Many approaches have been proposed in the literature to analyse and extract useful information from digital signals and images either in the spatial or transform domain [7H. Al-Assam, A.J. Abboud, and S.A. Jassim, "Hidden assumption of face recognition evaluation under different quality conditions"", IEEE International Conference on Information Society (i-Society), England., ., 8S. Bravo-Solorio, F. Calderon, C-T. Li, and A.K. Nandi, "Fast fragile watermark embedding and iterative mechanism with high self-restoration performance", Digital Signal Processing, vol. 73, pp. 83-92.
[http://dx.doi.org/10.1016/j.dsp.2017.11.005] , 9P. Dong, J.G. Brankov, N.P. Galatsanos, Y. Yang, and F. Davoine, "Digital watermarking robust to geometric distortions", IEEE Trans. Image Process., vol. 14, no. 12, pp. 2140-2150.
[http://dx.doi.org/10.1109/TIP.2005.857263] [PMID: 16370466] ]. However, transform domain based approaches look more robust to any geometric modifications and attacks on the medical images [10A. Al-Haj, "Combined DWT-DCT digital image watermarking", J. Comput. Sci., vol. 3, no. 9, pp. 740-746.
[http://dx.doi.org/10.3844/jcssp.2007.740.746] ]. Such of these popular transforms are discrete wavelet transform (DWT), Discrete Cosine Transform (DCT), and Discrete Fourier Transform (DFT) [11A.J. Abboud, and S.A. Jassim, "Incremental fusion of partial biometric information", Mobile Multimedia/Image Processing, Security, and Applications 2012 by International Society for Optics and Photonics, vol. Vol. 8406, .
[http://dx.doi.org/10.1117/12.918776] , 12A.J. Abboud, and S.A. Jassim, "Image quality guided approach for adaptive modelling of biometric intra-class variations", 2010 Proceedings of SPIE - The International Society for Optical Engineering, .
[http://dx.doi.org/10.1117/12.850592] ]. Wavelet transform is the set of basis functions copied from base mother wavelet and they are orthogonal to each other. It characterizes by decomposing the image into several successive levels depending on the decomposition level and the size of the image. In this research, DWT is used in our research as image transform tool with aim to obtain information about medical image simultaneously in the spatial and frequency domains as in Fig. (1).

Fig. (1) Discrete wavelet transform decomposition of medical multimedia images.

Image watermarking is the state of art technology to provide several security services simultaneously. These services are the source authentication, patient identity checking and digital multimedia integrity verification [13A. Kahate, Cryptography and network security., McGraw-Hill Education, .]. These services are satisfied by embedding robust, semi fragile and fragile watermarks in the medical multimedia images. These watermarks may be visible or invisible in the multimedia signal depending on the application. Furthermore, these watermarks signals may be hidden in the spatial or/and transform domain(s) of the multimedia signal. For medical multimedia images of the patients, the watermarking algorithm should be reversible (i.e. we can recover watermarks without causing any distortion to the medical image). In addition, the watermarking algorithms should embed watermarks such that be robust to different kinds of intentional or accidental attacks.

Singular Value Decomposition (SVD) is the mathematical tool to factorize matrix W into three matrices X, Y and Z [14A.N. Albu-Rghaif, A.K. Jassim, and A.J. Abboud, "A data structure encryption algorithm based on circular queue to enhance data security", Engineering Sciences-3^rd Scientific Conference of Engineering Science (ISCES), 2018 1^st International Scientific Conference of. IEEE, Baqubah, .
[http://dx.doi.org/10.1109/ISCES.2018.8340522] ]. If a matrix W of dimensions m x m, therefore the SVD of matrix W is:

(1)

Where X and Y are left and right orthonormal vectors and Y is the diagonal matrix of singular values. The singular values of Y are arranged in the diagonal in the descending order. The SVD is used in the signal and image processing for several reasons, which are [1A.K. Gupta, and M.S. Raval, "A robust and secure watermarking scheme based on singular values replacement", Sadhana, vol. 37, no. 4, pp. 425-440.
[http://dx.doi.org/10.1007/s12046-012-0089-x] ]: (1) there is a need to use less singular values to reproduce big part of signal power (2) we can use SVD with different sizes matrices (3) SVD singular values have good robustness to the attacks on the signal and multimedia images.

The performance measurement of the biomedical multimedia processing system is evaluated using three main measures described below as follows:

2.4.1. Peak-To-Signal-Noise-Ratio (Psnr) Measure

PSNR is the most used measure to quantify the quality of multimedia signals including image, voice and video. This measure is comparing the peak power between original and corrupted signals as shown below:

(2)

(3)

Where MSE is the mean square error between the original image (A) and noisy image (B).

2.4.2. Structural Similarity Index (SSIM)

SSIM is a novel measure to quantify the degree of similarity between referenced and corrupted signals. The concept of measurement for this metric is based on the structure human vision system [15Z. Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli, "Image quality assessment: from error visibility to structural similarity", IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612.
[http://dx.doi.org/10.1109/TIP.2003.819861] [PMID: 15376593] ]. It measures the structure, luminance and contrast using following equation:

(4)

The kernel sizes for images A and B are the variables a and b.

(5)

MISSIM represents the mean SSIM over number of kernels referred to by variable n.

2.4.3. Normalized Cross Correlation Coefficient (Nc)

The normalized cross correlation coefficient (NC) measures the similarity between original and referenced images such that the higher value for this measure is one. It can be calculated as follows:

(6)

Where A and B matrices represent the original and referenced signals (or images).

The procedure to embed watermarks in the medical multimedia image as follows:

1. Start
2. Segment the original multimedia medical image I into the ROI and RONI regions.
3. Determine the size and shape (S) of ROI in the medical image.
4. Based on the output (S) of step 3 specify the number (N: 1, 2, 3,4,5,6 or 7) and type (T: LL, LH, HL or HH) of decomposition levels of wavelet transform for medical cover image I. We will refer to the number of subands for embedding hospital watermark logo by (NS).
5. Apply wavelet transform of kind (Haar) on the cover medical image I using (T and N) from step 4.
6. Apply SVD on the selected subands (NS) of medical image I as follows:

   (7)

7. Compute SVD for the watermark logo W:

   (8)

8. Replace the diagonal singular values (YS(n)) of selected subands of medical image I by the diagonal singular values (Y_w) of W image.
9. Do inverse SVD to obtain changed selected subands (NSw):

   (9)

10. Do inverse DWT on the changed selected subands to obtain final watermarked cover image Iw.
11. End

The procedure to extract watermarks from the medical multimedia image as follows:

1. Start
2. Segment the watermarked medical cover image Iw into the ROI and RONI regions.
3. Determine the size and shape (S) of ROI in the medical image.
4. Based on the output (S) of step 3, specify the number (N: 1, 2, 3,4,5,6 or 7) and type (T: LL, LH, HL or HH) of decomposition levels of wavelet transform for watermarked medical cover image Iw. We will refer to the number of subands for embedding hospital watermark logo by (NS).
5. Apply wavelet transform of kind (Haar) on the watermarked cover medical image Iw using (T and N) from step 4.
6. Apply SVD on the selected subands (NS) of medical image Iw as follow:

   (10)

7. Extract the embedded singular values in the selected subands of cover image (YS(n)).
8. Compute SVD for the watermark logo W:

   (11)

9. Re building watermarks using the extracted singular values in step 7 and the left and right orthonormal vectors of matrix W of step 8.

   (12)

10. End

LH subband is used in this group of experiments to hide the hospital watermark logo. The medical image is decomposed from level one until level seven (1-7). It means that there are seven decomposition levels for each tested medical image. Where LH_n (i.e. LH₁, i.e. LH₂, i.e. LH₃, i.e. LH₄, LH₅, LH₆, LH₇) on the horizontal axis in the Fig. (5) below refers to the groups of LH subands and does not mean the LH level number as conventionally known. For example, LH₃ is the group of three LH subands {LH_{level 1} + LH_{level 2} + LH_{level 3}}. We have noticed from the experimental results presented in the Fig. (5), that all the applied attacks have worse effect on the watermark logo image. However, only the contrast attack has less or no influence on the reconstructed watermark and has the same metrics values similar to the case of no attack on the medical image. For the rest of the attacks, we can say that the noise is the most powerful attack on the watermarked medical image. The big impact of this attack is apparent in the experimental results by making SSIM measure value (< 0.1) and NC measure value (< 0.6) and the PSNR measure value (< 20 dB). In addition, we have noticed that the noise attack effect becomes worse when goes deeper in the decomposition levels. Mean and median are the next influential attacks that have apparent effect on the reconstructed watermark logo. We can observe from the presented results below that these attacks made the SSIM metric value (0.2) and NC metric value (<0.5) and PSNR metric value (< 30 dB). However, we have noticed that the mean attack has consistent worse effect among all decomposition levels while the median attack starts to have less influence on the performance of the system from level (LH3) onwards. The rotate and shear geometric attacks are the next group in this sequence of attacks. The deteriorated effect of geometric attacks begins to appear from third decomposition level onwards, hence, we advise to use third level to embed watermark logos. Now, let analyze the influence of the last two attacks (i.e. tampering and compression). The tampering attack has less influence on the performance of the system than compression attack as proved in the terms of SSIM and PSNR metrics values in the Fig. (5). However, the bad effect of those two attacks generally increases gradually from the lowest decomposition band to the highest decomposition subband as shown in the Fig. (5). To sum up, the worst attack on LH subband across all levels is the noise attack and the least effect (or no effect) attack on the shape adjustable system in this subband is the contrast attack.

HL subband is used in this group of experiments to embed the hospital watermark logo. The medical image is decomposed into seven levels to embed watermark inside them. Where HL_n (i.e. HL₁, HL₂, HL₃, HL₄, HL₅, HL₆, HL₇) on the horizontal axis in the Fig. (6) below refers to the groups of HL subands and does not mean the HL level number as conventionally known. For example, HL₃ is the group of three HL subands {HL_{level 1} + HL_{level 2} + HL_{level 3}}. We have noticed from the experimental results presented in the Fig. (6), that the all applied attacks have worse effect on the watermark logo image. This result add another evidence that the attacks have adverse effects on the performance of healthcare systems. However, only contrast attack has less or no influence on the reconstructed watermark and does not affect on medical processing system (i.e. similar to the case of no attack). For the remaining attacks, we can say that the noise is the most powerful attack on the watermarked medical image. The big impact of this attack is apparent in the experimental results by making SSIM measure value (< 0.1) and NC measure value (< 0.5) and the PSNR measure value (< 20 dB). In addition, we have noticed the same observation that the effect of noise attack becomes worst when goes deeper in the decomposition levels. Mean and median are the next influential attacks that have apparent effect on the reconstructed watermark logo. We can observe from the presented results below that these attacks made the SSIM metric value (0.2) and NC metric value (<0.5) and PSNR metric value (< 20 dB). However, we have noticed that the mean attack has consistent worse effect among all decomposition levels while the median attack starts to be less influence on the performance of the system from level (LH3) onwards. Hence, we advise to embed the watermarks from level three onwards. The rotate and shear geometric attacks are the next group in this sequence of attacks. The deteriorated effect of geometric attacks begins to appear from third decomposition level onwards, hence, we advise to use third level to embed watermark logos. Now, let analyze the influence of the last two attacks (i.e. tampering and compression). The tampering attack has less influence on the performance of the system than compression attack as proved in the terms of SSIM and PSNR metrics values in the (Fig. 6). In general, the bad effect of those two attacks increases gradually from the lowest decomposition band to the highest decomposition subband as shown in the (Fig. 6). Overall, the worst attack on HL subband across all levels is the noise attack and the least effect (or no effect) attack on the shape adjustable system in this subband is the contrast attack. Finally, we have noticed that the HL3, HL4 and HL5 are the best levels to embed watermark logos in the CT scan modality.

Fig. (5) The results of embedding hospital logo across seven level in the LH Subband for X-rays, MRI and CT scan modalities.

HH subband is used in this group of experiments to hide the hospital watermark logo. The medical image is decomposed into seven levels to embed watermark inside them. Where HH_n (i.e. HH₁, HH₂, HH₃, HH₄, HH₅, HH₆, HH₇) on the horizontal axis in the Fig. (7) below refers to the groups of HH subands and does not mean the HH level number as conventionally known. For example, HH₃ is the group of three HH subands {HH_{level 1} + HH_{level 2} + HH_{level 3}}. We have noticed from the experimental results presented in the Fig. (7), that the all applied attacks have worse effect on the watermark logo image. These results add another evidence that the attacks have adverse effects on the performance of healthcare systems. However, only contrast attack has no influence on the reconstructed watermark and does not disturb medical processing system (i.e. similar to the case of no attack). For the remaining attacks, we can say that the noise is the most powerful attack on the watermarked medical image. The big impact of this attack is apparent in the experimental results by making SSIM measure value (< 0.1) and NC measure value (< 0.2) and the PSNR measure value (< 20 dB). We have also noticed that the effect of noise attack is consistent among all the HH decomposition levels of medical image. In addition, we have observed interesting result that the noise influence becomes the least in the seventh decomposition level in contrast to the presented results in the earlier two subsections. Mean and median are the next influential attacks that have apparent effect on the reconstructed watermark logo. We can observe from the presented results below that these attacks made the SSIM metric value (0.1) and NC metric value (<0.2) and PSNR metric value (< 20 dB). However, we have noticed that the mean attack has consistent worse effect among all decomposition levels while the median attack starts to be less influence on the performance of the system from level (HH3) onwards. Hence, we advise to embed the watermarks from level three onwards especially in level (HH4). The rotate and shear geometric attacks are the next group in this sequence of attacks. The deteriorated effect of geometric attacks begins to appear from third decomposition level onwards, hence, we advise to use third level to embed watermark logos. Now, let analyze the influence of the last two attacks (i.e. tampering and compression). The tampering attack has less influence on the performance of the system than compression attack as proved in the terms of SSIM and PSNR metrics values in the (Fig. 7). In general, the bad effect of those two attacks increases gradually from the lowest decomposition band to the highest decomposition subband as shown in the (Fig. 7). Overall, the worst attack on HH subband across all levels is the noise attack and the least effect (or no effect) attack on the shape adjustable system in this subband is the contrast attack. Finally, we have noticed that the HH4, HL5 and HL6 are the best levels to embed watermark logos for all modalities.

In this subsection, we presented the experimental results of analyzing the effects of attacks on the medical cover image for X-rays, MRI and CT scan modalities as shown below in the Tables 1, 2 and 3. We have observed from these results that the X-rays modality images have higher metrics values than other two modalities. The median attack has higher metric values than other attacks on the medical image for all modalities. Compression and noise attacks have the least values for PSNR, SSIM and NC metrics among all presented attacks. In addition, the HH subband has the higher metric values among tested decomposition subands. These experimental results are consistent with the earlier presented results of embedded and extracted watermarks in the previous subsections.

Tables 4, 5, 6 and 7 are presented to show the number of coefficients of watermark image that can be embedded in the pixels of the cover image. In these tables, the following terms mean that the coefficients of one suband (1 Sub.), two subands (2 Sub.), three subands (3 Sub.) or four subands (4 Sub.) are used to embed the coefficient of watermark logo. Hence, if the size of image and the number of subands increased then we can hide more coefficients in the image. Figs. (8 and 9) are presented to show an example of reconstructed watermark logos after disturbing the cover image by a number of different attacks that are described earlier.

Table 1
Watermarked Medical Cover Image (Logo embedded in the LH subband).

Table 2
Watermarked Medical Cover Image (Logo embedded in the HL subband).

Table 3
Watermarked Medical Cover Image (Logo embedded in the HH subband).

Table 4
Number of coefficients for images of size (2048, 1024 and 512) among different subands.

Fig. (6) The results of embedding hospital logo across seven levels in the HL Subband for X-rays, MRI and CT scan modalities.

Table 5
Number of coefficients for images of size (256, 128, and 64) among different subands.

Fig. (7) The results of embedding hospital logo across seven level in the HH Subband for X-rays, MRI and CT scan modalities.

Table 6
Number of coefficients for images of size (32, 16, and 8) among different subands.

We have presented Table 1 to compare the performance of our approach with two approaches in the literature. We have noticed that in the LL suband, our approach outperforms other research works in the references [1A.K. Gupta, and M.S. Raval, "A robust and secure watermarking scheme based on singular values replacement", Sadhana, vol. 37, no. 4, pp. 425-440.
[http://dx.doi.org/10.1007/s12046-012-0089-x] , 16G. Emir, and A. Eskicioglu, "Robust DWT-SVD domain image watermarking: embedding data in all frequencies", Proceedings of the ACM 2004 Workshop on Multimedia and Security., .] for different listed attacks. In addition, we observed that the proposed approach exceeds other approaches for (LH, HL and HH) subands in terms of providing higher NC measure values. Hence, we can say that our approach is better those two approaches in all subands for various kinds of attacks listed in table below.