1 Introduction

In recent years the fast and significant advances in information technologies (IT) have grown conceptual and application-level of medical imaging. Information technologies are the backbone of fast and accurate results in medical healthcare because the medical healthcare system such as Hospital Information System (HIS) used these technologies to get fast transmission of digital medical images over the internet for the diagnosing purpose and distribution of medical data all over the world. Telediagnosis, teleconsultation, and telesurgery (e-learning of the medical staff) are the application of telemedicine where swapping of medical information is required. Medical imaging technologies such as CT-scan, MRI, Color Doppler have phenomenal contributions to the modern healthcare system. These medical modalities produce the medical image in various formats viz. DICOM, NRRD, MINC, ANALYZE, NIFT, etc. and communicate to radiologist over the internet for the diagnosing and doctors get the diagnosing result very fast and accurate in compared to film-based imaging technologies. These filmless technologies have a major advantage over film-based imaging is that many radiologists can access the same image at the same time at different places in the world and diagnose it. Filmless imaging technologies overcome the high printing cost and communication cost of these films, so film-based diagnosing shifted to filmless diagnosing. It is highly beneficial for the patient when he/she for from the doctor [34, 35]. Last some months COVID-19 spread all over the globe and affecting the social life of billions of peoples which arises the problem in front of the researchers to find the solution using digital imaging technologies to diagnose and estimation of COVID-19. But there is the main concern about the integrity and authenticity of electronic information and sensitive of medical information against malicious users and also concern the delivery of appropriate medical data too.

In the current COVID-19 situation, hospitals have a huge amount of patient’s data generated by medical imaging equipment (medical images of patients) along with patient diagnosing history, personal information, and other reports are communicated over the internet. Now it has become a common practice for various purposes like diagnosis, medical consultation, treatment, distance learning, and training, which is not enough secure. Medical practitioners viz. doctors, radiologists, and image providers do not take the security concerns seriously. Thus, at the time of medical image generation or communication, it can be intentionally or accidentally manipulated which leads to serious ramifications on the diagnosing of patient. Now a major challenge arises in front of researchers to maintain the integrity and authenticity of this sensitive medical image in an unsecured communication network. Usually, digital watermarking is suitable to ensure the authenticity and integrity of the image [6, 10, 37]. It is a technique that inserted a digital watermark (it is an image or logo which contains some meaningful information), in the host image without altering anything about the image i.e., format of image, size of the image, and keeping the data and image quality intact [30]. In the future when needed this watermark can be successfully extracted from the image to confirm the authenticity. In the medical domain, if a medical image is modified during the watermarking a breakdown in trust regarding the legitimacy of the image is generated. Any slight change in the image could provoke misdiagnosing, which prompts perilous outcomes and legitimate implications. Fundamentally, watermarking schemes are categorized as transform domain and spatial domain. In spatial domain watermarking schemes, the watermark’s bits are directly embedded in the host image [17] whereas in transform domain watermarking schemes, initially, the host image is transformed into the frequency domain using the several wavelets transforms viz. LWT, DCT, DFT, DWT. Transform domain schemes are more robust than the spatial domain schemes, robustness is the main challenge for every digital watermarking technique [12, 21]. Therefore, Lifting Wavelet Transform is applied in the proposed scheme. Many authors have investigated the watermarking scheme for .tif, .png .bmp and .jpg medical images [24, 34], or some of them have developed the watermarking schemes for DICOM medical images. In the present medical situation, numerous innovative medical imaging technologies have been industrialized which generates the NIFTI format images (.nii file extension) rather than .bmp, .jpg, DICOM (.dcm file extension) like CT-Scan, MRI etc. NIFTI images contain very sensitive medical data of the brain in form of multiple slices. So, the world medical healthcare system required a robust watermarking scheme for the authentication of the NIFTI images before the diagnosing. If watermarking scheme successful authenticate the medical image (means successful extraction of the watermark from the NIFTI image) at that point radiologist take the decision whether they go for diagnosing or not because in the present time millions of CT-Scans performed on COVID-19 patient’s and transmitted over the internet. Therefore, radiologist getaway to waste their time on imprecise medical data for diagnosing. Proposed watermarking scheme accomplished this and might be utilized in this corona pandemic to authenticate the NIFTI images for appropriate diagnosing.

In this scheme, initially apply the LWT on the image, which decomposes the image into four sub-bands (like LH, HL, LL, and HH). Select the LL band and applied the MSVD which decomposed the image into four bands LH, HL, LL, and HH, and select LL to embed the QR factorized watermark because it contains most of the image’s energy. The presented scheme is robust against the various noise attacks. The significant contributions of this watermarking scheme are as follows

  • A novel non-blind watermarking scheme for NIFTI (CT-Scan and MRI images) images based on 2-D LWT, MSVD, and QR factorization has proposed. The combination of LWT and MSVD has provided the better robustness than existing schemes.

  • It is an efficient watermarking scheme for NIFTI images, multiple watermarks are embedded into the image and extracted successfully from the watermarked image even after several kinds of attacks.

  • The evaluation of the proposed scheme is performed on NIFTI (.nii format) and the significant results achieved by the proposed scheme i.e. Peak Signal-to-Noise Ratio (PSNR) from 56 db to 57.27 db, Signal-to-Noise Ratio (SNR) from 45 db to 47 db, Structural Similarity Index Measure (SSIM) from .94 to .99, the Quality of Image index is 0.99 and the Normalized Correlation is .99.

This paper is organized as follows: In Section 2 summary of some recently published study related to proposed work has been discussed in Section 2. LWT, QR, and MSVD are reviewed in Section 3 and the proposed watermarking scheme is introduced in Section 4. Experimental results and analysis of proposed work with some medical images are described in Section 5. Robustness analysis of the proposed scheme is discussed in Section 6. Finally, the conclusions are given in Section 7.

2 Related work

The remarkable advances in telemedicine applications to enrapture attention and stimulate the researchers to work for the authentication and security of digital medical imaging. Basically, medical images are extensively delegated color and grayscale. In addition, most medical instruments like CT-Scan, MRI, X-Ray, Ultrasound, etc. are frequently producing a grayscale image in numerous formats like .tiff, .png, .bmp, DICOM, and so on. Hence, the researchers give more consideration to medical imaging in view of its wide applications in the advanced medical care framework. To maintain the integrity and authenticity of these medical images several watermarking schemes have been reported in the literature. N. Lin et al. [18] initially applied DWT on the image after that QR decomposition applied on the LL band and then inserted the encrypted watermark in the first row of the R matrix. Thanki & Kothari [32] proposed a Finite ridge transform and SVD based hybrid scheme for telemedicine application and use the Arnold scrambling for watermark encryption to provide more security. This scheme is robust against jpeg compression and various noise attacks. Alshanbari [2] proposed ROI based watermarking scheme for medical images for the ownership& tamper detection. The author used the DWT and SVD for better robustness and claim that the scheme is performed well against sharpening, compression, and Rescaling. LWT and a chaotic system based a reversible watermarking scheme is proposed by Tie-Gang Gao et al. [11]. The author initially applied LWT on the non-overlapping block and then LL band select for watermark insertion and the scheme is robust against cropping and compression attacks.

Su et al. [29] presented a scheme for the color image, which is based on QR decomposition and DWT, here the author initially divided the host image into 4 X 4 non-overlapping blocks and then applied QR decomposition on each block. After that watermark is embedded in the first-row fourth column element in the matrix R and the scheme is robust against cropping, blurring, rotation, scaling, adding noise, and sharpening. R. Ni. et.al [25] applied the LWT host image and then insert the watermark in LL sub-bands where selection is based on the location of spatial tempering. In this scheme, a chaotic sequence is used to estimate the location of spatial tempering. Mehta et al. [22] proposed LWT based watermarking scheme and incorporate with QR and Lagrangian support vector regression to provide more robustness and security. In this scheme, the author initially applied the LWT on the host image then decompose the LL band into 4 × 4 size non-overlapping blocks. Further, QR decomposition is performed on these blocks and watermark insertion is done in the first row of the R matrix of each of the blocks. This scheme performed good against the cropping, scaling, salt and pepper noise, and JPEG compression attacks. Chamlawi et al. [5] proposed a LWT based novel semi-fragile watermarking approach, here author insert, two watermarks i.e., authentication watermark and recovery watermark used for image recovery and authentication. They claim that the scheme is efficient and secure in the presence of JPEG compression. Zairi et al. [37] proposed a scheme based on two wavelets transform, in this scheme author used DWT, DCT, and QR decomposition for more security. Watermark insertion has been done according to its entropy values on specific blocks of the image.

Gong et al. [14] proposed a scheme based on Canny edge detection, SVD, and contourlet transform. The author initially applied the contourlet transform and then divide the low-frequency band into 4 × 4 non-overlapping. Furthermore, SVD is applied on these blocks which are selected by canny edge detection and watermarking is done into the matrix U. Verma et al. proposed an LWT based watermarking scheme where author applied three-level LWT then divide LH band into non-overlapping blocks and then random shuffling is performed of these blocks. After that binary watermark is embedded into these blocks. The major drawback of this scheme is that it cannot sustain against the salt and pepper noise attack, rotation. Filtering. Hence, the stability between robustness and imperceptibility is continuously a challenge within the field of medical image watermarking. Tjokorda Agung B.W et al. [34] proposed a watermarking scheme for medical images based on the least significant bit (LSB) modification technique and region of Non-Interest. Initially, the original image split into the region of Interest (ROI) and region of Non-Interest (RONI). Watermark’s bits have been embedded into the LSB of NROI of the image. A hybrid watermarking scheme based on DWT, SVD and DCT proposed by Takore et al. [31]. Authors initially applied DWT and the apply the DCT and SVD on the LL band of the DWT transform. Insertion of watermark’s bit has been done by the modifying the coefficients of the LL sub band. Thanki et al. (2017) [33] proposed a watermarking scheme based on DCT and Fast Discrete Curvelet Transform (FDCuT). authors initially applied FDCuT on medical image and then DCT applied over the high-frequency Curvelet coefficients of the FDCuT to find the different frequency sab bands. Finally, watermark bits are embedded in the mid-band frequency of the DCT coefficients.

Most of the research works in the area of medical image watermarking has proposed the watermarking scheme for .tiff, .bmp, DICOM and .jpg image formats. Although some researcher recommended Color Doppler images in DICOM format for watermarking but the NIFTI images have the different file structure than the DICOM. But in current medical situation, numerous imaging technologies like Ct-Scan and MRI produced the 3D images in NIFTI format instead of flat and featureless .tiff, .bmp or .jpg images. These images are much transmitted over the internet for the diagnosing purpose in this covid pandemic situation. After studying the literature, we realized that little state-of-the-art contributions are found in the earlier published research for the authentication of the NIFTI images. Keeping in mind, the importance of NIFTI images in medical health care system a watermarking scheme especially for NIFTI images generated by various modern medical equipment is proposed. These images are very sensitive images, so we cannot compromise with the quality of the image. In this scheme, multiple watermarks are embedded in a slice of the NIFTI images without degrading the quality of the original image. It is a secure and robust hybrid watermarking scheme based on LWT, MSVD, and QR factorization. To ensure the image quality various image quality metrics have been evaluated and found the significant results i.e., PSNR is between 56 to 57.5, image quality index and NC (normalized correlation) is near about one.

3 Preliminaries

This section describes the methodology used in this research. In this research Multiresolution Singular Value Decomposition (MSVD), QR Factorization and, Lifting Wavelet Transform (LWT) have been used to develop a robust and secure hybrid watermarking scheme for NIFTI images.

3.1 Lifting wavelet transform

Daubechies & Sweldens [7] proposed Lifting Wavelet Transform, in this transform construction is done in the spatial domain this is the main feature of the lifting scheme. It overcomes the limitations of the conventional wavelet transformation by decreasing the complexity of time and space (because it does not require complex mathematical calculations, unlike traditional wavelet transform). So computing wavelet transforms an efficient and most straightforward algorithm. Lifting Scheme does not rely on transforms from Fourier. Digital signals are basically a sequence of integers, but after the wavelet transform, the resultant message is a sequence of floating-point numbers as well; this hinders the possibility of a perfect or a reasonable reconstruction of the signal. A transformation algorithm should have a feasible reversible implementation. It preserves the domain of the message even after the transform i.e., it behaves as an operator, which transforms integer-based sequences again into integer-based sequence signals. Lifting scheme provides this facility that the domain of transform can be preserved (i.e., integer to integer) with better computational efficiency than the conventional wavelet transformations, making it a commonly used change in image processing [9, 19, 28]. Construction of a signal by using a lifting scheme consists of the following three steps:

  • Split - In the split phase, the given signal ω(n) is split into non-overlapping odd ωo(n) and even ωe(n) sets as: ωe(n) = ω(2n), ωo(n) = ω(2n + 1)

  • Predict – In this step, odd set is predicted from even set. The polynomial components occurring are compensated in the high pass by the predict phase. So this phase is also known as high pass filtering operation phase. Now odd sets ωo(n) are predicted using even set ωe(n) and the difference φ(n) is produced as

    $$ \varphi (n)={\omega}_o(n)-{P}_r\left[{\omega}_e(n)\right], $$

Where Pr[.] is the predict operator and φ(n) is high-frequency component. φ(n) is the error between original set and the predicted value.

  • Update - The even set ωe(n) are updated using wavelet coefficient to calculate scaling function. In this stage, moments in low pass is also preserved. Therefore, this phase is also known as low pass filtering operation phase. By applying an update operator, Up[.] the low-frequency component L(n) represents a coarse approximation of the original signal ω(n) defined as

    $$ L(n)={\omega}_e(n)+{U}_p\left[\varphi (n)\right] $$

LWT decomposes the host image into four sub-bands viz. LLLH, HL, and HH. LL sub-band has the low-frequency components that contain most of the energy of the image and other sub-bands (LH, HL, and HH) have high-frequency components that contain less energy of the image. The LWT can be applied several times on the LL band to decomposing into sub-bands because the LL band contains most of the energy of the image. Figure 1 shows the 2-level LWT. Here in Fig. 1(b) the blue square portion shows the LL sub band.

Fig. 1
figure 1

2-Level LWT: (a) Original Image (b) After Applied two level LWT

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3.2 Theorem: QR factorization

In QR decomposition [1], a non-singular matrix of size m × n .

$$ \mathrm{A}=\mathrm{Q}.\mathrm{R} $$

Where Q is an orthogonal matrix with size m × m and R is an upper triangular matrix. The row of Q matrix is generated by the applying Gram-Schmidt. A and Q is denoted as A = [a1, a2, ……. ., an] and Q = [q1, q2, ……. ., qn] The upper triangular matrix R can be computed as:

$$ \left[{a}_1,{a}_2,\ldots \ldots ,{a}_n\right]=\left[{q}_1,{q}_2,\ldots \ldots,{q}_n\right]\left[ \matrix{ {\mathrm{r}}_{11} &{\mathrm{r}}_{12} &{\mathrm{r}}_{1\mathrm{n}}\\ {}0 &{\mathrm{r}}_{22} &{\mathrm{r}}_{2\mathrm{n}}\\ {}0 & 0 &{\mathrm{r}}_{\mathrm{nn}}} \right] \ldots \ldots \ldots \kern0.5em $$
(1)
$$ R=\left[\matrix{ \left\langle {a}_1,{q}_1\right\rangle & \left\langle {a}_2,{q}_1\right\rangle & \cdots & \left\langle {a}_n,{q}_1\right\rangle \\ {}0 & \left\langle {a}_2,{q}_2\right\rangle & \cdots & \left\langle {a}_n,{q}_2\right\rangle \\ {}\vdots & \vdots & \ddots & \vdots \\ {}0 & 0 & 0 & \left\langle {a}_n,{q}_n\right\rangle} \right] $$

For example, A is an image block size of 3 × 3 is represented as follows:

$$ A=\left[\matrix{11 & 21 & 31\\ {}46 & 44 & 48\\ {}56 & 84 & 97}\right] $$

Using Eq. (1), its matrix Q and upper triangular matrix R can be obtained.

$$ Q=\left[\matrix{-0.1501 & 0.3296 & -0.9321\\ {}-0.6276 & -0.7603 & -0.1678\\ {}-0.7640 & 0.5598 & 0.3209}\right] $$
$$ R=\left[\matrix{-73.3008 & -94.9376 & -108.8802\\ {}0 & 20.4901 & 28.0219\\ {}0 & 0 & -5.8208}\right] $$

After multiplying both matrix Q and R, the original matrix A can be obtained.

$$ Q\ast R=A $$
$$ A=\left[\matrix{11.0000 & 21.0000 & 31.0000\\ {}46.0000 & 44.0000 & 48.0000\\ {}56.0000 & 84.0000 & 97.0000}\right] $$

3.3 Multiresolution singular value decomposition (MSVD)

MSVD basically used in real-time applications, its computational process is very simple. It doesn’t have a fixed set based on vectors like Discrete Cosine Transform (DCT), Fast Fourier Transform (FFT) and Wavelet. One resolution feature is simple to distinguish, but the characteristics of multiresolution approaches are imperceptible. It is the substitution of the wavelets and is comparable to the Wavelet Multi-Resolution Analysis (MRA) since it breaks down the host picture into distinctive frequency bands (lower frequency and higher frequency LL, LH, HL and, HH) [23]. MSVD has low computational than the wavelet transformation, and directional information such as in wavelet transformations is not given. In MSVD, decomposition is based on the data set [27]. It can be utilized at many levels and deliver robustness against the various geometrical image processing attack viz. cropping, and rotation.

For a matrix, A with dimension M * N, the singular value decomposition (SVD) of A into the three-matrix as shown in Eq. (2)

$$ A= US{V}^T $$
(2)

Here V and U are orthonormal, and matrix S is a diagonal matrix in descending order of singular values.

MSVD for image (I) of size M × N is computed by initially reshaping I to a matrix I′ of size 4 × MN/4. Therefore, the singular value decomposition of I′ is shown in Eq. (3) as:

$$ \left[\mathrm{U},\mathrm{S}\right]=\mathrm{SVD}\left(\mathrm{I}^{\prime}\right) $$
(3)

Now, matrix T is shown by Eq. (4) as:

$$ T={V}^T\mathrm{I}^{\prime } $$
(4)

where matrix U of size 4X4, matrix S of size 4 × MN/4 and matrix T of size [4 × MN/4]. In matrix T rows I, II, III, and IV are reshaped to produce size matrices M/2 × M/2. Such reformatted matrices are the image sub-bands i.e., LH, HL, LL, HH. The LL band includes the lower frequency information, and the high-frequency information is found in other sub-bands i.e., HL, LH, and HH. In this paper, we use LH band for watermarking. Figure 2 depict the structure of MSVD.

Fig. 2
figure 2

Structure of Multiresolution Singular Value decomposition

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4 Proposed algorithm

NIFTI images are widely used in medical imaging, as they contain metadata and a number of image slices. Watermarking of NIFTI images is a crucial task in comparison to the other image formats viz. .tiff, .png, .jpg, .bmp, DICOM, etc. The watermarking scheme must be robust and imperceptible. There must not be any noticeable modification in color, hue, and intensity, which may hamper the image’s diagnosis. Metadata of the NIFTI image is exceptionally sensitive, so it must be preserved carefully. In this paper, we propose a new watermarking algorithm for NIFTI image based on MSVD, LWT, and QR factorization that incorporates the watermark embedding and extraction process.

4.1 Watermark embedding

Slices of NIFTI image and watermark both are grayscale scale. At first, metadata is put away securely from the NIFTI image, and then select the first slice for watermarking to insert the watermark. Initially apply the MSVD on this slice which breaking down it into four distinctive frequency sub-bands i.e. LL, LH, HL, and HH. Now select the HL sub-bands because it contains the most positive values. Furthermore, we apply the LWT on the HL band which decompose it into four different sub-band frequency, viz. LL, LH, HL, and HH. The LL frequency sub-band contains the vital data of the image and is resilient to the de-noising attack. Paralleling, the primary components of the watermark are subjected to QR factorization and the formation of a new vector. The augmentation of the watermark in the host slice is controlled via the scaling factor (alpha). Furthermore, inverse transformed (ILWT) is performed to reconstruct the slice. Finally, augment the metadata with this watermarked slice and generate the watermarked NIFTI image. The proposed algorithm is illustrated below and is also explained pictorially in Fig. 3.

Fig. 3
figure 3

Block diagram of hybrid scheme for digital watermarking process

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  • Input: CT-Scan NIFTI image Size (630 X 630)

Grayscale Watermark Size (32X32) in .bmp format

  • Output: Watermarked NIFTI image

  1. Step 1

    Extract metadata from the host NIFTI image and select the first slice for watermarking.

  2. Step 2

    Perform MSVD on the selected slice that decompose it in four sub-bands LL, LH, HL and HH.

  3. Step 3

    Perform two-level LWT on the HL band of MSVD which decompose the image into four sub-bands LH, HL, LL, and HH

  4. Step 4

    Apply the QR Factorization on the watermark and generate the new vector V.

  5. Step 5

    Vector V is embedded into transformed components of the host image by selecting the LL band. Watermark is embedded in the image as below

    $$ {x}^{\prime }=x+\alpha y $$

where

x′ is the transformed component of the watermark image.

y is the factorized watermark component.

x is the transform image of host image.

α is the embedding strength.

  1. Step 6

    Perform Inverse Lifting Wavelet Transformation of the final watermarked image.

  2. Step 7

    Perform inverse Multiresolution Singular Value Decomposition on the final watermarked image.

  3. Step 8

    Embedded the metadata in the watermarked image and generate the watermarked NIFTI image.

4.2 Watermark extraction

The watermark extraction is a crucial task of watermarking scheme; Fig. 4 depicts the watermark extraction process of the proposed watermarking scheme. It shows that the original and watermarked NIFTI image is needed to separate the watermark from the watermarked NIFTI image. At first, metadata is isolated from both original and watermarked image and then select the first image slice. Furthermore, we apply the MSVD and LWT on the original and watermarked to get the embedded noisy component and afterward perform the inverse QR factorization on these noisy segments to produce the watermarks.

Fig. 4
figure 4

Block diagram of hybrid scheme for watermark extraction

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  • Input: M x N NIFTI image I; and M x N NIFTI watermarked image I+.

  • Output: Watermark W

  1. Step 1

    Extract metadata from both the NIFTI images i.e. I and I+.

  2. Step 2

    Select the first slice of both images I and I+.

  3. Step 3

    Perform MSVD on both images I and I+ to obtain LL, LH, HL and, HH sub-bands.

  4. Step 4

    Perform LWT on HL band of both images I and I+ to obtain LL, LH, HL and, HH sub-bands.

  5. Step 5

    Extract the watermark from the watermarked image using the original image by performing the reverse watermark embedding steps.

    $$ y=\left({I}^{+}-I\right)/\alpha $$

where

I′ is the watermarked image.

y is the factorized watermark component.

I is the original image.

α is the embedding strength.

  1. Step 6

    Perform inverse QR factorization on extracted components to get the extracted watermark.

5 Results and discussion

In this section, the results of the proposed watermarking scheme are tested over NIFTI images generated by the CT-Scan taken from public medical databases https://zenodo.org/record/3757476#.X0pwCnkzZPZ [20] under ethical medical practices, without revealing the patient’s identity and only for the experimental purpose. The proposed watermarking scheme has been executed on the intel Core TM i7-5500U CPU 2.5 GHz Windows10 machine with 8 GB RAM on the MATLAB platform. Various NIFTI images with a resolution of 630 × 630 pixels and 8-bit grayscale watermark of BMP format with resolution 32 × 32 pixels are used for experiment.

5.1 Performance measures

The analysis of the proposed watermarking technique is verified over the ten different NIFTI images. The outcomes are investigated with respect to image quality estimations viz. PSNR (Peak Signal to Noise Ratio), MSE (Mean Square Error), NC (Normalized Correlation), SSIM (Structural Similarity Index Measure) and Q. PSNR and NC, SSIM are utilized as a measure for perceptual imperceptibility. For the watermark detectable quality assessment, PSNR is used, which is delineated as follows [16, 26, 33]:

$$ MSE=\frac{1}{m\ast n}\sum_{i=0}^m\sum_{j=0}^n{\left({A}_{ij}-{B}_{ij}\right)}^2 $$
$$ PSNR=10\ast {\log}_{10}\frac{{\left(\mathit{\operatorname{Max}}\right)}^2}{\frac{1}{m\ast n}\sum_{i=0}^m\sum_{j=0}^n{\left({A}_{ij}-{B}_{ij}\right)}^2} $$
$$ SNR=10\ast {\mathit{\log}}_{10}\frac{\sum_{i=1}^n\sum_{j=1}^m{\left({A}_{ij}\right)}^2}{\sum_{i=1}^n\sum_{j=1}^m{\left({A}_{ij}-{B}_{ij}\right)}^2} $$

To measure the robustness of the watermarking scheme NC are utilized between the original image I and the watermarked image I+, if NC is near to one then the robustness of the scheme is significant. NC is evaluated using the following equation [32].

$$ NC=\frac{\sum_{x=1}^M\sum_{y=1}^Nw\left(x,y\right)\times w\ast \left(x,y\right)}{\sum_{x=1}^M\sum_{y=1}^N{w}^2\left(x,y\right)} $$

Universal image quality index Q [36] is defined as follows.

$$ Q=\frac{4{\sigma}_{xy}{\overline x}\, { \overline y} }{\left({\sigma}_x^2+{\sigma}_y^2\right)\left[{\left(\overline{x}\right)}^2+{\left(\overline{y}\right)}^2\right]} $$

where, \( \overline{x}=\frac{1}{N}\sum_{i=1}^N{x}_i \) and \( \overline{y}=\frac{1}{N}\sum_{i=1}^N{y}_i \)

$$ {\sigma}_x^2=\frac{1}{N-1}\sum_{i=1}^N{\left({x}_i-\overline{x}\right)}^2\ \left(\mathrm{and}\right) $$
$$ {\sigma}_y^2=\frac{1}{N-1}\sum_{i=1}^N{\left({y}_i-\overline{y}\right)}^2 $$
$$ {\sigma}_{xy}=\frac{1}{N-1}\sum_{i=1}^N\left({x}_i-\overline{x}\right)\left({y}_i-\overline{y}\right) $$

x = {xi| i = 1, 2, 3…. ., N} and y = {yi| i = 1, 2, 3…. ., N.}x and y are the original and the test image signals respectively.

Universal image quality index Q is the product of three components can be defined as:

$$ Q=\frac{\sigma_{xy}}{\sigma_x{\sigma}_y}\times \frac{2\overline{x}\overline{y}}{{\left(\overline{x}\right)}^2+{\left(\overline{y}\right)}^2}\times \frac{2{\sigma}_x{\sigma}_y}{\sigma_x^2+{\sigma}_y^2} $$

Structural Similarity Index Measure (SSIM), is utilized to assess the likeness between the actual image and watermark image. SSIM value lies between −1 to +1, if SSIM = 1, at that point, original image and watermark image are exactly similar.

SSIM (\( {x;y} \)) =\( \frac{\left(\ 2{\mu}_x{\mu}_y\kern0.5em +\kern0.75em {c}_1\right)\ \left(2{\sigma}_{\mathcal{x}y}+{c}_2\right)}{\kern0.5em \left({\mu}_{\mathcal{x}\kern0.75em }^2+\kern0.5em {\mu}_y^{2\kern0.75em }+\kern0.5em {c}_1\right)\ \left({\sigma}_{\mathcal{x}}^2+\kern0.5em {\sigma}_y^2+{c}_2\right)} \)

Where μx: the average of actual image and μy: the average of watermarked image.

σ2x: the variance of original cover and σ2y: the variance of watermarked image with covariance σxy. Where, c1and c2 are free parameters.

5.2 Analysis of proposed scheme

The analysis and testing of the proposed scheme has been done on ten different NIFTI images, taken from public database [20], which are Img1, Img2, Img3, Img4, Img5 and Img6 to determine the imperceptibility and robustness. The test results of the proposed scheme are depicted in Figs. 5 and 6. The metadata of the original NIFTI image is also preserved inside the watermarked NIFTI image.

Fig. 5
figure 5

First slice of NIFTI images used for experiment and watermark image in BMP format

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Fig. 6
figure 6

Extracted watermarks from Ten medical images

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Table 1 exhibits the performance proportions of watermarking scheme over the NIFTI images from Img1 to Img6. Figure 7(a) exhibits the graphical understanding of NC between the first NIFTI image slice and watermarked image slice. Figure 7(b) & (c) shows the PSNR and SNR between the original and watermarked image respectively. Figure 7(d) speaks to the SSIM of the proposed which is more like one. Figure 8 depicts the graphical interpretation of quality measurements Q of the scheme.

Table 1 Qualitative analysis of watermarked images
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Fig. 7
figure 7

Performance of Proposed Scheme for Various Medical Images: (a) Normalized Correlation (b) PSNR (c) SNR (d) SSIM measures of all ten images

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Fig. 8
figure 8

Quality matrices of all ten images

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Analysis of the proposed scheme has been done based on NC, SSIM and Q are having values roughly near one; that indicating excellent robustness and imperceptibility between the original and watermarked images. PSNR of the proposed scheme is more than 57 dB, which recommends that the watermarked image quality is extremely considerable.

Note: After successful extraction of the watermark from the received NIFTI image medical practitioners or radiologists assure that they diagnose the impeccable medical image. It is very important for both doctors and radiologists because it causes the life or death of a patient. Another smart role of the watermark is that it can be a logo or an image that contains some unique patient’s information such as patient id, patient name, etc. as per convenience. Therefore, this scheme may play a vital role in the authentication of the NIFTI images to produce correct diagnosing which are procreate in huge amounts due to COVID-19.

5.3 Analysis of the proposed scheme for different number of watermarks insertion

The results of the proposed scheme are compared with the other existing scheme in Table 3 that the results are more The proposed watermarking scheme embedded the different quantities of watermarks over the image slice. The most extreme watermark inclusions in the NIFTI image without hampering the diagnosis of watermarked NIFTI image exhibited in Table 2. These images contain sensitive patient’s clinical data as well. In this way, it is fundamental that the nature of these images must not be debased subsequent to watermarking. This scheme is tested and analyzed with a different number of watermark addition and found that the outcomes are promising. Table 2 exhibits that the image quality measurements are legitimately relative to the quantity of watermarks addition and no noticeable change has been noticed.

Table 2 Performance verification of the proposed scheme for different number of color watermark insertion with watermark image size of 32 × 32
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Figure 9, represent the PSNR, of the proposed scheme with the different number of watermark insertion. The PSNR evaluation has been done at ten different NIFTI images. In Fig. 9 we can see that the estimation of PSNR is increased when the decreasing the number of inserted watermarks. In the event that we assess the PSNR and SNR of the img1 at 24 watermark insertions & 2 watermark insertions, there are serious variation in PSNR is 45.95 dB to 57.27 dB. Thus, if the number of wateremark insertion is incresead then the PSNR value will be decrease.

Fig. 9
figure 9

PSNR comparison at different Number of Inserted Watermarks

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There is no huge difference in NC which is evaluated on ten different images. The NC results of the proposed scheme with the different number of watermark insertions are depicted in Fig. 10. The graph shows that the higher values of NC will be obtained when minimum insertion has been done in the original image. The high correlation at the two watermark insertion is 0.9999 i.e. image quality is good. But when the 24 watermarks inserted in the NIFTI image the NC value is 0.9978 which is also considerable for the scheme.

Fig. 10
figure 10

Normalized Correlation comparison at different number of watermark insertion

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Figure 11 depicted the image quality index (Q) of the proposed watermarking scheme at the different number of watermarks insertion and reported that there is no massive difference in Q. The image quality has been evaluated on various NIFTI images, graph shows that if the number of watermarks insertion is increased the value of Q has decreased and vice versa. The value of Q is high at the minimum insertion i.e., 0.9999 and at the 24 watermarks insertion value is 0.9986 which is also good. Thus, the proposed watermarking scheme gives good results even when the number of watermark insertion is increased.

Fig. 11
figure 11

Image Quality comparison at different number of watermark insertion

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SNR is another important performance measure of the watermarking scheme. In above Figure (Fig. 12) we can see that the SNR of the proposed watermarking scheme at the different number of watermarks insertion. The SNR has been assessed on different NIFTI images, graph shows that if the number of watermarks insertion is increased the value of SNR has decreased and vice versa. The value of SNR is high at the two watermark insertion i.e., 47.10 and at the 24 watermarks insertion value is 35.95 which is likewise acceptable. Consequently, the proposed watermarking scheme gives great outcomes in any event when the quantity of watermark insertion is increased.

Fig. 12
figure 12

SNR comparison at different number of watermark insertion

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The results of the proposed scheme are compared with the other existing scheme (Zairi et al. [37], Takore et al. [31], BW & Permana [34], Thanki et al. [33], Hsu et al. [15], Goli & Naghsh [13], Ernawan et al. [8], Awasthi et al. [3]) in Table 3. The PSNR of proposed scheme is 56.76 to 57.28 and NC is .9993 to .9998 whereas the PSNR and NC values of other existing scheme is lies between 32.66 to 52.02. and 0.9647 to 1 respectively. Therefore, the outcomes of the proposed watermarking scheme are more significant.

Table 3 Performance comparison of NC an PSNR values comparison between proposed and existing scheme
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The above Figure (Fig. 13) depicted the comparison of the PSNR of the proposed scheme with the other existing scheme (Zairi et al. [37], Takore et al. [31], BW & Permana [34], Thanki et al. [33], Hsu et al. [15], Goli & Naghsh [13], Ernawan et al. [8], Awasthi et al. [3]). The PSNR of the proposed scheme is evaluated over the ten different NIFTI images which lie between 56.76 to 57.28 whereas the PSNR of other existing scheme is lies between 32.66 to 52.02 (PSNR of Zairi et al. [37] is 32.66 to 46.95, Takore et al. [31] is 44.52 to 44.58, BW & Permana [34] is 47.49 to 48.57, Thanki et al. [33] is 46.55 to 47.18, Hsu et al. [15] is 40.16 to 40.49, Goli & Naghsh [13] is 38.37 to 39.93, Ernawan et al. [8] is 46.11 to 47.91, Awasthi et al. [3] is 48.92 to 52.02. Therefore, the PSNR of the proposed watermarking scheme is more significant than the other schemes.

Fig. 13
figure 13

Comparison of PSNR (db) Values of Proposed Scheme with Existing Schemes

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Figure 14 shows the comparison of the NC of the proposed scheme with the other existing scheme (Zairi et al. [37], and Thanki et al. [33]). The PSNR of the proposed scheme lies between 56.76 to 57.28 whereas the PSNR of other existing schemes is lies between .9993 to .9998 (NC of Zairi et al. [37] is 1, and the NC of Thanki et al. [33] is 0.9647to 0.9827. Therefore, the NC of the proposed watermarking scheme is significant. After the compression of PSNR and NC values of the proposed scheme with existing schemes (Zairi et al. [37], Takore et al. [31], BW & Permana [34], Thanki et al. [33], Hsu et al. [15], Goli & Naghsh [13], Ernawan et al. [8], Awasthi et al. [3]) we observed that the outcomes are more significant.

Fig. 14
figure 14

Comparison of Normalized Correlation Values of Proposed Scheme with Existing Schemes

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6 Robustness analysis

Robustness test of proposed watermarking scheme has done, by performing the various image processing attacks viz. Salt & Pepper, Gaussian noise, Poisson, Speckle on watermarked image which may incite the clearing of watermarks. After applying the attack, if the extraction of the inserted watermark is successfully done from the altered watermarked image then the scheme is robust and legitimate in nature. A major requirement of any significant watermarking scheme is the sustenance of the scheme against these attacks. Insertion of watermarks and quality of watermarked image is inversely proportional to each other but as per the necessity, a trade-off must be considered. Subsequently, this scheme is tested with various watermarks insertion which prompts increments in robustness and degradation in image quality, but the minimum number of watermarks insertion increases the quality of the image. Various noise attacks have been applied over the watermarked image to determine the robustness of the scheme. Proposed scheme designed for CT-Scan medical image, so the diagnosis will be framed on this watermarked NIFTI image. Along these lines, any critical degradation in the watermarked image quality isn’t worthy since it might cause the life and demise of the patient. Thus, the scheme is tested with the various noise attacks with the various boundaries, till the quality measurements indorse that the altered watermarked image is of high calibre.

6.1 JPEG compression

JPEG compression with quality factor 90 and 75 applied over the watermarked slice and embedded watermark extracted successfully. Table 4 depict this attack for the NIFTI images and the findings define that the efficiency of the is promising.

Table 4 Parameters values of watermarked image after JPEG compression attack with quality factor 90 and 75 and extracted watermarks
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6.2 Salt & Pepper Noise Attack

Salt and pepper noise with noise density 0.001 to 0.004 applied on the watermarked slice of NIFTI image, and the watermark is successfully extracted. Table 5 depict that this attack for the slices of the NIFTI images and the findings define that the efficiency of the scheme is promising.

Table 5 Parameters values of watermarked image after Salt & pepper noise attack with variance from 0.001 to 0.004 and extracted watermarks
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6.3 Speckle noise attack

Speckle noise attack applied with variance 0.001 to 0.003 on the watermarked slice of the NIFTI image and the watermark is successfully extracted by the proposed watermarking scheme. Table 6 depict the evaluation of the attack over the slice of the NIFTI image and the findings show that the result of scheme is significant.

Table 6 Parameters values of watermarked image after Speckle noise attack with variance from 0.001 to 0.003 and extracted watermarks
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6.4 Poisson noise attack

Poisson noise attack applied over the watermarked slice of the NIFTI image and then watermark is extracted successfully by the proposed scheme. In Table 7, analysis of the attack for the NIFTI images are tabulated and the results show that the performance of proposed scheme is favourable.

Table 7 Parameters values of watermarked image after Poisson noise attack and extracted watermarks
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6.5 Gaussian noise attack

Gaussian noise attack applied with variance 0.001 and varying it from 0.001 to 0.004 on the watermarked slice of the NIFTI image. After the attack extraction of watermark is successful. In Table 8, analysis of the attack for the slice of NIFTI images are tabulated and the results show that the performance of proposed scheme for NIFTI images is promising.

Table 8 Parameters values of watermarked image after Gaussian noise attack with variance from 0.001 to 0.004 and extracted watermarks
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7 Conclusions

In this paper, a novel non-blind watermarking scheme based on LWT, QR, and MSVD for NIFTI images is proposed. These images have delicate clinical image data, so the watermarking of these images is a very crucial task. For the experimental purpose we have used NIFTI images (630 × 630) sourced from CT-Scan and grayscale watermark (32 × 32). The obtained outcomes of the measuring parameter of the watermarked image (NC, Q, SNR, PSNR, and SSIM) are acceptable are par tradeoff among the imperceptibility, robustness, and number of watermark insertion. The quality of the image is much significant that lie between .99994 to .99998 and SSIM reported from .94 to .99. Whereas the PSNR of the proposed scheme lies between 56.76 to 57.28 db and NC values lie between .9993 to .9998. which shows that the results are better than the existing schemes where PSNR is lies between 32.66 to 52.02 db. After the compression of PSNR and NC values of the proposed scheme with existing schemes (Zairi et al. [37], Takore et al. [31], BW & Permana [34], Thanki et al. [33], Hsu et al. [15], Goli & Naghsh [13], Ernawan et al. [8], Awasthi et al. [3]) we observed that the outcomes are more significant.The proposed scheme is robust against the various noise attacks and JPEG compression. Further, the comparison of the outcomes of the proposed scheme with the existing scheme showed that the performance proposed scheme better than the existing schemes. In this scheme first slice of the NIFTI image (NIFTI images have various numbers of slices) is used for the watermarking to authenticate the NIFTI image. If someone wants to insert watermark in more than one or all slice of the image, then this scheme can be applied on each slice of NIFTI image which he/she want to use for the authentication purpose. Thus, the proposed watermarking scheme can be used for the authentication and identification of the appropriate medical image for the diagnosing of CT-Scan and MRI image in NIFTI images format.