a watermarked image using different keys, and extract a watermark from a nonwatermarked image respectively. In the two cases, the maximum correlation obtained has not exceeded the value 0.59, which points out a negative presence.

5. Conclusion

The mean value of DWT’s vertical and horizontal subbands coefficients is highly robust and imperceptible. In fact, these two advantages were exploited in the design of a robust and blind watermarking approach. The embedding method consisted in modulating the BMV in accordance with the quantization technique. The use of a single transformation domain alongside with a simple embedding technique makes from the proposed algorithm computationally undemanding. At the extraction phase the watermark bits were identified by the BMV position with respect to the zero value. Unlike some existing schemes, the extraction rules did not require to be adjusted to the applied attacks to fulfill a high robustness. In fact the inserted watermark was capable to withstand with no error after JPEG compression up to a quality factor of 30, Gaussian filter, and other attacks.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


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