{'fraction_non_alphanumeric': 0.027820851956581228, 'fraction_numerical': 0.010520234728936727, 'mean_word_length': 4.910152740341419, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 3, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Prediction Error Nonlinear Difference Expansion Reversible Watermarking for Integrity and Authenticity of DICOM Medical Images

—It is paramount to ensure the integrity and authenticity of medical images in telemedicine. This paper proposes an imperceptible and reversible Medical Image Watermarking (MIW) scheme based on image segmentation, image prediction and nonlinear difference expansion for integrity and authenticity of medical images and detection of both intentional and unintentional manipulations. The metadata from the Digital Imaging and Communications in Medicine (DICOM) file constitutes the authentication watermark while the integrity watermark is computed from Secure Hash Algorithm (SHA)-256. The two watermarks are combined and compressed using the Lempel Ziv (LZ) -77 algorithm. The scheme takes advantage of the large smooth areas prevalent in medical images. It predicts the smooth regions with zero error or values close to zero error, while non-smooth areas are predicted with large error values. The binary watermark is encoded and extracted in the zero-prediction error using a nonlinear difference expansion. The binary watermark is concentrated more on the Region of non-interest (RONI) than the Region of interest (ROI) to ensure a high visual quality while maintaining a high capacity. The paper also presents a separate low degradation side information processing algorithm to handle overflow. Experimental results show that the scheme is reversible and has a remarkable imperceptibility and capacity that are comparable to current works reported in literature.


I. INTRODUCTION
Medical images and patient data are often shared in ediagnosis over open communication channels. The transmission of such data is prone to intentional and unintentional manipulations, affecting confidentiality, integrity and authenticity. Such manipulations can result in misdiagnosis and even lead to lose of life hence the need to ensure reliability [1][2].
Medical images and patient information are transmitted, stored, retrieved, printed, processed and displayed through Digital Imaging and Communications in Medicine (DICOM) standards [3]. In DICOM, metadata which is the patient report and information that connects to the image ensures reliability of medical images data. The metadata is saved in the image file header [3]. This technique is insecure as the metadata can be easily modified, destroyed, or disconnected from the medical image [4].
Digital image watermarking, a branch of information hiding technology where a secret message is hidden in public data, can overcome these challenges. The secret message can be the metadata, a hospital logo, an electronic signature, or any other identifier in medical images. The requirements for medical image watermarking are reversibility, imperceptibility and reliability [2].
Digital image watermarking is classified into several classes based on the method of embedding the secret message, reversibility, application and region(s) used to encode the secret message [5]. It can be either frequency or spatial domain based on the method of encoding the secret message. Spatial domain techniques [4], [6] changes the pixel intensities of the image directly to implant the secret message. Frequency domain techniques [7][8] implants the secret message by changing the coefficient values of the transformed image. Digital image watermarking techniques are classified as reversible, semi-reversible or irreversible based on reversibility. In reversible techniques [9][10], the original image and the secret message are losslessly restored, while in irreversible techniques [11], the secret message and the original image cannot be losslessly restored. Semi-reversible techniques [12] restore some regions of the original image while others cannot be restored. Therefore, reversible techniques are preferred for watermarking medical images. Depending on the application of digital image watermarking, the schemes are classified as either fragile or robust. Robust watermarking techniques emphasize the robustness of the encoded message. The encoded watermark can resist legitimate and illegitimate attacks during image transmission in robust schemes. Therefore, robust watermarking strategies [13][14] are mainly used for copyright protection of images. Fragile watermarking methods emphasize on detection of manipulations during image transmission. Hence, fragile watermarking techniques [4], [6] are used to confirm the integrity of images. The watermarking can be further classified as ROI or RONI based. The anatomical details are contained in ROI whereas RONI carries the uninformative background usually black in color [15]. In ROI techniques [4], [16] the secret message is hidden in ROI while RONI techniques [17][18] hides it in RONI.
In this paper, a novel reversible MIW scheme based on prediction error nonlinear difference expansion for authenticity *Corresponding Author. www.ijacsa.thesai.org and integrity of medical images is proposed. The scheme has the following objectives: 1) Predicting the medical image with zero error or values close to zero for smooth regions while non-smooth regions are predicted with large error values. Smooth regions are characterized by zero or slight differences in adjacent pixel intensities. Hiding the watermark in these regions is less visible.
2) Concentrating the watermark mainly in RONI to ensure excellent visual quality on the ROI while maintaining its security.
3) Determining an optimum point for trade-of between capacity and imperceptibility for prediction error nonlinear difference expansion watermarking.

4)
Attaining good visual quality of watermarked images that supersede the benchmark value and the perceptual boundary.
5) Providing a low degradation approach to handle the overflow.
6) Lossless recovery of the medical image without the need of a location map.
The rest of this paper is organized as follows; The second section provides medical image watermarking schemes reported in the literature. The third section describes the proposed work. The fourth section presents the results and discussion. The fifth section, which is the final section, presents the conclusion and suggestion for further work.

II. RELATED WORK
Researchers have recently presented Medical Image Watermarking (MIW) techniques. This section analyzes some of these techniques. Roček et al. [12] presented a new MIW strategy that merges RONI watermarking method with zerowatermarking principle and reversibility features. The scheme uses a reversible watermarking in the RONI, which achieves a high capacity and implants data using the zero-watermarking principle. A Dual Tree Complex Wavelet Transform (DT-CWT) is used to merge these techniques. The limitation of the approach is the need for a location map at extraction to recover the image and the encoded watermark.
Gao et al. [19] presented a reversible MIW approach that achieves tamper detection and enhances ROI contrast. It utilizes Otsu's thresholding method to differentiate the RONI from the ROI. The scheme expands the peak-pairs of ROI histogram to achieve data encoding alongside a less distortion contrast enhancement. This approach creates a feature bit matrix from ROI and encodes it in the least significant bits of RONI to guarantee ROI reversibility. The limitations of the scheme are; (i) the scheme is semi-reversible as it can restore only the ROI at reception and (ii) the need for implanting the feature bit matrix.
Atta-ur-Rahman et al. [20] presented a reversible MIW approach for the integrity of medical images and the secrecy of patient data. The watermark is created chaotically and encoded using a chaotic key in selected pixels. The selected pixels are divided using a primitive polynomial of degree four and the remainder appended to the secret message. At the reception, the computed reminder validates the watermark. In this approach, a high imperceptibility was exhibited. The approach's limitations were; the hiding capacity was not measured and the method is not region-based hence making it impossible to select hiding regions.
Liu et al. [21] presented a novel robust reversible MIW to protect the integrity and authenticity of medical images. This method addresses the challenge of losing information in watermark embedding due to image segmentation. It avoids biases during diagnosis by designing a recursive dither modulation (RDM) based watermarking. RDM is later combined with Singular Value Decomposition (SVD) and Slantlet Transform (ST) to protect image authenticity. The RONI and ROI are divided to generate the watermark encoded into the whole image, thus avoiding risk related to image segmentation.
Swaraja et al. [22] presented a MIW technique that conceals a dual watermark on RONI blocks for authenticity and tampers recognition in medical images. This procedure uses the lossless Lempel-Ziv-Welch compression algorithm to compress the dual watermark, thus increasing capacity. The embedding blocks are chosen based on the human visual systems characteristics, integrating Discrete Wavelet Transform (DWT) and Schur transform alongside Particle Swarm Bacterial Foraging Optimization Algorithm (PSBFO). The scheme is robust against signal attacks and compression and shows transparency from the simulation results.
Fares et al. [23] proposed a MIW approach based on Discrete Cosine Transform (DCT) and DWT for protecting patient data. The scheme proposes two approaches. The first approach combines DCT and Schur Decomposition (SD) and performs integration in medium frequencies thus achieving a good compromise between visual quality and robustness. The second approach combines SD and DWT to achieve a robust watermark distribution. The proposed schemes maintain good visual quality and are robust against attacks. The capacity of the first approach is 682 bits which correspond to 85 characters only. Therefore, the capacity of the first approach is limited. The second approach conceals 1024 bits equivalent to 128 characters. Therefore, the capacity of the second approach is certainly reduced.

III. METHODOLOGY
A fragile Medical Image Watermarking (MIW) scheme is presented for detecting both intentional and unintentional manipulations and ensuring the authenticity and integrity of DICOM medical images. The approach also presents a separate low degradation side information processing algorithm to handle overflow. The sub-sections are as follows.

A. Watermark Creation and Compression
There exist several ways for creating an authentication watermark [24]. The DICOM files consist of image data and metadata in a single .dcm file. The metadata contains patient information, image dimensions, parameters of modality acquisition and operator identification [24]. The scheme uses the metadata of DICOM images as the authentication watermark. It also employs the Secure Hash Algorithm (SHA) www.ijacsa.thesai.org -256 to compute the integrity watermark. This is a patent cryptographic hash function used in data integrity and digital certificates [25]. The output is a 64-digit hexadecimal number and is strong, and easy to compute [25]. The method detects manipulations by comparing the hidden and extracted integrity watermark. It also combines the authentication and integrity watermark to form the total watermark. The text string is compressed to a binary string using the Lempel Ziv -77 compression algorithm. Table I shows a summary of the watermark creation and compression data features.

B. Image Prediction
Any image pixel is predictable using an expression that constitutes its neighboring pixels [26]. The hiding capacity of prediction-error expansion depends on how close the predicted image resembles the original image. Medical images are characterized by a large smooth area, unlike other images and hiding the watermark in these areas is less distinguishable by the human visual system [4]. The scheme predicts the smooth areas of the medical image with zero error or values close to zero and non-smooth areas with large error values using (1). The predicted pixel is .

C. Image Segmentation
There exist several techniques to segment medical images into ROI and RONI. The techniques can be manual, like use of polygons and freehand sketching, or automatic. A radiographer divides a medical image using a technique of his/her choice. The scheme automatically segments the medical image using a thresholding technique that utilizes the mean of pixels and morphological operations. The specific medical image segmentation procedure is as follows.

1) Load the medical image MI. 2)
Compute the mean of all pixels and consider it as the initial threshold TO.
3) Divide the pixels into two groups such that pixels greater than TO form the ROI, otherwise RONI. 4) Compute the mean of ROI MROI and RONI MRONI separately.

5)
Compute the new threshold T1 as the average of MROI and MRONI. 6) Repeat steps (iv) and (v) until the new threshold converges.
7) Convert the medical image into a binary image using the last threshold by making all pixels less than it black otherwise white.

8)
Perform morphological filtering on the binary image obtained from step (vii). 9) Perform region filling on the binary image from step (viii).
10) Display the binary image. 11) Obtain the indices MI0 and MI1 corresponding to the pixels with values 0 and 1 of the binary image, respectively.
12) The RONI and ROI of the medical image correspond to M10 and MI1 respectively.

D. Prediction Error Nonlinear Difference Expansion
The basic prediction error difference expansion first proposed by [27] is given as follows; Let be the pixels of the original image and ̂ be the predicted pixel. The prediction error is computed as; Let be a binary watermark. The watermark bits are embedded by expanding the prediction error as; Let > 0, be the threshold to increase capacity and control degradation. It is directly proportional to degradation and capacity but inversely proportional to visual quality. The threshold T can be varied from 1 to the maximum possible gray intensity value of an image. The watermarked pixels are given by (4).
If | | ≥ , the pixels cannot carry a watermark bit and are shifted to provide a greater prediction error than the carrier pixels at detection using (5).
The embedding threshold and the predicted image are transmitted as side information alongside the watermarked image to the receiver [26]. The problem of overflow and underflow is re-solved by creating a location map or using flag bits [26][27][28]. At detection, if the same predicted value for the original image is available, then the error is computed as in (6).
The prediction error differentiates the embedded and shifted pixels. If −2 ≤ ̅ ≤ 2 + 1 , then it is a carrier pixel and the error is computed as ̅ = 2 + , where b is the least significant bit of ̅ . The original and shifted pixels are recovered as in (7) and (8) respectively. To overcome the challenge of high degradation caused by increasing T while increasing capacity, the transmission of the predicted image and T as side information, overflow and underflow in the basic prediction error linear difference expansion, the scheme uses a prediction error nonlinear difference expansion. It uses systematic multiple predictions and expansions of the zero -prediction error. The binary watermark is divided into sections equal to the number of expansions. The original image is predicted using (1). The error is computed using (2). The carrier and non-carrier pixels are embedded and shifted as in (9) and (10) respectively.
The first row and column are not used in embedding. The rest of the rows and columns are embedded in intervals of two pixels, with the initial pixels being P22, P23, P32 and P33 until all the other pixels are used in embedding the watermark. The image is predicted in each initial pixel embedding stage. This is the prediction error-linear difference expansion (PE-LDE) with a threshold T=1. To increase capacity with low distortion, unlike the basic prediction error difference expansion which increases T, the scheme uses a prediction error quadratic difference expansion (PE-QDE) considered as a cascade of the PE-LDE described as follows: The image ′ is used again to perform PE-QDE and is predicted using (1) to obtain ̂′ . The error is computed as; Let ′ be the watermark to be embedded in PE-QDE. The carrier and non-carrier pixel are embedded and shifted as in (12) and (13) respectively.
The embedding in PE-QDE follows the same order as in PE-LDE. The process is repeated so as to increase the capacity at low distortion until saturation is reached.
The watermarked image is predicted at the reception using the same prediction technique used in embedding. During extraction, at any instance of image prediction that corresponds to an image prediction during embedding, the same predicted image is obtained. This guarantees reversibility. The error is computed as in (14). ̇ is the obtained predicted image.
The error obtained is the same as the expanded error in the last embedding stage of initial pixel P33 in PE-QDE. If the ̇ is either 0 or 1 then it is a carrier pixel, else a non-carrier pixel. For carrier pixels, the watermark is extracted as follows.

=̇
The carrier and non-carrier pixels are recovered as; The first row and column remain unaltered as it is not used in embedding. The rest of the rows and columns are extracted in intervals of two pixels with the initial pixels being P33, P32, P23 and P22, an inverse order to that of embedding. This is the inverse PE-QDE. The inverse PE-LDE is as follows; The image ′ is predicted using the same technique and the error is computed as in (17). ̈ is the obtained predicted image.
If ̈ is either 0 or 1 then it is a carrier pixel else a noncarrier pixel. For carrier pixels, the watermark is extracted as; =̈ (18) The original carrier and non-carrier pixels are recovered as; The inverse PE-LDE follows the same order as inverse PE-QDE. Therefore, the binary watermark and the original image are restored. Fig. 1 shows the flow chart of the watermark embedding and the specific procedure is as follows:

E. Watermark Encoding
1) Read the DICOM file.
2) Segment the image data using the segmentation procedure to obtain the binary mask.
3) Obtain the authentication watermark (AW) from the DICOM metadata.
4) Compute SHA-256 on the image data to get the integrity watermark (IW).

5)
Concatenate the authentication and integrity watermark to form the total watermark. 6) Compress the total watermark using LZ-77 compression algorithm.
7) Divide the binary watermark into sections equal to the knee point less one. 8) Embed the first and second section of the binary watermark using the PE-LDE and PE-QDE respectively as described in section D to obtain the partial watermarked image. 9) Using the binary mask obtained in step (ii), segment the partial watermarked image such that the RONI and ROI region of the partial watermarked image corresponds to '0' and '1' of the binary watermark respectively.
10) Embed the third, fourth and fifth sections of the binary watermark using prediction error -third order difference www.ijacsa.thesai.org expansion (PE-TODE), prediction error -fourth order difference expansion (PE-FODE) and prediction error -fifth order difference expansion (PE-FIODE) respectively on RONI only. Consider these expansions as cascades of PE-LDE.
11) Obtain the watermarked image which may exhibit overflow.

F. Side Information Processing
Overflow and underflow problems in reversible watermarking are essential as it can lead to irreversibility or heavy distortion. Overflow occurs when the maximum gray level is exceeded, while underflow occurs when the minimum gray level is exceeded. The scheme does not exhibit underflow as pixel intensity are not decreased during processing. However, the approach can exbibit overflow. The maximum overflow is equals to the number of expansions used during embedding. The scheme preserves the last prediction error expansion to hide the side information. The scheme considers the length of the watermark, segmentation threshold, and locations of maximum gray level and overflowed pixels as side information. The procedure for Side Information Processing (SIP) can be described as follows: 1) Scan the watermark image and record the locations of maximum and overflowed gray levels.
2) Modify the maximum and overflowed gray pixels by subtracting the number of expansions used in embedding.
3) Concatenate the locations, segmentation threshold and length of the watermark and consider it as side information.
4) Compress the side information.

5)
Hide the side information on the whole image using the last prediction error difference expansion. 6) Finally, obtain the watermarked image that caries the watermark and side information without exhibiting overflow for transmission.

G. Side Information Recovery
The side information is first recovered at extraction and the maximum and overflowed pixels are restored before extracting the watermark. The side information is recovered using the following steps.
1) Perform the sixth inverse prediction error difference expansion on the whole image to obtain the side information binary watermark.
2) Decompress the side information binary watermark.
3) Modify the locations obtained in step (ii) by adding the number of expansions used in embedding to restore the overflowed watermark image. Fig. 2 shows a flow chart of the watermark extraction and the specific procedure is as follows:

H. Watermark Extraction
1) Using the side information recovery procedure, recover the side information and restore the maximum and overflowed pixels.
2) Separate the RONI and ROI of the watermarked image using the segmentation procedure. Use the recovered segmentation threshold 3) Extract the fifth, fourth and third sections of the binary watermark using inverse PE-FIODE, PE-FODE and PE-TODE respectively on the RONI only to recover the partial watermarked image 4) Extract the second and first sections of the binary watermark using inverse PE-QDE and PE-LDE respectively on the whole image to recover the original image 5) Concatenate the recovered sections of the binary watermark and decompress using LZ-77 decompression algorithm 6) Compare the recovered and hidden authenticity watermark for authentication verification 7) Compute the SHA-256 of the recovered image and compare it with the hidden integrity watermark to verify that the image has been transmitted without manipulation.

I. Performance Measures
The proposed scheme is evaluated in terms of capacity, imperceptibility, reversibility and robustness to provide a fair comparison with other relevant schemes. The capacity of the proposed scheme in bits per pixel (bpp) is computed using (20). The capacity of the scheme depends on the accurate prediction of the image. To increase capacity, systematic multiple predictions and expansions are employed.

=
Where HP is the highest possible pixel value for the images. PSNR values range between 0 and +∞. A higher PSNR value shows low image distortion and high visual quality.
Where , ′ are the averages of , ′ respectively, , ′ are variances of , ′ respectively, 1 , 2 are balancing constants and 2 ′ are the covariance for , ′ respectively. The SSIM is a quality measure based on Human Visual System to measure image distortion in structural information. Its values lie between 0 and 1. An SSIM of 1 indicates complete similarity.
The IF parameter measures similarity between two images. An IF value of 1 between two images indicates that they are similar.
At extraction, the proposed scheme evaluates the reversibility of the image and the watermark. In evaluating the reversibility of the image, PSNR and Root Mean Square Error (RMSE) between the extracted and original image are used to verify that two images are 100% numerically identical. The RMSE is computed using (24).
A PSNR and RMSE of +∞ and 0 respectively indicate that the image has been recovered without any loss else otherwise. In evaluating the watermark reversibility, Accuracy Ratio (AR) and Bit Error Rate (BER) between the embedded and extracted binary string is used. The BER and AR are computed as; A BER and AR value of 0 and 1 respectively indicate that the watermark has been recovered without any loss. The scheme also computes the BER between the original and extracted binary watermark as in (25) to evaluate robustness against attacks. A BER value closer to 0 indicate stronger robustness.

A. Experimental Setup
The experimental results were obtained using a PC with an Intel CPU of 2.6 GHz and 8GB RAM. The scheme was implemented in MATLAB 2021a to test the reversibility, imperceptibility, robustness and capacity. A set of 270 medical images in DICOM format comprising of 30 brain Magnetic Resonance Images (MRI) images, 30 [29][30]. All images were 16 bpp and were resized to 512 x 512.

B. Imperceptibility
The imperceptibility of the scheme was evaluated using PSNR, SSIM and IF and the results given in Table II. The minimum PSNR value between the original and watermarked images is 83.0 dB, which is above the acceptable benchmark value of 40 dB [5] and the perceptual boundary of 82 dB [4] for the human visual system. Qasim et al. [4] conducted a relative Visual Grading Analysis (VGA) trial and determined that the modification of images to 82 dB or higher is unnoticeable to all observers. Therefore, the original and watermarked image are visually indistinguishable by the human eye. The SSIM and IF are either unity or close to unity indicating that the watermarked was hidden invisibly. A small set of the medical images and their corresponding watermarked images are shown in Fig. 3

C. Reversibility
The reversibility of the scheme was assessed at reception for both the extracted image and the watermark. The BER and AR values between the embedded and extracted binary watermark were used to evaluate the watermark reversibility. The values of zero and one respectively were obtained, demonstrating that the watermark was extracted without loss. This is a confirmation of the integrity and authenticity of the watermark. At the reception, the medical image is restored for diagnosis. The PSNR, RMSE, SSIM and IF between the original and extracted image were used to evaluate the image reversibility. The PSNR and RMSE values were positive infinity and zero respectively indicating that the two images are 100% numerically identical. The SSIM and IF were both unity demonstrating that the extracted image is identical to the original image.

D. Capacity
The binary watermark is encoded in the zero error pixels. To increase capacity, the number of iterations is increased. For the first and second iteration, that is the PE-LDE and PE-QDE, the binary watermark is encoded in the whole image, while for iterations above two, the binary watermark is encoded in the RONI only. A binary image obtained from the image segmentation procedure is used to distinguish the ROI from the RONI. This controls degradation in ROI as increasing capacity distorts the watermarked image. Fig. 4 shows the capacity of the scheme versus the number of iterations.
In Fig. 4, the capacity of the scheme increases steadily with an increase in the number of iterations until the knee point. After the knee point, increasing the number of iterations results in a low increase in capacity but still degrades the image due to the shifting of non-carrier pixels. The complexity of the approach and consequently the computational time increases with an increase in the number of iterations. After 30 iterations, an increase in the number of iterations increases capacity by less than 0.001bpp. This is the saturation point of the scheme. The scheme limits the number of iterations to 6 which correspond to the knee point. The capacity created in the 6th iteration hides the side information and is performed on both RONI and ROI. Fig. 5 shows PSNR as a function of capacity.   From Fig. 5, it can be noted that an increase in capacity distorts the watermarked image. An increase in capacity degrades the image until saturation. After saturation, increasing the number of iterations results in a negligible increase in capacity but continues to degrade the image due to the shifting of non-carrier pixels. Table III shows the specific number of bits in Kbytes hidden and the resultant PSNR for the images in Fig. 3. The cervix MRI image had the highest capacity of 36.57 Kbytes, while the lung CT had the lowest capacity of 12.87 Kbytes. Fig. 6 shows a sample binary image of MRI image (a) shown in Fig. 3. Fig. 6. Binary Image of MRI Image in Fig. 3 (a).

E. Robustness
The robustness of the scheme was assessed using BER between the encoded and extracted binary watermark under various attacks. The average PSNR and BER of the scheme under various intentional and unintentional attacks are shown in Table IV. In this table, adding or removing a region illustrate intentional attacks while the rest demonstrate unintentional attacks. The integrity and authenticity of the medical images are confirmed when the encoded and extracted watermark are completely identical. However, intentional and unintentional manipulations on the medical image result in a mismatch between the encoded and extracted watermark. The latter are malicious manipulations where a region is added or removed while the former are accidental manipulations occurring during transmission. The reversibility of the medical image under various attacks was also assessed using PSNR. The PSNR obtained for each image under attack was not positive infinity, indicating that the original medical image was not recovered. The BER obtained under various attacks for each image was non-zero, demonstrating a mismatch between the encoded and extracted watermark. Therefore, the authenticity and integrity of the medical images under attack is not confirmed. This shows that the approach is fragile to manipulations.

F. Comparison with Relevant Schemes
The developed scheme has been compared with other relevant MIW schemes as shown in Table V and Table VI. The approaches are compared in terms of location map, reversibility, capacity and visual quality. The developed approach uses a non-linear difference expansion that does not need a location map at the extraction for recovery of the watermark and the image to guarantee reversibility thus is better than the approach [12]. The side information of the developed approach is hidden in the last iteration leading to a low degradation approach to handle the overflow. The developed scheme performs better than the scheme reported in [19] in terms of reversibility as it recovers the whole image while the former recovers only the ROI. The medical image is restored in its pristine state in the developed approach. Additionally, it gives a higher performance than schemes [19] and [22][23] in terms of capacity as it achieves a higher capacity at a lower degradation. Also, the developed scheme achieved the highest PSNR of 83.0 to 86.2 dB and a SSIM of unity compared to the scheme [12] and [19][20][21][22][23], demonstrating a better visual quality.  The developed scheme is further compared to a linear difference expansion scheme [28], a prediction-error linear difference expansion scheme [31] and a fragile SVD with grouped block-based scheme [32]. The average performance in terms of PSNR and Capacity in bpp for the medical images shown in Fig. 3 are used for comparison. The scheme has a better performance than schemes in [28] and [31] in terms of capacity as it has a higher payload. The scheme has a better performance than the scheme [28] and [31][32] in terms of visual quality as it has the highest PSNR value.

V. CONCLUSION
An imperceptible and reversible watermarking scheme based on prediction error and non-linear difference expansion to ensure integrity, authenticity and detect manipulations on DICOM medical images has been proposed. The experimental results obtained demonstrate that the approach is reversible and provides remarkable visual quality and capacity. The scheme yields PSNR values which are above the benchmark value and the perceptual boundary, demonstrating that it is imperceptible. The approach is fragile to manipulations making it suitable for detecting them. The approach also yields superior performance in terms of visual quality and compares favorably in terms of capacity to schemes available in the literature. It also yields superior results compared to other linear difference expansionbased schemes, demonstrating that the nonlinear difference expansion is superior to linear difference expansion in capacity and visual quality. The future work will involve developing a watermarking system that will not only detect manipulation but also restore the tampered regions.