1 Introduction

The watermarking scheme should provide enough imperceptibility, trustworthiness and robustness to protect the secret watermark from various noise attacks and offer proof for protection of rightful ownership [18, 22, 29]. These watermarking schemes are divided into two different domains: spatial-domain and frequency-domain. The spatial domain watermarking is less complex and easily implementable and mostly used as fragile watermarking techniques. Contrary, the frequency domain watermarking are the computationally complex and used as a robust watermarking techniques [17].

To protect the copyright information in network environment the watermarking techniques are proposed [5, 22]. The Singular Value Decomposition (SVD) based watermarking algorithms are implemented to get better robustness under variety of noise attacks [1,2,3,4, 14, 15, 17, 18, 21,22,23, 28, 29, 32]. The SVD based techniques proposed by [22] is implemented by [30, 36] and commented that the given technique is not protecting the rightful ownership. The reliable watermarking technique based on Principle Components (PCs) is proposed in [14] which remove the problem of rightful ownership associated with SVD based technique but this PCs based technique is more sensitive to any noise attack. This limitation of PCs based technique is removed using optimization techniques like Particle Swarm Optimization (PSO) and Differential Evaluation (DE) in [1, 28, 29]. The SVD, Discrete Wavelet Transform (DWT) and Chebyshev chaotic map based watermarking technique is given in [32] for the rightful ownership protection. The Integer Wavelet Transform (IWT) based watermarking technique is used to get better robustness is presented in [23]. The watermark is embedded three times into the SVD blocks of cover image to get better security and robustness [21]. The watermark image is directly embedded inside the singular values of DWT coefficients of cover image to get better imperceptibility and robustness [15]. To increase security, robustness and rightful ownership the non-overlapping block based SVD with basic watermarking algorithm [7, 8, 13, 25] is used. Different transforms like Binomial, Stirling and Lah are used in [9,10,11] for watermarking and security of image data to archive higher payload.

Many evolutionary and swarm intelligent based algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to solve different types of optimization problems. Essentially they are probabilistic type and solve optimization problems using variety of controlling parameters like population size, elite size and number of iteration or generation etc. These parameters are varied from one type of algorithm to other [27]. For example, GA uses probability of mutation and crossover along with selection parameters. PSO uses inertia weight as well as social and cognitive parameters. To optimize robustness and fidelity of watermarked image the Genetic Algorithm (GA) is used in [12, 31] whereas the PSO based watermarking technique is proposed in [34] to increase the robustness and imperceptibility. The Arnold Transform (AT) based watermarking technique in the Discrete Cosine Transform (DCT) and DWT domains are given in [19, 26, 33].

It is found that the algorithm given in [15] suffers from lower robustness and imperceptibility due to improper method is used to select the scale factor. The diagonal line is also present in the extracted watermark image. In the scheme proposed in this paper, the scale factor selection methodology is improved with two different approaches. The first approach is based on the PSO which improves the robustness and imperceptibility but the diagonal line is still present in the extracted watermark. To remove this diagonal line from extracted watermark and increase security, the Arnold Transform (AT) along with PSO based technique is proposed. This technique also increases the imperceptibility of the algorithm.

The rest of the paper is organized as follows. Section 2 describes main contribution of this paper, preliminaries on PSO, AT, SVD and DWT is given in section 3. The proposed watermark embedding and extraction algorithms are presented in section 4. The performance measures like PSNR, Normalized Correlation Coefficient (NCC) and Normalized Similarity Ratio (NSR) is given in section 5. In section 6, the experimental results are presented and discussed. In the last, conclusions about the proposed techniques are given.

2 Main contribution of the work

In the proposed work, SVD is applied on the low frequency wavelet coefficients of cover image. A scaled pixel values of watermark image are embedded and modified the singular values of selected wavelet coefficients. A scale factor is decided by the evolutionary algorithm PSO. Further, SVD is applied on these modified singular value matrix. A modified low frequency wavelet coefficients set is generated using inverse singular value decomposition (ISVD) applied on generated singular values along with orthogonal matrices of low frequency wavelet coefficients of cover image.

Adaptive to different groups of images

In existing schemes like [15] and others, the scale factor selection is manual and based on cover and watermark image dependent. To eliminate this limitation of such schemes, PSO is incorporated which is suggested a suitable scale factor for given pair of cover and watermark image in this proposed work.

Free from False positive problem

In most SVD based watermarking algorithms [5, 22], a false positive problem is common which is reported in [35]. Here it is shown that, extraction of original watermark was possible using singular values of image than original one. This problem has been eliminated by proposed algorithm of this paper using dual SVD of selective components of cover image.

Removal of diagonal Line and Security Assurance

As singular value modification based watermarking algorithms are embedded the singular values of watermark content into the Host image, the diagonal line is visible in extracted watermark content. In this proposed scheme use of Arnold Transform leads to eliminate a diagonal line from extracted watermark. Moreover, AT is also offered secure information transmission using this proposed algorithm [6, 20].

3 Preliminaries

3.1 Particle swarm optimization

A PSO has been used due to its certain attractive features like ease of implementation and it can optimum solution of problem without gradient information. Nowadays, it is rigorously used to solve neural network training and function minimization types of wide array problem [34]. In addition to that, tuning of the PSO based algorithm require very few parameters as compared to other Heuristic algorithms which leads to its faster convergence with higher accuracy [16]. It is also used in image processing applications like compression and watermarking.

The PSO is initialized with random particles in respective search space. These random particles are tuned on the search space by adjusting their velocities [16]. Each particle have two information, first is its own best experience (position, Pi and objective value, Pbest) and best experience from whole swarm (position, Pg and objective value, Pbest). The mathematical formulation of velocity and position is given below

$$ {x}_i=\left({x}_{i1},{x}_{i2},\dots, {x}_{in}\right) $$
(1)
$$ {v}_i=\left({v}_{i1},{v}_{i2},\dots, {v}_{in}\right) $$
(2)

These positions, xi and velocity, vi are updated using following Eqs. (3) and (4) and fitness function value is checked with its best value. This process is repeated until the desired value of fitness function is achieved.

$$ {v}_{im}\left(n+1\right)={v}_{im}(n)+{c}_1{r}_{1m}\left({p}_{im}-{x}_{im}\right)+{c}_2{r}_{2m}\left({p}_{gm}-{x}_{im}\right) $$
(3)
$$ {x}_{im}\left(n+1\right)={x}_{im}(n)+{v}_{im}\left(n+1\right) $$
(4)

Where C1 and C2 are acceleration coefficients numbers whereas the r1m and r2m are uniformly distributed random number in the range [0, 1]. A flow chart of PSO which executed in proposed work of this paper is depicted in following Fig. 1.

Fig. 1
figure 1

Particle swarm optimization

Full size image

3.2 Singular value decomposition

Singular value decomposition (SVD) is a tool which is used in various numerical applications. It can partition any rectangular or square matrix M into three matrices; U and V are the orthogonal matrices whereas S is the diagonal matrix which contains singular values of original matrix M [1, 23]. The mathematical formulation for the same is given in following equation:

$$ M={USV}^T $$
(5)

The SVD is widely used in various image processing applications due to its some of the characteristics;

  • If small perturbation is added to singular value, S there is no significant change in visual quality of image.

  • The singular value S gives luminance detail of image whereas the diagonal matrices U and V contain the geometrical detail.

$$ A=\left(\begin{array}{ccc}{u}_{1,1}& \cdots & {u}_{1,M}\\ {}{u}_{2,1}& \dots & {u}_{2,M}\\ {}\vdots & \ddots & \vdots \\ {}{u}_{M,1}& \cdots & {u}_{M,M,}\end{array}\right)\left(\begin{array}{ccc}{s}_{1,1}& 0& 0\\ {}0& {s}_{2,2}& 0\\ {}\vdots & \ddots & \vdots \\ {}0& \cdots & {s}_{M,N}\end{array}\right){\left(\begin{array}{ccc}{v}_{1,1}& \cdots & {v}_{1,N}\\ {}{v}_{2,1}& \dots & {v}_{2,N}\\ {}\vdots & \ddots & \vdots \\ {}{v}_{N,1}& \cdots & {v}_{N,N}\end{array}\right)}^T $$

3.3 Arnold transform

The Arnold Transform (AT) is the scrambling technique which rearranges the pixels of image such a way that the original image looks like disorganized and encrypted image. The AT on two dimensional digital image with dimension N × N is define as

$$ \left(\begin{array}{l}{x}^{\hbox{'}}\\ {}{y}^{\hbox{'}}\end{array}\right)=\left(\begin{array}{l}1\\ {}1\end{array}\right.\kern0.48em \left.\begin{array}{l}1\\ {}2\end{array}\right)\left(\begin{array}{l}x\\ {}y\end{array}\right)\left(\operatorname{mod}(N)\right) $$
(6)

Here, the x and y are the pixel positions of the digital image whereas the x’ and y’ are the pixel positions of scramble image as a result of AT [23, 33, 35].

3.4 Discrete wavelet transform

The Discrete Wavelet Transform (DWT) offers good energy compaction property and multi resolution analysis; therefore it is widely used in various image processing applications. The DWT decompose the signal into different frequency components. At each level DWT decomposes the image into four different frequency subbands. These subbands named as lower frequency approximate subband (LL) and three other high frequency subbands: horizontal (HL), vertical (LH) and diagonal (HH). At higher level, wavelet transform further decomposes each LL subband into four different subbands as mention above. Low pass filtering in both Horizontal and vertical direction on image generates the LL subband. The low pass and high pass filtering in two different directions produced LH or HL subbands. The high pass filtering in both directions gives the HH subband. This is depicted in following Fig. 2.

Fig. 2
figure 2

Single level discrete wavelet transform and respective subbands

Full size image

4 Proposed work

In different algorithms like [15] and others, there is a need of optimization to overcome the manual efforts in selection of proper values. To make it possible, PSO based technique is incorporated in this manuscript. Here as per the flow chart of the algorithm shown in Fig. 3, two techniques are proposed namely PSO and AT-PSO are proposed. In first method, tuning of the PSO technique is carried out in such a way that it can provide optimum performance in terms of not only PSNR but also NSS and NCC. The security feature is also incorporated in second method using AT to maintain rightful ownership.

Fig. 3
figure 3

Flow chart for proposed algorithms PSO and AT-PSO

Full size image

It is depicted in Fig. 3 that, proposed algorithm is embedding the watermark content into the singular values of LL subband of the cover image. A weight factor (α) is chosen using PSO optimization algorithm due to its advantages like fast convergence and capability to tune an algorithm with a few parameters. An inverse transform is carried out in terms of SVD and DWT after embed the watermark image successfully into the singular matrix of LL subband’. This first proposed algorithm is named as Image watermarking using PSO optimization technique. In Second proposed algorithm, an AT is incorporated with First proposed algorithm and thus it is termed as AT-PSO based image watermarking. Second algorithm offers high security without much computational complexity over first algorithm. The selection of method is given with decision making symbol in the flow chart.

4.1 Watermark embedding algorithm

In technique proposed this paper, the Arnold Transform scramble the watermark image which is embedded inside the singular value matrix of LL subband of cover image. This embedding process uses PSO to select weight (scale) factor. SVD is applied on this LL subband. Singular value matrix is modified with scramble watermark image and then using inverse SVD the modified LL subband is generated. Inverse DWT is applied on this modified LL subband along with remaining subband generates the watermarked image. The block diagram for the same is given in Fig. 4 and mathematical steps are given below.

  • Step 1. Decompose the cover image C into LL, HL, LH and HH subbands using DWT.

  • Step 2. Apply SVD on the LL subband;

Fig. 4
figure 4

Proposed scheme for watermark embedded into cover image

Full size image
$$ {U}_{LL}{S}_{LL}{V}_{LL}= LL $$
(7)

  • Step 3. AT is applied on the watermark image to generate scrambled image W.

  • Step 4. Modify the singular value matrix SLL with W image using a scale factor α selected by PSO;

$$ {S}_{LL M}={S}_{LL}+\alpha \ast W $$
(8)

  • Step 5. Now, apply the SVD on the Modify the singular value matrix SLLM;

$$ {U}_{LLM A}{S}_{LLM A}{V}_{LLM A}={S}_{LLM} $$
(9)

  • Step 6. The Inverse SVD applied on SLLMA with orthogonal matrices ULL and VLL of LL subband, gives modified LL’ subband;

$$ {LL}^{\hbox{'}}={U}_{LL}{S}_{LL MA}{V}_{LL}^T $$
(10)

  • Step 7. The Inverse DWT of the modified LL’ subband along with other high frequency subband LH, HL and HH gives the watermarked image Cw.

4.2 Watermark extraction algorithm

The watermarked image Cw may suffer from various geometric and non-geometric type of noise attacks. The mathematical steps to extract the watermark from this noisy watermarked image Cw* is given below whereas the block diagram is given in Fig. 5.

  • Step 1. Decompose the noisy watermarked image into LL*’, HL*, LH* and HH* subbands using DWT. Here subband LL*’ is the modified and noisy subband.

  • Step 2. Apply SVD on LL*’ subband;

Fig. 5
figure 5

Proposed scheme for watermark extraction from noisy watermarked image

Full size image
$$ {U}_{LL}^{\hbox{'}}{S}_{LL MA}^{\hbox{'}}{V}_{LL}^{\hbox{'}}={LL}^{\hbox{'}\ast } $$
(11)

  • Step 3. The inverse SVD is applied on respective orthogonal matrices along with SLLMA’ to get SLLM’;

$$ {S}_{LLM}^{\hbox{'}}={U}_{LLM A}^{\hbox{'}}{S}_{LLM A}^{\hbox{'}}{V}_{LLM A}^{T^{\hbox{'}}} $$
(12)

  • Step 4. The scrambled watermark image W′ is reconstructed with SLLM’ and SLL;

$$ {W}^{\hbox{'}}=\left({S}_{LL M}^{\hbox{'}}-{S}_{LL}\right)/\alpha $$
(13)

  • Step 5. The inverse AT applied on the scrambled watermark W′ to reconstruct the original watermark image with threshold value 0.5. This threshold value decides the value of pixel 0 or 1.

The mathematical formulation of PSO to get the proper value of scale factor is given below.

  • The acceleration coefficients C1 and C2 are 2,

  • The lower and upper velocities are 10 and 150,

  • The maximum iterations are 8.

  • The total number of particles is five.

To maximize the imperceptibility and robustness of watermarked image and extracted watermark image the following fitness function [28] is used.

$$ f=\max \left[\frac{1}{R}\left(\sum \limits_{i=1}^R{corr}_i\left(w,{w}^{\hbox{'}}\right)\right)+ corr\left(c,{c}_w\right)\right] $$
(14)

In this above equation, the total number of attacks is R whereas the Corr is the Normalized Correlation Coefficient.

As discussed above, It is required to select appropriate parameters for PSO to get better performance. The above parameters like C1, C2, Vmax, Vmin, Iterations and total number of particles are chosen such a way that PSO can maximally optimized the solution. Thus, in a way it is parameter selection impose certain limitations in of the algorithm in which i. e. inappropriate parameters values may leads erroneous output.

5 Performance measures

The robustness of proposed algorithm is verified using Normalized Correlation Coefficient (NCC) and Normalized Similarity Ratio (NSR) whereas imperceptibility is judged using Peak Signal-to-Noise Ratio (PSNR).

The NSR is defined by Eq. (15) which depends on Similarity ratio (SR).

$$ NSR=\frac{SR-\min (SR)}{1-\min (SR)} $$
(15)
$$ SR=\frac{S}{S+D} $$
(16)

The SR is defined in Eq. (16) in which S is total number of similar pixels whereas the D is total number of dissimilar pixels in the original and extracted watermark [15]. The min(SR) is the value of SR which can be achieved for original binary watermark image with respect to an image containing either all white or all black pixels. The NCC and PSNR are defined as following Eqs. (17) and (18) respectively.

$$ NCC=\frac{\sum_{i=1}^N{\sum}_{j=1}^N\left({w}_{ij}-\overline{w}\right)\left({w}_{ij}^{\ast }-{\overline{w}}^{\ast}\right)}{\sqrt{\sum_{i=1}^N{\sum}_{j=1}^N{\left({w}_{ij}-\overline{w}\right)}^2}\sqrt{\sum_{i=1}^N{\sum}_{j=1}^N{\left({w}_{ij}^{\ast }-{\overline{w}}^{\ast}\right)}^2}} $$
(17)
$$ PSNR=10{\log}_{10}\frac{255^2}{MSE} $$
(18)

Where, \( MSE=\frac{1}{N^2}{\sum}_{i=1}^N{\sum}_{j=1}^N{\left[C\left(i,j\right)-{C}^{\ast}\left(i,j\right)\right]}^2 \)

In Eqs. (17) and (18), the w is original watermark image and w* is the extracted watermark image whereas the C indicates cover image and C* is the watermarked image.

6 Results and discussion

The performance of proposed technique is verified using four different cover images and EC logo as the watermark image, they are depicted in Fig. 6.

Fig. 6
figure 6

The cover images a Pepper b Elaine c Lena d Baboon e Goldhill f Barbara and g Cameraman with dimension 512 × 512, and the watermark image h EC logo with dimension 256 × 256

Full size image

The performance analysis in terms of NCC, NSR and PSNR of both the proposed algorithms i.e. PSO based and PSO-AT based algorithms are given in the Tables 1 and 2 respectively. In existing algorithm [15] the selection procedure of scale factor to embed the watermark is empirical and limited up to specific images. Therefore, the NSR of extracted watermark and PSNR of noisy watermarked images are not satisfactory. To improve the existing technique and make it applicable to any type of cover image, the PSO is incorporated in the proposed scheme.

Table 1 The NCC and NSR values of extracted watermark image and PSNR values of noisy watermarked image against various noise attacks for different cover images watermarked with proposed algorithm using PSO
Full size table
Table 2 The NCC and NSR values of extracted watermark image and PSNR values of noisy watermarked image against various noise attacks for different cover images watermarked with proposed algorithm using PSO and AT
Full size table

The diagonal line problem is present in the extracted watermark image with existing technique as well as the PSO based proposed technique as shown in the Fig. 7. The Arnold Transform (AT) is included in the PSO based proposed technique which not only remove the diagonal line from extracted watermark image but also increases the imperceptibility of the noisy watermarked image. The NCC and NSR value of the extracted watermark image using both the proposed techniques is above 0.99 against all the types of noise attacks as given in Tables 1 and 2. The PSNR values of noisy watermarked images are also better under all the noise attacks except rotation and cropping.

Fig. 7
figure 7

The extracted watermark images a, b and c using PSO based proposed algorithm d, e and f using AT- PSO based algorithm under attacks Histogram Equalization, Rotation and salt & pepper noise respectively

Full size image

The imperceptibility and robustness of PSO based proposed algorithm and AT-PSO based proposed algorithm are compared with existing algorithm [15] in Tables 3 and 4 for Pepper and Goldhill cover images respectively. In Table 3, the NSR and PSNR values offered by both proposed algorithms are better as compare to the existing algorithm under all the types of noise attacks except rotation and histogram equalization attacks where the PSNR values of noisy watermarked image are slightly less than the existing algorithm. The graphical analysis in Figs. 8 and 9 show the comparison of NSR and PSNR values between existing and AT-PSO based proposed algorithms for Pepper cover image. In Tables 3 and 4, it is also noticeable that the imperceptibility of AT-PSO based proposed algorithm is better than only PSO based proposed algorithm but it is less robust in terms of NSR.

Table 3 Comparative analysis of NSR and PSNR values between existing and proposed techniques for Pepper cover image
Full size table
Table 4 Comparative analysis of NSR and PSNR values between existing and proposed techniques for Goldhill cover image
Full size table
Fig. 8
figure 8

The comparison of NSR values of extracted watermark of existing algorithm with the AT-PSO based proposed technique for Pepper cover image against different noise attacks

Full size image
Fig. 9
figure 9

The comparison of PSNR values of noisy watermarked image of existing algorithm with the AT-PSO based proposed technique for Pepper cover image against different noise attacks

Full size image

It is obvious from Tables 1 and 2 that, robustness parameters NCC and NSR offering by a proposed algorithm 1 (using only PSO) is little more as compared to algorithm 2 (using PSO and AT both) against different types of noise attacks.

However, the presence of diagonal line in Fig. 7a to c is showing limitation of PSO based algorithm 1. Also, use of AT along with PSO in proposed algorithm 2 is eliminate the problem of diagonal line in the extracted watermark image and offering NCC and NSR values closer to the algorithm 1. In addition, the PSNR value of noisy watermarked image in proposed algorithm 2 is better than algorithm 1 in case of most images in presence of variety of attacks.

Comparative analysis between proposed and existing scheme has been carried out and results are mentioned in Tables 3 and 4. The value of NSR using proposed algorithm is better than existing algorithm [15]. The performance of algorithm is more accurate and robust against Salt and Pepper image with their NSR values 0.9898 and 0.9954 respectively PSO and AT-PSO based algorithm. Moreover, PSNR value of noisy watermarked image using proposed and existing algorithm is depicted in Tables 1 and 3. Analysis of these characteristic show that PSNR of proposed algorithm is greater than existing algorithm in presence of any of the type of noise attack.

A comparison of proposed algorithm is also carried out with three different state-of-the-art algorithms and it is tabulated in Table 5. These algorithms are using optimization techniques like PSO and DE to embed watermark image into cover image. Here, a comparative analysis shows that against every reported attack both the proposed schemes are performed better as compared to all the existing watermarking algorithm. An analysis for PSNR Vs Payload is also carried out with different size like 256 × 256, 128 × 128 and 64 × 64. With these analysis, Obtained PSNR values 30.5614, 32.3426 and 33.8793 sequentially for Goldhill Cover image with the size of 512 × 512.

Table 5 Comparative analysis of NCC values between existing and proposed techniques for Pepper cover image
Full size table

Many researchers have tried to improve the algorithm proposed in [15] using various optimization algorithm. Among them Bi-directional Extreme Learning Machine (B-ELM) based semi-blind watermarking is proposed in [24]. This algorithm is not only optimized RMSE but also scaling factor. The comparative analysis in Table 5 show that both PSO and AT-PSO algorithms both are performed better as compared to the algorithm given in [24].

7 Conclusion

A reliable watermarking technique is proposed in [15] which is robust and imperceptible, but the procedure to select scale factor for embedding watermark is not adequate to get the maximum imperceptibility and robustness and limited up to a particular image. To make existing algorithm generalized for variety of images and to improve the imperceptibility and robustness, the PSO is incorporate. The comparative analysis of Tables 3 and 4 are showing that proposed PSO based approach not only increasing the robustness of algorithm but also the imperceptibility. In addition to that, Table 5 is also representing the better performance of the proposed algorithm as compared to existing algorithm [24] which is extended version of the algorithm used in [15].

The diagonal line problem of existing algorithm is not resolve by proposed approach based on PSO, therefore to remove this diagonal line from extracted watermark image the AT along with PSO is used. This AT-PSO based approach increases the robustness and imperceptibility as compare to existing algorithm. The reliability of existing algorithm is good and which further increases by use of AT in this paper.