1 Introduction

Owing to the popularity of the Internet and the rapid growth of multimedia technology, interactive media have become the most important gadgets for transmitting information [1]. Day by day, the scenario of the global pandemic situations is increasing, which makes the mode of business and communication is converted into digital form. This means that there are a lot of data are moving worldwide in the digital platform. Consequently, due to the pandemic situation of COVID-19, exchanging digital multimedia data has become a very frequently task and has caused considerable interest within the community. However, such open access to Internet makes way for digital multimedia data such as text, image, audio and video to be easily duplicated, modified and redistributed without the owner’s permission. So, protecting ownership of digital media content has become a paramount issue. Digital watermarking stands here as suitable solution to verify the authenticity and to solve ownership issues. Digital watermarking is a technique for hiding data, which can be a logo for an organization, digital signature or image of an author, into multimedia object like text, image, audio or video. Furthermore, high security requirements of images in many scenarios such as military and trade stimulate the development of digital image encryption [2,3,4,5] and forensic algorithms [6]. Transparency and robustness are considered two mainly important properties for digital watermarking algorithm [7], as well they are measured using a quality metric: peak signal-to-noise ratio and normalized correlation, respectively.

According to the domain in which the watermark is inserted, digital watermarking techniques could be classified into two main categories that are in spatial domain and in frequency domain transform. The least significant bit (LSB) substitution, pixel value differencing (PVD), exploiting modification direction (EMD), and modulus function (MF) are some of the well-known approaches in spatial domain [8]. On the contrary, transformed domain-based watermark embedding technique inserts a watermark by altering the transformed coefficients of the original image. There are a lot of transform domain watermarking methods which are available in the various literature such as discrete wavelet transform (DWT) [9], singular value decomposition (SVD) [10], discrete cosine transforms (DCT) [11], discrete Fourier transforms (DFT) [12], discrete Hadamard transform (DHT) [13] and redundant wavelet transform (RWT) [14]. It is said that, in terms of resisting attacks, the frequency domain techniques are not only better than most of spatial domain techniques but also further complex than the spatial method [15] and require higher computational cost [16].

Depending on its objective, data hiding can be divided into watermarking for copyright protection and steganography for securing confidentiality [17]. Researchers have proposed a lot of effective techniques to overcome some of the inherent limitations of data hiding. Therefore, the design of a simple and efficient, yet sufficiently imperceptible and robust watermarking method still constitutes a challenging task. The LSB approaches hide the secret data directly inside the cover image pixel [18]. Wu and Hwang [19] proposed an improved LSB substitution using a group of three pixels as an embedding unit to hide three bit of secret data. The possible modification for each pixel is at most ±1. Sahu and Swain [20] improved the hiding capacity (HC) using the concept of bit differencing and modified LSB matching.

The motivation behind pixel value differencing (PVD) steganography [21] is to make a clear distinction among the smooth and textured areas of an image. The smooth areas are the low-intensity sections where the neighboring pixel values are close to each other, but texture areas have a considerable difference. Hence, the smooth areas cannot tolerate high changes as compared to the textured areas. An adaptive PVD approach has been proposed by Swain [22], to improve the HC. The data embedding is performed in both horizontal and vertical directions. Various articles have been proposed in the literature using PVD approaches [23, 24].

Aiming to secure information, and copyright protection authentication, the solution is also to apply an appropriate hybrid method. Wu et al. [25] combined the LSB substitution and PVD approach. This improved the HC as compared to the PVD approach of Wu and Tsai [21]. The work has been carried out by many researchers [26,27,28] to improve the HC as well as security. In the same context, a lot of attention has also been paid to combine the frequency domain with the eigendecomposition values of the image, i.e., the use of the frequency channels and thus the eigenvalues and their corresponding eigenfunctions of the image. Due to its excellent spatio-frequency localization properties, the DWT is very suitable to identify areas in the cover image where a watermark can be imperceptibly embedded. One of attractive mathematical properties of SVD is that slight variations of singular values do not affect the visual perception of the cover image, which motivates the watermark embedding procedure to achieve better transparency and robustness. Consequently, many image watermarking techniques combining these two transform methods have been proposed. For example, Yasmeen and Uddin [29] proposed an improved DWT–SVD-based hybrid approach to further ensure the robustness and protection of digital data. This method contrasted with existing schemes and proved to be a good mechanism for both grayscale and color images. Makbol et al. [30] used DWT-SVD image transform and human visual system (HVS) to improve performance of watermarking scheme where watermark was embedded by modifying several elements in its U matrix. Recently, similar work also has been pursued by Ahmadi et al. [31] in which a hybrid (DWT–SVD) watermarking scheme, human visual system and an intelligence optimization algorithm known as PSO (particle swarm optimization) are used to provide high robustness and capacity. However, their method is not invariant against rotational attacks. Moreover, its security needs to be improved by encrypting the watermark image before embedding. DWT and SVD were also employed in a robust and secure watermarking scheme by Ansari et al. [32]. Zear et al. [33] studied a blind watermarking method by fusing DWT, DCT and SVD, where the noise effects in watermark extraction are suppressed by the back propagation neural network (BPNN). Liu Y et al. [34] designed a non-blind watermarking scheme with DWT and SVD, the security of watermarks has been improved significantly with RSA encryption algorithm. For further detailed description on the aforementioned approaches, we refer keen reader to [35,36,37].

Further, Liao et al. [38] introduced a novel amplifying channel modification probabilities (ACMP) approach for color images. The traditional steganographic approaches conceal the secret data equally in the RGB channels. On the contrary, Liao et al. explored the correlations among the RGB channels and conceals the data adaptively to achieve high HC and resistance against various steganalysis attacks. Various steganographic approaches utilizing color images were presented in the literature [39, 40]. Liao et al. in [41] have newly proposed two payload strategies, which are based on the image texture complexity and the distortion distribution as indicator for secure capacity of each cover image. These strategies are applied on single image steganographic algorithms and experiments shown better resistance to modern universal pooled steganalysis compared to existing methods.

Fig. 1
figure 1

Example of two-level DWT transform

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1.1 Contributions

This paper introduces a sophisticated hybrid SVD-DWT for an efficient image watermarking technique for grayscale image hiding. Because of the conflict between invisibility and robustness, the insertion of watermark is usually made in LH, HL and HH sub-bands to maintain the quality of the original image. As HVS (human visual system) is less sensitive to high-frequency parts, HH sub-band is chosen for embedding watermark as it contains finer details and contributes insignificantly toward signal energy. Hence, watermarking embedding in this region will furnish better image quality, but at the same time yields to poor results when extracting watermark. However, our proposed technique has highly overcome this issue in the watermark extraction process. We aggregated DWT-SVD domain with the chosen HH sub-band in which the watermark should be embedded and extracted too. At last, with these observations in mind, we construct our watermarking approach and demonstrate that guarantees to achieve high invisibility and robustness.

The rest of the paper is structured as follows. Section 2 shows the relevant theoretical background information. The watermark embedding and extraction algorithms proposed in this paper are described in detail in Sect. 3. Section 4 introduces the image quality measures. Section 5 presents the experimental setup and simulation results of the proposed approach with imperceptibility, robustness, computational complexity and capacity analysis and compares its performance with other related algorithms. Finally, conclusions and future work are provided in Sect. 6.

2 Background

This section is devoted to the brief explanations of the concepts being used in the proposed scheme such as DWT and SVD transforms. Interested to know more in detail may refer to the respective studies [10, 42,43,44,45,46,47].

2.1 Discrete wavelet transform (DWT)

Discrete wavelet transform (DWT) is widely used as an ideal tool in the field of frequency analyzing and signal processing, including image watermarking. It is indeed a multiscale signal analysis method, inherits and develops the idea of Fourier transform fixed resolution, having features of multiresolution and local signal analysis [44]. The strength of DWT over Fourier transform is its ability to produce a temporal resolution in which it captures both frequency and location information.

One-level DWT or one-dimensional DWT splits an original image into four non-overlapping multiresolution sub-bands, including a low-frequency sub-band LL and three high-frequency sub-bands HL, LH, HH [42, 43]. Among them LL, standing for the coarse-level coefficients is the most similar sub-image to the original image, called approximation sub-band. The other three sub-bands LH, HL and HH represent the finest scale wavelet coefficients denoting horizontal direction detail, vertical and diagonal detail direction image, respectively. Moreover, the low-frequency sub-band can be further decomposed into another four different sub-bands. Two-level DWT decomposition is shown in Fig. 1, where the low-frequency component represents the most contents of the original image and the high-frequency represents the edge, contour and texture characteristics of the original image. Figure 1b expresses the different frequency schematic picture of the original image ‘Lena,’ and Fig. 1c shows the structures of ‘Lena’ image after the two-level discrete wavelet transform decomposition.

2.2 Singular value decomposition (SVD)

Singular value decomposition (SVD) is a matrix diagonalization efficient algorithm in the numerical linear algebra technique for a variety of applications [10, 45,46,47]. The basic idea behind the SVD-based watermarking techniques is to find the SVD of the cover image or each block of the cover image and then modify the singular values to embed the watermark. There are three main key features of SVD in digital image watermarking techniques:

  1. 1.

    The singular value of an image has very good stability and noise immunity. When a small perturbation is added to an image, large variation of its singular values does not occur.

  2. 2.

    The singular value in the value sequence obtained by SVD operation of an image specifies the luminance of an image layer, where pairs of singular vectors specify the geometry of the image.

  3. 3.

    The inherent algebraic image properties are demonstrated by the singular values [44, 47]. The extracted watermark image will always be disturbed by the process of geometric manipulations, especially the extraction of blind or semi-blind watermarking algorithm. According to the characteristics of SVD, the cover image is able to withstand certain geometric distortions, if singular value decomposition is performed on the processes of watermark embedding and extraction.

From the perspective of image processing, an image can be viewed as a matrix with non-negative scalar entries. Let A be a rectangular matrix with \(m\times n\) size; then according to SVD, it can be decomposed mathematically into three matrices as

$$\begin{aligned} A=USV^{T}, \end{aligned}$$
(1)

where U and V are orthogonal (or unitary) matrices, i.e., \(UU^{T}=I\), \(VV^{T}=I\); S is non-negative diagonal matrix whose diagonal elements (singular values) coincide with the square roots of the eigenvalues of \(A^{T}A\) and arranged in descending order as \(\uplambda _1\ge \uplambda _2\ge \ldots \ge \uplambda _{n}\ge 0\). Thus, the columns of U are the left singular vectors, whereas the columns of V are the right singular vectors of A. A graphical description of the procedure of SVD of an \(m\times n\) image is presented in Fig. 2 [48].

3 Proposed watermarking system

In this section, grayscale image watermarking approach is proposed. It is based on SVD and DWT techniques. The major goal of this proposal is to embed a grayscale watermark image into a grayscale image without perceptual degradation of watermark taking into account robustness against several kinds of attacks. Moreover, both imperceptibility and robustness can be achieved simultaneously. The suggested algorithm for secure communication of image belongs to two parts: the watermark embedding and extraction algorithm. Embedding and extraction processes are two main phases for image-watermarking scheme. Both parts along with respective flowcharts are described in detail in Sects. 3.1 and 3.2.

Fig. 2
figure 2

The procedure of SVD decomposition

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Fig. 3
figure 3

Block diagram of the proposed embedding algorithm

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3.1 Embedding process for sending side

A step-by-step procedure of the embedding algorithm at the sender side as illustrated in Fig. 3 is explained below:

Step 1::

Apply one-level DWT to the original image A to decompose it into four sub-bands as given in Eq. (2).

$$\begin{aligned} \left[ \text {LL}~\text {LH}~\text {HL}~\text {HH}\right] =\text {DWT}\left( A\right) \end{aligned}$$
(2)
Step 2::

Apply the eigendecomposition SVD to the high-frequency sub-band HH as given in Eq. (3).

$$\begin{aligned} \left[ U_O S_O V_O\right] =\text {SVD}\left( \text {HH}\right) \end{aligned}$$
(3)

where the unitary and diagonal matrices are \(U_O\), \(V_O\) and \(S_O\); superscript O corresponds to original image.

Step 3::

Repeat steps 1 to 2 for watermark image W and after eigendecomposition the corresponding matrices are \(U_W\), \(V_W\) and \(S_W\); where superscript W represents watermark image.

Step 4::

Modify the singular value of the decomposed image with the singular value of the watermark image using a scaling factor \(\alpha \) which controls the strength of the watermark to be inserted. This is given in (4).

$$\begin{aligned} S_2 = S_O+\alpha \times S_W \end{aligned}$$
(4)
Step 5::

Combine the orthogonal matrices of the decomposed original image with the modified singular value matrix to obtain a modified DWT coefficients as given in (5).

$$\begin{aligned} \text {HH}_2=U_O S_2 V_O^T \end{aligned}$$
(5)

where T is transpose of a matrix.

Step 6::

Apply one-level inverse DWT (iDWT) to resultant image \(\hbox {HH}_2\) instead of HH sub-band to produce the watermarked image, as shown in (6).

$$\begin{aligned} A_W=\text {iDWT}\left( \text {LL}~\text {LH}~\text {HL}~\text {HH}_2\right) \end{aligned}$$
(6)
Step 7::

Transmit through a secure channel the diagonal matrix \(S_O\) of the original image, the unitary matrices \(U_W\) and \(V_W\) of the watermark image, and the first three non-modified DWT sub-bands of the watermark to be subsequently used at the receiver side for the extraction watermarking process.

3.2 Extraction process for receiving side

A step-by-step procedure of the extraction algorithm at the receiver side as illustrated in Fig. 4 is detailed below:

Step 1::

Apply DWT to the watermarked (possibly distorted) image \(A_W^*\), that we receive it from the public channel, to decompose it into four sub-bands as given in Eq. (7).

$$\begin{aligned} \left[ \text {LL}_2~\text {LH}_2~\text {HL}_2~\text {HH}_2\right] =\text {DWT}\left( A_W^{*}\right) \end{aligned}$$
(7)

where \(^*\) is a mark of probable corruption resultant from attacks.

Step 2::

Apply SVD to the high-frequency sub-band \(\hbox {HH}_2\) as given in Eq. (8).

$$\begin{aligned} \left[ U_O^* S_O^* V_O^*\right] =\text {SVD}\left( \text {HH}_2\right) \end{aligned}$$
(8)
Fig. 4
figure 4

Block diagram of the proposed extracting algorithm

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Step 3::

The diagonal matrix \(S_O\) of the decomposed original image is already received from the private channel. Compute the correlation coefficient (Cr) to measure closeness between the diagonal components \(S_O\) and \(S_O^*\) of the decomposed original image and the decomposed watermarked image, respectively, such that \(Cr\left( S_O,S_O^*\right) =\dfrac{\sum _m\sum _n\left( S_O-{\bar{S}}_O\right) \left( S_O^*-{\bar{S}}_O^*\right) }{\sqrt{\left( \sum _m\sum _n\left( S_O-{\bar{S}}_O\right) ^2\right) \left( \sum _m\sum _n\left( S_O^*-{\bar{S}}_O^*\right) ^2\right) }},\) where \({\bar{S}}_O\) and \({\bar{S}}_O^*\) are the average values of \(S_O\) and \(S_O^*\), respectively. The value of Cr ranges between \(-1\) and \(+1\). The Cr gives numerical result that expresses how well two diagonal components match. The higher the metric, the more accurate the match.

Step 4::

At this stage, even before constructing the watermark, a preliminary decision could be taken to claim that the watermark will be successfully extracted or not. Depending on the Cr value, verify the following conditions:

(i):

If \(\text {Cr}=1\), this means that the watermarked image was not attacked. So subtract the received singular value \(S_O\) of the decomposed original image from the singular value \(S_O^*\) of the decomposed watermarked image and divide the values by the scaling factor \(\alpha \) to obtain the singular value of the watermark image. This is given in Eq. (9).

$$\begin{aligned} S_W^*=\left( S_O^*-S_O\right) {}/\alpha \end{aligned}$$
(9)
(ii):

If not, i.e., \(\text {Cr}<1\) which means that the watermarked image was indeed attacked; recompute the singular value of the watermark without dividing by the scaling factor using Eq. (10).

$$\begin{aligned} S_W^*=S_O^*-S_O \end{aligned}$$
(10)
Step 5::

The orthogonal matrices of the watermark image are also already received from the private channel; combine them with the recovered singular value matrix \(S_W^*\) to obtain a modified DWT coefficients as given in Eq. (11)

$$\begin{aligned} \text {hh}_{2} = U_WS_W^*V_W^T \end{aligned}$$
(11)
Step 6::

By using the obtained \(\text {hh}_2\) sub-band together with the three other sub-bands of one-level DWT of watermark image, recreate the watermark image \(W^*\) by performing the one-level inverse DWT, as shown in Eq. (12)

$$\begin{aligned} W^* = \text {iDWT}\left( \text {ll}~\text {lh}~\text {hl}~\text {hh}_2\right) \end{aligned}$$
(12)
Step 7::

Finally, the sending watermark image W and the recovered image \(W^*\) are compared using common performance metrics for image quality assessment.

4 Performance evaluation metrics

Watermarking algorithms are usually evaluated with respect to imperceptibility and robustness. In this paper, PSNR, mean square error (MSE), structural similarity (SSIM) index measure, universal image quality index (UIQI) and normalized correlation (NC) are chosen as quality assessment parameters.

4.1 Peak signal to noise ratio

The peak signal-to-noise ratio (PSNR) is used to measure a watermarked image quality. The PSNR, which is measured in decibels, defines the resemblance between an original image and the reconstructed image [49]. In the ideal case, the PSNR should be infinite [50]. In fact, this cannot be accomplished with watermarked image. So, the larger PSNR the better. The PSNR in decibels (dB) can be calculated using Eq. (13).

$$\begin{aligned} PSNR_{\mathrm{dB}}=10\log _{10}\left( \frac{A_{\mathrm{max}}^2}{MSE}\right) \end{aligned}$$
(13)

where \(A_{\mathrm{max}}\) is the maximum possible pixel value of the grayscale image A.

4.2 Mean square error

Mean square error (MSE) is a standard quality measurement. It is the average of the pixel difference between two images. In ideal case, the MSE must be zero. In fact, this is cannot be reached with watermarked image [51]. So, the smaller the value of MSE, the better the quality is. MSE is defined as

$$\begin{aligned} MSE=\frac{1}{M\times N}\sum _i^M\sum _j^N\left( A\left( i,j\right) -A_W\left( i,j\right) \right) ^2 \end{aligned}$$
(14)

where A is the original image before watermarking, \(A_W\) is the watermarked image, and M & N are the original image width and height, respectively.

4.3 Structural similarity

Structural similarity (SSIM) index measure is a method for quality assessment used as a performance metric to evaluate invisibility between two images. It is considered as a full reference metric; in other words, the prediction or measurement of image quality is based on an initial distortion-free or uncompressed image as reference. The SSIM index is defined by

$$\begin{aligned} SSIM=\frac{(2\mu _A\mu _{A^*}+c_1)(2\sigma _{AA^*}+c_2)}{(\mu _A^2+\mu _{A^*}^2+c_1)(\sigma _A^2+\sigma _{A^*}^2+c_2)} \end{aligned}$$
(15)

here, \(\mu _A\) and \(\mu _{A^*}\) are the average of image A and \(A^*\), respectively. \(\sigma _A^2\) and \(\sigma _{A^*}^2\) are the variance of image A and \(A^*\), respectively. \(\sigma _{AA^*}\) is the covariance of image A and \(A^*\), respectively. \(c_1=(k_1L)^2\), \(c_2=(k_2L)^2\) are used to keep the stabilization of the division with a weak denominator. L is the dynamic range of the pixel-values (typically \(L=255\)), with \(k_1=0.01\) and \(k_2=0.03\) by default [52].

4.4 Universal image quality index

Watermarked image quality can be also measured by using universal image quality index (UIQI). In fact, this quality index models any distortion as a combination of three different factors: loss of correlation, luminance distortion, and contrast distortion [53]. The dynamic range of UIQI is \([-1~~1]\). A UIQI value closer to 1 specifies that the watermarked image is indistinguishable to the cover image. The UIQI between two images can be calculated as follows:

$$\begin{aligned} UIQI=\frac{4\sigma _{AA^*}{\bar{A}}{\bar{A}}^*}{(\sigma ^2_{A}+\sigma ^2_{A^*})\left[ ({\bar{A}})^2+({\bar{A}}^*)^2\right] } \end{aligned}$$
(16)

where \({\bar{A}}\) and \({\bar{A}}^*\) are the average of image A and \(A^*\), respectively. \(\sigma _A^2\) and \(\sigma _{A^*}^2\) are the variance of image A and \(A^*\), respectively. \(\sigma _{AA^*}\) is the covariance of image A and \(A^*\), respectively.

4.5 Normalized correlation

Normalized correlation (NC) can be used to measure the degree to which the used algorithm can withstand attack. In ideal case, NC should equal 1 [54]. In real, this could be achieved unless the watermarked image does not undergo any kind of attack. A larger NC value means a higher degree of similarity between two images. The NC is defined as follows:

$$\begin{aligned} NC=\frac{\sum _i^m\sum _j^nW\left( i,j\right) W^*\left( i,j\right) }{\sqrt{\sum _i^m\sum _j^nW\left( i,j\right) ^2}\sqrt{\sum _i^m\sum _j^nW^{*}\left( i,j\right) ^2}} \end{aligned}$$
(17)

where W is the original watermark image and \(W^*\) is the corresponding extracted watermark.

5 Experiments and results

In this section, we present the qualitative and quantitative results for image watermarking to evaluate the performance of our proposed framework. Note that reading input images, performing discrete wavelet transform, solving eigenproblem, and computing performance evaluation metrics are all of them implemented in MATLAB© R2015b environment. The effectiveness of our approach is validated by carrying out a comprehensive comparison with several state-of-the-art methods.

Fig. 5
figure 5

a–g Cover images for test: ‘Zelda,’ ‘Lena,’ ‘Goldhill,’ ‘Peppers,’ ‘Butterfly,’ ‘Baboon,’ ‘Lake,’ respectively; h Watermark image

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5.1 Datasets

The performance of the proposed framework is tested for two different tasks, i.e., for watermark embedding and extraction; as well as it is evaluated on a two challenging standard test images: we use dataset of standard \(512\times 512\) grayscale test images provided by computer vision group [55] which contains 49 test images, and image repository provided by the waterloo fractal coding and analysis group [56] that is divided into three sets from which we use 12 images existing in Grayscale Set 2.

Table 1 List of various attacking operations and their parameter values
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5.2 Experimental settings

Several experiments are performed comprehensively for evaluating effectiveness of the proposed algorithm. Seven standard grayscale images, namely ‘Zelda,’ ‘Lena,’ ‘Goldhill,’ ‘Peppers,’ ‘Butterfly,’ ‘Baboon’ and ‘Lake,’ are taken as cover images of size \(512\times 512\) as depicted in Fig. 5a–g, whereas WaterMark logo of size \(512\times 512\) is used as a watermark image presented in Fig. 5h. Although we have shown just seven test images, the proposed algorithm was also executed on other standard test images obtained from the same aforementioned image databases.

Relative parameter used in the proposed algorithm is set up according to the experiment results. Associated parameter setting is the scaling factor alpha of the watermark image. The scaling factor alpha is chosen manually through a trial-and-error basis. In order to pull the essence of our watermarking algorithm, we recommend \(\alpha =0.01\). This allows our watermarking algorithm itself to achieve its satisfactory performance and thus to fulfill a better trade-off between imperceptibility and robustness as simultaneously as possible.

To estimate the robustness and reliability of the proposed method, watermarked images are exposed against different kinds of image attacks. The image attacks can be divided into four categories and are listed as follows: (1) noising attack: Gaussian noise (Gs), salt & pepper noise (Slp), and speckle noise (Spn); (2) denoising attack: Gaussian filter (GF), average filter (Avg), median filter (Md) and Wiener filter (WF); (3) image-processing attack: histogram equalization (HE), sharpening (Shp) and gamma correction (Gc); (4) geometrical attack: rotation \(+\) crop (Rtc), cropping (Cr), translation (Tr), rescaling (Rsc), flipping of rows (Fpr) and flipping of columns (Fpc), which are listed in Table 1 with their corresponding attack parameters, where abbreviation of TL donates the position of top-left corner.

Fig. 6
figure 6

Results of watermarked images and corresponding extracted watermarks without attack: a–g watermarked images; a1–g1 extracted watermarks

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5.3 Proof of imperceptibility

Imperceptibility is an important feature of the watermarking scheme. In this subsection, the imperceptibility analysis of the proposed scheme is done. PSNR and SSIM are most commonly used objective performance metrics to examine the perceptual transparency of the watermarking techniques. In general, if the PSNR value is \(\ge \) 48 dB that means the quality of image is excellent and there is no changes which can be noticed. PSNR value in between 35 and 48 dB means good image quality and PSNR value ranging from 29 to 35 dB signifies acceptable image quality. PSNR value below 25 dB means the image is perceptible. Figure 6a–g illustrates the watermarked versions of original images after applying the proposed embedding algorithm. Table 2 displays the testimony of these images, and tabulates PSNR, MSE, SSIM, UIQI and NC values of all watermarked images under no attack. Still referring to Table 2, the proposed watermarking method is excellent in terms of imperceptibility since the average PSNR value is 48.1308 dB, and the PSNR values from all watermarked images are above 48 dB. Maximum PSNR and UIQI values are obtained for ‘Baboon’ image and are found here as 48.1314 dB and 1.0000, respectively. Moreover, SSIM, UIQI and NC are greater than 0.999 in each case. MSE, in turn, as a distortion index, illustrates low values that indicate higher quality. So, all values of these metrics provide well-founded results for the watermarked images. Obviously, no matter which cover image is used, the transparency of the image is always very good; which means that the proposed method performs well in imperceptibility.

Table 2 PSNR (dB), MSE, SSIM, UIQI and NC values of watermarked images under no attack
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Table 3 PSNR (dB), MSE, SSIM, UIQI and NC values of extracted watermark image under no attack
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Table 4 Comparison chart of the proposed method with the state-of-the-art methods under no attack. All methods used ‘Lena’ as a test image
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Table 5 Comparison chart of the proposed method with the state-of-the-art methods under no attack. All methods used ‘Peppers’ as a test image
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Furthermore, PSNR, MSE SSIM, UIQI and NC are reused to evaluate the proposed extracting algorithm under no attack. Figure 6a1–g1 illustrates the extracted watermarks from the watermarked images, and the subsequent Table 3 conveys all their numerical results between original and extracted watermark. As can be seen in this table, maximum SSIM of 1.0000 is obtained for all extracted watermark images, while UIQI and NC values are very close to 1; that shows a high reconstruction of the extracted watermark images. In addition, PSNR and MSE values also validate the output. In short, original grayscale watermark image could be extracted completely without attack .

Table 5 indicates the comparison of the watermarked image and extracted watermark for the proposed method against several baseline approaches (see [29, 31, 49, 52, 57,58,59,60,61,62,63,64] and references therein); in which all methods used ‘Lena’ as a test image. As is observed from this table, especially compared to the methods of [29, 31, 49, 52, 58,59,60,61,62, 64], our proposal obtains better results in terms of PSNR and SSIM. For instance, the proposed method significantly outperforms [29] by 4.2946 dB and 0.91%, respectively, in PSNR and SSIM for watermarked image; 9.8433 dB and 0.62%, respectively, in PSNR and NC for extracted watermark. [57] and [63] also obtain good invisibility, and their average PSNRs are greater than 55 dB. However, the invisibility of [49] is poor so that PSNR value is less than 30 dB.

Fig. 7
figure 7figure 7

The watermarked images and their corresponding PSNR values after sixteen attacks

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Again, the three performance criteria, i.e., PSNR, SSIM and NC, are used in order to evaluate the quality of the watermarked image and the extracted watermark quantitatively. Table 5 illustrates the quality using these metrics and the comparison between the proposed method and the state-of-the-art methods [49, 52, 57,58,59, 63, 65,66,67,68,69,70] without attacks. Note that all these methods used ‘Peppers’ as a test image. As can be seen in this table, maximum SSIM of 1.0000 is obtained for the proposed scheme, which means that the visual quality of the watermarked image is excellent. For the extracted watermark, our proposed method performs better than [52] by 1.24%, whereas is slightly lower than [49, 57,58,59, 63, 65,66,67,68,69,70] with a very little difference of 0.0004 in terms of the NC metric.

In summary, with regard to the result of Fig 6, Tables 5 and 6 and the brief discussion, it is obvious that the proposed algorithm achieves good transparency whether for the watermarked image or the extracted watermark under no attack.

5.4 Proof of robustness

Robustness implies that how efficiently the watermark can be extracted from various intention or accidental types of attacks employed in the watermarked image. To test the robustness and reliability of the proposed method, sixteen common attacks are performed on watermarked images, and their descriptions are given in Table 1. Thus, to show the performance of our algorithm more intuitively, the seven watermarked images of the proposed algorithm are exposed to these attacks, the corrupted watermarked test images are shown in Fig. 7 and then the corresponding UIQI and NC values of the extracted watermarks are given in Table 6. As illustrated in the table, the average values of UIQI and NC metrics for each extracted watermark remained above 0.88 and 0.999, respectively. Moreover, the proposed algorithm has strong resistance to sharpening, rotation\(+\)cropping (Rtc), cropping and other attacks. Even if the watermarked images are simultaneously rotated by 45\(^{\circ }\) and cropped to fit the size of the input images, good watermarks can still be extracted, and the mean value of NC reaches 0.999. Still referring to Fig. 7 and Table 6, when the top-left corner of the watermarked images is cropped by 1/4, we have noticed that they are strongly distorted as their mean value of PSNR is under 13 dB; nevertheless, the extracted watermarks are easily identifiable according to the mean value of NC which is still greater than 0.999, while the mean value of UIQI reaches 0.97, which in turns indicate the high robustness of the system.

Table 6 UIQI and NC values of the watermarks extracted from the watermarked image under sixteen different attacks
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s

In order to ensure the fairness and show the advantage of the proposed scheme in terms of robustness, experimental and comparative results of NC values with other previous watermarking methods [49, 52, 58, 59, 66, 67, 71] for cover images ‘Lena’ and ‘Peppers’ are performed and compiled in Tables 7 and 8, respectively. From these tables, we briefly detail our observations of the behavior of these algorithms including our algorithm. It can be clearly seen that the proposed algorithm has strong robustness, especially against rotation\(+\)cropping (Rtc), cropping and translation attacks, and the NC value under each attack is greater than 0.9995. The performance of [49] to deal with the flipping of columns attack is better than that of the proposed algorithm, but this algorithm is less resistant to Gaussian noise, histogram equalization, rescaling, sharpening and gamma correction attacks than the proposed algorithm. NC values of the extracted watermarks computed only for ‘Lena’ image show that [52] is highly robust to histogram equalization and sharpening but performs poorly against salt and pepper noise, speckle noise, 45-degree rotation\(+\)cropping (Rtc), cropping, translation and denoising attacks. On the other hand, by calculating the average NC values for the two used test images, we surprisingly realized that our proposed scheme is superior to [52] method for all listed attacks. Moreover, the proposed algorithm outperforms [58, 59, 66] in each case. In terms of its resistance to the unique attack namely Gaussian filtering (GF), [67] shows stronger robustness than our algorithm, but for other attacks, the proposed algorithm is superior to [67].

As a remark, despite the fact that our watermarked images were undergo severe attacks, since we have set the parameters of the attacks with values greater than or equal to that used in the aforementioned watermarking techniques (see Tables 7 and 8 then compare data in parentheses), the proposed algorithm shows stronger resistance to sharpening, rotation\(+\)cropping (Rtc), and histogram equalization attacks, and has strong robustness under each attack.

Table 7 Comparison of NC values of the extracted watermark computed for ‘Lena’ image under different types of attacks
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Table 8 Comparison of NC values of the extracted watermark computed for ‘Peppers’ image under different types of attacks. The horizontal bar indicates that there is no relevant data in the corresponding paper. The data in parentheses represent the parameters of the attacks. Bold values represent the data with the best comparison results
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5.5 Computational complexity

This section describes the computational complexity of the proposed approach in terms of big-Oh notation, where worst-case scenarios are considered. The complexity of digital image watermarking approaches is usually assessed in terms of required number of different operations. Let us remind the reader that we have introduced a grayscale image watermarking system using DWT-SVD domain. The complexity of the proposed watermarking scheme is therefore determined by analyzing independently the time complexity of these two frequency domains. Generally speaking, the time complexity of DWT of size \(M\times N\) is O(MN); the wavelet transforms incur lesser time complexity due to nice features of space-frequency localization and multiresolutions. Here, the size of cover image is \(M\times N\) and the size of watermark image is \(m\times n\), where \(M=m\) and \(N=n\). Further, the dimension of cover image in this scheme is the same, i.e., \(M=N\). So, the time complexity of DWT in our watermarking method is \(T_{DWT _{|M=N}}=O(M^2)\). On the other hand, the time complexity of SVD in general case requires \(O\left( min \left( M\times N^2,M^2\times N\right) \right) \), wherefore its complexity in the proposed scheme is \(T_{SVD _{|M=N}}=O(M^3)\). Therefore, the overall time complexity (T) for the presented algorithm is given by

$$\begin{aligned} T=T_{DWT _{|M=N}}+T_{SVD _{|M=N}}=O(M^3) \end{aligned}$$

from which we deduce that this technique has cubic complexity. All in all, according to the chosen solution, the moderate computational complexity and the high results in terms of imperceptibility and robustness make the proposed approach practical for real-time applications.

5.6 Capacity analysis

In this section, we provide a detailed analysis of the capacity of the proposed watermarking algorithm and compare it with other seven related algorithms [72,73,74,75,76,77,78]. The capacity of a watermarking algorithm is defined as the ratio of the number of bits contained in the maximum embeddable watermark to the number of pixels in the cover image. In the proposed watermarking algorithm, the 8 bits grayscale watermark image of size \(512\times 512\) is embedded in the cover image of size \(512\times 512\). The number of bits contained in this watermark is \(512^*512^*8=2097152\), so the capacity of our algorithm is \(2097152/(512^*512)=8\). Table 9 gives the capacity of the proposed algorithm and those of the related comparison algorithms [72,73,74,75,76,77,78]. From Table 9, we can see that [72, 73] and [77] have the same capacity, namely 0.015625, and the capacity of the proposed algorithm is 512 times that of these three algorithms. Moreover, our algorithm is superior to [74, 75] and [76] in terms of capacity, whereas it has the same capacity as [78]. In brief, our algorithm has a large capacity.

Table 9 Capacity comparison between the proposed algorithm and related algorithms
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Table 10 Comparative analysis of the proposed algorithm and other related algorithms
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5.7 Comparative analysis

Based on the sizes and types of the cover image and the watermark image, the comparison results of the proposed algorithm and those of the main related algorithms [72,73,74,75,76,77,78] are given in Table 10. It can be concluded from the table that all the algorithms use \(512\times 512\) grayscale images as the cover image; the proposed algorithm and the algorithms in [74,75,76, 78] use grayscale watermarks, while [72, 73] and [77] are only applicable to binary watermark images. [73, 74] embed watermarks into some selected blocks of the redistributed invariant discrete wavelet transform (RIDWT), wherefore [74], in particular, did not well satisfy the invisibility requirement. [76] embeds watermarks in the integer wavelet transform (IWT), whereas [78] uses a DCT on the basis of the RIDWT, and selects low-frequency and high-frequency regions for embedding watermarks; both schemes, despite competitiveness, have less invisibility than the proposed algorithm. Differently, the proposed algorithm and [75] embed watermarks in the discrete wavelet domain, but this algorithm uses a blend of DWT-SVD domain, and selects high-frequency region for embedding watermarks, which results higher robustness. Obviously, the proposed algorithm has higher reliability and invisibility. Moreover, except for [78] with which we are equal, the proposed algorithm is superior to the other algorithms in terms of capacity.

6 Conclusions and future work

In this paper, a revisited hybrid watermarking technique based on DWT and SVD has been presented to achieve simultaneously the trade-off between robustness and invisibility. At the sender side, the one-level DWT is used to decompose the original image to seek for the embedding position and then the watermark is inserted. Some key parameters are transmitted through a private channel to later recover the watermark image. At the receiver end, our system can recognize if the received watermarked image is attacked or not by computing Cr value. The use of the scaling factor is mandatory for extracting watermark from merely watermarked image; otherwise, the watermark is correctly and efficiently extracted from the watermarked attacked image as long as the scaling factor is no longer used. Comprehensive performance analysis of the proposed scheme is conducted including imperceptibility analysis, robustness analysis, computational complexity and capacity analysis. The proposed approach has been implemented with acceptable computational complexity of \(O(M)^3\). This result remains encouraging and ensures that the proposed approach would be practical for real time processes. Besides that, experimental results of the proposed algorithm clearly account for high level of robustness, security, reliability and imperceptibility, so it can be used for copyright protection and content authentication.

The limitations of this paper and future research directions are given below. First, as watermarking is carried out in HH sub-band, robustness of the proposed scheme against salt and pepper attack is moderate. We see, as well, some future directions for our work. Our algorithm is designed for gray cover images and watermarks, and it is not suitable for binary watermarks. Based on the proposed watermarking algorithm, the study of watermarking algorithms for embedding binary watermarks is a first direction for future research. Second, we will also work on hiding multiple grayscale or binary watermarks into the gray cover image for more flexibility.