Introduction

During the past several decades, security has become a significant issue due to the rapid expansion of digital media1,2. The global population utilises mobile phones, cameras, laptops, or comparable electronic equipment. These electronic devices produce a substantial amount of digital information. Each of the data produced may be either significant or inconsequential. The digital data generated encompasses many areas, such as a photograph capturing a child’s smile or the digital signature of extremely private documents between two countries. While the domain can vary, security remains the primary concern. Protecting digital data might involve encryption, steganography, or watermarking techniques. This paper specifically focuses on the confidentiality of medical images using digital image watermarking, proposing a new and effective hybrid watermarking scheme. A significant issue with medical data is the urgent necessity for data to remain unaltered and easily accessible.3,4,5,6. For instance, any security measures applied to an individual’s X-ray must not be tampered with, as it contains crucial information that cannot be seen or detected by the human eye or other senses.

Watermarking offers a means to verify the authenticity of medical digital content7,8. Implementing invisible watermarking with optimal robustness and imperceptibility guarantees the secure transmission of non-altered content across any network9,10. The general watermarking11,12 method is shown in Fig. 1. The diagram shows how the binary watermark (W) is embedded into the host medical image (HMI) to create the watermarked image (W*). W* can be transmitted over the network or kept as a legitimate replica. W is carefully created to closely resemble the original image, allowing the authenticity of the image to be verified by extracting the binary watermark and matching it to the original(W). Any disparities between the two could indicate potential counterfeit activity.

$${\text{W*}}\left( {{\text{x}},{\text{y}}} \right) = {\text{HMI}}\left( {{\text{x}},{\text{y}}} \right) + \alpha \cdot {\text{W}}\left( {{\text{x}},{\text{y}}} \right)$$
Fig. 1
figure 1

Watermarking process.

Full size image

In this paper, medical images13,14,15,16,17 are considered as HMI for watermarking, which are transformed before watermarking. The dimensions of the HMI are taken as 512* 512. The watermark taken in the experiment is 64* 64, and it is scrambled and then decomposed orthogonally to provide more confidentiality of the algorithm. The proposed work integrates DWT, HD and SVD transforms for image watermarking which enhances the robustness and imperceptibility of the watermark image. To improve the security of the watermark added, Arnold based scrambling scheme has been implemented in the work.

The main highlight of this paper is:

  1. 1.

    A novel hybrid algorithm has been developed, incorporating Arnold Scrambling, Discrete Wavelet Transform (DWT), Hessenberg Matrix Decomposition(HMD) and Singular Value Decomposition(SVD) algorithms for enhanced watermark security and robustness against different image processing attacks.

  2. 2.

    Being a dual domain transformation propounded algorithm is much helpful in increasing imperceptibility and by applying transformations in both spatial (Arnold) and frequency domains (DWT, SVD) that makes the propounded scheme for an embedding of watermark into image without affecting its visual quality.

  3. 3.

    Compressive watermarking is still sensitive to common attacks like compression, noise addition and geometric distortions. All these attacks conspire against the watermark arguably, the combination of several or all transforms can provide assurance for a resilient watermark.

Paper Organization: Section "Background" elucidates the literature review in the domain of image watermarking. Section "Preliminaries" elucidates all the preliminaries employed in the paper. Following this, section "Methodology" elaborates on the propounded methodology, while section "Results and discussion" provides a comprehensive analysis of the results.

Background

The protection of medical images has become an essential issue for societies due to the simplicity of accessing and distributing them through the Internet18. Author19 uses the watermarking method Quaternion FrOOFMMs, a new algorithm to capture intensity and phase information and geometric correction mechanisms to handle rotation, scaling, and translation distortions. Least Squares Support Vector Regression for the watermark’s removal process is enhanced and improves noise recovery accuracy, image integrity, and security, proving robust against attacks. The paper20 mainly proposes digital image watermarking technology to improve the security of image transmission in UAVs (Unmanned Aerial Vehicles). A watermarking method based on H-Grey is propounded to embed secure information in images captured by UAVs and applied in this work. The ultimate objective of this approach is to safeguard the integrity and confidentiality of transmitted data, which, in other words, protects a piece of data from being altered with or accessed by an unofficial party. The technical realisation of SampleML and analysis of its performance capability side-by-side with state-of-the-art methods that aim to secure inference in edge devices while simultaneously keeping image quality. The propounded H-Grey watermarking method efficiently delivers a UAV secure image and has achieved both security and fidelity. The paper21 focuses on a new watermarking method that significantly balances between imperceptibility and robustness. The approach merges Zernike Moments (ZMs), valid for translational invariant image representation, and the integer wavelet transform, which can decompose an image into four frequency components without losing information. The stated algorithm confirms that the reversible watermark can be implanted in a way that makes it retrievable afterwards to reconstruct 100% of an original image under various attacks. This method aims to be computationally efficient, thus allowing practical use in circumstances where the preservation of watermarked signal and quality of the host medical image are significant. As a result, the stated method provides an excellent equilibrium between robustness and imperceptibility while delivering efficiency in digital watermarking applications.

An article22 analyses a security method for protecting healthcare data through a hybrid watermarking technique. The propounded algorithm integrates DWT, HMD, and SVD to watermark healthcare data. The technique is designed to cater for watermarks of different sizes, so even after changing the dimension of the watermark, these security measures will still be effective. This algorithm can completely protect the storage and transmission of health information, resisting authorised access from outsiders to guarantee patient privacy. The paper can thus be viewed as a significant advancement in healthcare data security, showing a reliable method for protecting medical records. The paper23 offers a complete survey about the recent strategies and techniques in image watermarking into digital images. The article provides an exhaustive study of different watermarking techniques adopted for digital copyright. The survey includes several methodologies, such as spatial and transform domain techniques, robust watermarking algorithms, and reversible watermarking schemes employing machine learning or deep learning to boost performance. This paper also presents the challenges, including robustness against attacks, imperceptibility, and computational efficiency in watermarking, as well as a few trends shaping future research. It can be considered a valuable survey on current digital image watermarking and future trends. The article24 proposes a novel approach to detect and localise areas of copy-move forgery in digital images. The forgery consists of copying the image’s content and placing it over another part to hide or change information. This is done by applying advanced algorithms on the blocks of images and detecting repeated regions, even if rotated, scaled or noise added. The emphasis of the propounded method focuses on robustness so that the forgeries can be reliably detected in various situations, thereby enhancing localisation accuracy. The algorithm offers a valuable tool in forensic analysis, improving the capacity to identify digital photos and discover tampering legitimately.

The paper25 proposes a new SVD-based image watermarking method. This slightly differs from typical SVD-based watermarking schemes that use only one set of orthogonal vectors (U-S-V). The scheme embeds the watermark using orthogonal vectors: U and V. The combination of these algorithms derives a dual-vector approach, which simultaneously makes the watermark more robust against different types of attacks, like noise, compression and cropping on one hand side, while maintaining its imperceptibility for the human eye. Mixing the strength of the watermark with quality can provide a good trade-off between levels, offering broad applicability for securing image-appropriated digital content in cases where security and visual integrity are crucial. The author26 introduces a watermarking technique that utilises the Discrete Non-separable Shearlet Transform (DNST) via an extension named Phase-Shifted Fractional Fourier Moments (PHFMs). This technique digitally embeds watermarks in cerebral magnetic resonance images with high symmetry and reliability into their magnitude domain. The method improves robustness against attacks while transmitting high image fidelity and providing watermark security and imperceptibility using the AGGM-HMT (Adaptive Gaussian Generalized Markov Random Field with Hidden Markov Tree) model.

In the paper27, the author proposes a novel differential evolution (DE) algorithm that could vastly improve the ability to optimise. The algorithm includes a coevolution population that is reevaluated with two functions and slows the convergence process. Furthermore, a segmentation-based evolution strategy was adopted to learn how the evolutionary process could evolve with an adaptive bias towards exploring better solutions (explore) versus converging quickly on well-known ones without significantly compromising efficiency and solution quality. These improvements lead to a more robust and efficient DE algorithm for solving complex optimisation problems with higher accuracy and convergence speed. The article28 introduces a watermarking technique for the contourlet transform (CT) based on the associative CT & Second DCT (Discrete Cosine Transform). The method can obtain optimal embedding parameters using the Artificial Bee Colony (ABC) optimisation algorithm, leading to balanced robustness and imperceptibility. The features are extracted, and then the same is accomplished using contourlet followed by DCT, which captures the details of the watermark at multiple scales and orientations because the combination resists attacks such as compression, noise addition or filtering. Moreover, including the ABC algorithm in this method improves its fidelity capability during watermarking. It has provided a potential solution for robust, high-quality, water-marked images. The paper29 presents watermarking for medical images, i.e., a reversible watermark technique with high image quality and security preservation, because in the case of medical imaging, maintaining information and security is a more significant subject matter. The problem is to do that and put a watermark in such a way with little visible evidence by humans of the degraded diagnostic quality of medical images. Meanwhile, it improves the robustness of the watermark and can defend against various image-processing attacks like cropping, noise, or compression attack. Thus, the watermark yields adequate protection for medical images by focusing both on invisibility within these complex data and robustness against manipulations that come to be necessary in clinical settings.

The propounded paper30 presents a watermarking method to detect satellite image forgery and localisation attacks. Even slight modifications can be distinguished using a delicate watermark that varies with changes made to the image. The watermark is broken when tampering occurs, accurate to the point of that alteration. In the case of satellite images, for example, a type of data often used in critical applications like environmental monitoring or security. This approach can help guarantee integrity and authenticity. This propounded method is also efficient because the time required for watermarking does not significantly modify an image’s quality or processing time. The article31 introduced an image watermarking method combining two images to enhance tamper detection and localisation. The method corrupts the watermark embedding scheme, inserting semi-transparent watermarks into two images. It can detect any alterations by verifying the consistency between these two copies, and tampering changes the watermark so the scheme can detect where this has occurred in an image. The key is that the method can be reversed, returning to the original image without any damage to protect the interests of confidential information during practical applications. However, it helps a lot in critical conditions for security and authenticity issues. In the fragile watermarking scheme32 the watermarks are propounded to be embedded in an image’s DWT domain. The tamper detection and location technique flag any unseen changes made accurately. The combination of tamper localisation and the ability to reverse forged parts makes this method ideal for scenarios that require high security. It keeps most of the original image intact, ensuring dependable digital authentication. The article33 presents an advanced technique for digital watermarking that uses deep learning, and the hybrid approach based on DWT combined with SVD. The propounded method utilises a deep learning model to adaptively optimise the watermark embedding and extraction, improving robustness against various deceptions while guaranteeing the imperceptibility of embedded watermarks. When encapsulating DWT and SVD together, multi-level image decomposition is considered using DWT. Combining the best of classic methods with cutting-edge deep learning techniques provides a robust solution for embedding watermarks in images secretly and reliably. The paper34 evaluates a secure transmission method of medical data within mobile healthcare systems. The technique embeds valuable medical data like patient datasets within the images, for which a watermarking method will be applied. So, in addition to keeping the data secure while it is on the move, this also validates and safeguards that same information from corrupt usage. The propounded watermarking techniques are developed to keep medical images’ quality and diagnostic information unchanged but preserve their robustness against unauthorised access, tampering, and disclosure. By introducing this layer of security, the patient owner and organisational integrity safeguarding data privacy and protection in a digital world are provided for modern mobile healthcare systems.

Recent years have witnessed significant progress in digital image watermarking and the security of medical imaging that merits consideration35. Authors36 have created a state-of-the-art blind image watermarking technique that emphasizes interest points, exhibiting remarkable resistance to diverse attacks while maintaining imperceptibility. This novel approach seamlessly matches our goal of improving resilience in medical image watermarking applications. The paramount significance of preserving the integrity and quality of medical images is emphasized in the context of 3D volume visualization for medical content-based image retrieval. This highlights the imperative for secure image management in medical systems, where the risks are significant37. Moreover, intrinsic picture decomposition techniques, particularly those focused on separating step and drift shading, have effectively enhanced image processing tasks. The insights presented by Sheng et al. improve decomposition procedures, providing a viable avenue for hybrid watermarking frameworks like the one provided in this study38.

Preliminaries

Dataset

The host medical image is taken from the dataset13,14,15,16,17. These are medical images that shows a covid-infected lung images, pneumonia images, Brain tumor images, Breast ultrasound images, lung CT scan images. This image is preprocessed for the experiment, converted to a grayscale picture of size 512*512, and shown in Fig. 2. The Watermark taken is self-generated. It is black and white, with the size of 64*64 and shown in Fig. 4.

Fig. 2
figure 2

Host medical images considered for experiment.

Full size image

A heat map in Fig. 3 shows the visual depiction of differences in the intensity values of a collection of quantified medical images. If both the pixel intensities are same the value is highest. Darker colour (towards blue) means less difference between the images, and colour scan is similar (pixels with a value than 0 to n); light colour (towards yellow) means a large difference given, showing more variation could be there in each image. E.g., images from the same category (e.g., brain or pneumonia scans) have low-intensity differences (only keep blue region). In contrast, cross-categories comparisons, e.g. Brain and covid scans, report the highest dissimilarities (yellow regions), meaning they have different appearances. Instead, the heatmap identifies how each specific pair of images features similarities and differences relevant to their pairing (Fig. 4).

Fig. 3
figure 3

Heat Map showing the difference between the intensity values of all host medical images.

Full size image
Fig. 4
figure 4

Watermark Image.

Full size image

Techniques applied

DWT

DWT43,44 is a powerful digital image processing tool. It decomposes an input image into various lower and higher frequency subbands. This decomposition allows localised image analysis at different scales, thus providing DWT with an excellent solution to applications in compression and watermarking45. It divides the image into two frequency subbands, low and high, allowing for a detailed examination while holding huge highlights.

The general mathematical expression for a 1D DWT of a signal x(t) is written as:

$$x\left( t \right) = \mathop \sum \limits_{j,k} c_{j,k} \cdot \psi_{j,k} \left( t \right)$$

where:

  • cj,k are the wavelet coefficients.

  • ψj,k(t) are the wavelet basis functions derived by scaling and translating.

DWT decomposed images of one of the image taken as input is shown in Fig. 5.

Fig. 5
figure 5

DWT 1 Level Decomposition representation of Host medical image.

Full size image

HMD

HMD is a matrix factorisation technique that simplifies matrices into a Hessenberg form46,47, a nearly triangular matrix. In this form, all elements below the first subdiagonal are zero. This decomposition is computationally efficient and particularly useful in eigenvalue algorithms and solving linear systems.

For a given square matrix A, Hessenberg decomposition transforms it into an upper Hessenberg matrix H, where:

$$A = M \cdot H \cdot M^{T}$$

In expression, M and H are matrices; M is orthogonal, and H is Hessenberg. In an upper Hessenberg matrix, every entry below the first subdiagonal is 0.

SVD

SVD48 is a powerful linear algebra technique used to decompose a matrix into three constituent parts. These parts consist of an orthogonal matrix, a diagonal matrix containing the singular values, and another orthogonal matrix. In the context of image processing, SVD is widely employed due to its exceptional ability to extract and represent the essential features of an image in a compact and efficient manner49. This makes it especially suitable for tasks such as image compression and noise reduction.

For an image matrix A, the SVD is expressed as:

$$A = U \cdot \Sigma \cdot V^{T}$$

where U and V are orthogonal matrices, the symbol Σ, often known as Sigma, is a diagonal matrix that accommodates the singular values of A.

Arnold scramble

In image processing50, the chaotic map known as the Arnold Transform randomly shuffles the positions of pixels in an image, giving the impression that the image is warped. Due to its reversible nature, this transformation is beneficial for image encryption and watermarking51.

For a two-dimensional image of size X*X times, the Arnold Transform is defined by the following mapping:

$$\left( {c^{\prime},d^{\prime}} \right) = \left( {\left( {c + d} \right)\backslash \bmod X,\left( {c + 2d} \right)\backslash \bmod X} \right)$$

where:

  • (c,d) are the primary pixel coordinates.

  • (c′,d′) are the transformed pixel coordinates.

Arnold Scramble image of one of the image taken as input is shown in Fig. 6.

Fig. 6
figure 6

Arnold Scramble Demonstration on one of the input image.

Full size image

Metrics used

PSNR evaluates various experiments52, e.g., watermarked images and visual and analytical models. It is a handy parameter for comparing how unnatural a watermark that will not retrieve our visual quality is enough to deem the image original.

PSNR measures the ratio of an image at the original during watermark embedding52,53. Conversely, a higher PSNR means the distance between the original image and the watermark is less, so the watermark is invisible. PSNR is expressed as:

$$PSNR = 10 \cdot \log_{10} \left( {\frac{{255^{2} }}{ERR}} \right)$$
(1)

where, ERR is the mean square error, which measures the average squared difference between the pixel intensities of the HMI and W*.

NC is a metric used in image watermarking to measure how similar the extracted watermark(EW) is to the W53. It helps determine the accuracy of the watermark extraction process. The value of NC ranges from 0 to 1, where:

NC = 1 depicts that EW is identical to the W.

NC = 0 depicts the similarity between the EW and W.

A higher NC value specifies a better watermark extraction, reflecting that the watermark has been embedded and extracted successfully, even after potential attacks or distortions.

NC is expressed

$$NC = \frac{{\mathop \sum \nolimits_{i = 0}^{M - 1} \mathop \sum \nolimits_{j = 0}^{N - 1} OW\left( {i,j} \right) \cdot \widehat{EW}\left( {i,j} \right)}}{{\sqrt {\mathop \sum \nolimits_{i = 0}^{M - 1} \mathop \sum \nolimits_{j = 0}^{N - 1} OW\left( {i,j} \right)^{2} \cdot \mathop \sum \nolimits_{i = 0}^{M - 1} \mathop \sum \nolimits_{j = 0}^{N - 1} \widehat{EW}\left( {i,j} \right)^{2} } }}$$

OW: The original watermark’s pixel value at position (i,j).

EW: The pixel value is at the same position in the EW.

M and N: The dimensions of the watermark image.

SSIM is an image quality metric54,55 usually used in digital watermarking to check the impact of the watermarking process or adversarial attacks on image quality.

For digital watermarking, the SSIM score is a value ranging from 0 to 1, with:

The closer the result is to 1, the higher perceptual similarity between watermarked and attacked images, i.e., no visible distortion due to watermarking or/and attacks.

Since the data is normalised, anything close to 0 indicates significant visual degradation or distortion.

Since its inception, SSIM has been one of the most popular visual quality metrics, reflecting human perception and correlations with real images.

The UACI is a metric used in digital watermarking and cryptography to quantify the intensity of differences between an original image and an image being watermarked or attacked. UACI56,57,58 measures the pixel value difference on original and distorted images which leads to robustness against, for example, noise addition or cropping the watermark.

The UACI is defined as:

$$UACI = \frac{1}{M \times N}\mathop \sum \limits_{i = 1}^{M} \mathop \sum \limits_{j = 1}^{N} \frac{{\left| {I_{1} \left( {i,j} \right) - I_{2} \left( {i,j} \right)} \right|}}{255} \times 100\backslash \%$$

where:

  • I1(i,j)and I2(i,j)I are the pixel values of the original and modified images, respectively.

  • M and N represent the dimensions of the image.

  • 255 is the maximum possible intensity value for an 8-bit grayscale image.

This concept is helpful because a more excellent value of UACI stopped the original and watermarked (attacked) images closer together regarding changes between them, which can mean more resistance to attacks.

NPCR shows the percentage of pixels that have been changed after applying a watermark or attack against their original positions56,57,58. It is especially helpful in assessing the effectiveness of watermarking schemes against noise, rotation, or compression attacks.

NPCR is defined as

$$NPCR = \frac{{\mathop \sum \nolimits_{i = 1}^{M} \mathop \sum \nolimits_{j = 1}^{N} D\left( {i,j} \right)}}{M \times N} \times 100\backslash \%$$

where:

D(i,j) is a binary indicator that is 1 if the pixel values at position (i,j) in the two images are different, and 0 otherwise.

M and N are the dimensions of the image.

A larger value of NPCR (close to one (i.e. 100%) indicates high sensitivity with many pixel changes in the compared image. It detects the watermarking or encryption method is sensitive to attacks or modifications in an image.

Methodology

The propounded watermarking algorithm starts with DWT, which is applied to the HMI. DWT decomposes the image into multiple frequency sub-bands, effectively separating the image into different bands. The LL sub-band, chosen for its containment of the most significant visual information and its superior robustness for watermark embedding, undergoes HMD. This process simplifies the sub-band matrix into a more straightforward, nearly triangular form, enhancing computational efficiency while preserving critical image properties. Once HD is applied, the matrix is further processed using SVD. SVD, a key component in our algorithm, decomposes the simplified matrix into three components-two orthogonal matrices and a diagonal matrix of singular values. These singular values represent the fundamental features of the HMI and are less susceptible to degradation from attacks. By working on these singular values, watermark embedding is done with minimal impact on the image quality, ensuring imperceptibility and thereby maintaining the integrity of the original image.SVD suffers from the false- positive problem where, the extracted watermark may look similar to the original one, even when they are not same To eliminate this problem in the proposed work the SVD scheme is combined with the HMD so that the pixel values modified will spread across both frequency and structural components, making watermark detection more reliable.

Meanwhile, the watermark image undergoes Arnold Transform Scrambling, a crucial step in algorithm, to randomize its pixel positions, which enhances its security by making the watermark harder to detect. After scrambling, SVD is applied to the scrambled watermark image to extract its singular values shown in Fig. 7. The embedding process is then performed by integrating these singular values into the singular values of the HMI. This integration in the transformed domain ensures that the watermark is embedded in the most essential features of the HMI, providing a robust and imperceptible. Finally, the inverse SVD and inverse HD are applied to reconstruct the watermarked image, followed by the inverse DWT to transform it back to the spatial domain.

Fig. 7
figure 7

Watermark Processing in the propounded algorithm.

Full size image

The embedding process for the hybrid DWT-HMD-SVD is shown in Fig. 8. Robustness and imperceptibility of W* is analysed against various attacks. The results indicate that the combination exhibits greater resilience to attacks than their modifications.

Fig. 8
figure 8

Block Diagram of Propounded Algorithm Hybrid DWT-HMD-SVD-Arnold transform-Embedding of Watermark.

Full size image

Table 1 describes the propounded watermarking algorithm. The algorithm writes the Host image as HMI and the Watermark image as W.

Table 1 Literature review.
Full size table

Preprocessing of watermark

Experiment

The propounded algorithm is experimented with using HMI as 2 randomly selected brain tumours15, 2 chest Xray16, 2 Breast Ultrasound14, 2 COVID-19 CT-Scan13, and 2 COVID-19 Xray17. They are shown in Fig. 2. All the HMIs were pre-processed to size 512*512 and grayscale. The W considered for the propounded algorithm is shown in Fig. 4 and is in size 64*64 and in black and white nature. The attacks are listed in Table 2. The propounded method shows promising results against the no-attacks and attacks and adequately balances the robustness and imperceptibility. Addition to it, security and effectiveness is also ensured by getting satisfactory results of NPCR and UACI. The primary motivation of the propounded algorithm is to provide an extra dimension of security to the watermark by scrambling it before watermarking it to the HMI. The results of the propounded watermarking techniques are also compared with those of competent methods. Simulation parameters specifications are tabulated below in Table 2.

Table 2 Propounded Algorithm- Hybrid DWT-HMD-SVD-Arnold Transform.
Full size table

Results and discussion

The robustness between the original and extracted watermarks is evaluated using metric NC. The NC is an evaluation metric that quantifies how similar the extracted watermark is to its original form, with values closer to 1, meaning better robustness across different types of attacks. The propounded watermarking technique is tested for robustness under different attacks with NC values before and after the NO attack. Figure 9 shows that propounded algorithm shows NC value as 1 when no attack and considerable good results can also be seen when attack is applied. The robust watermark can be detected reliably in various image quality degradations, including high lossy compression, as JPEG or JPEG2000 has produced near-maximal NC values. On the other hand, the watermarking method fails to be as resilient against blurring attacks because small details necessary for detecting watermarks are lost. Because of the significant contrasts in pixel intensity, the vast loss of likeness is due to a histogram equalisation attack. For more clarity Table 2 shows the Results of Robustness (NC) for all Host medical images against all attacks. Table 2 shows one of the Sample watermark images (COVID-19 Xray in Table 2), attack type and their respective extracted watermark with PSNR and NC value. Table 3 shows the results of Robustness (NC) for all Host medical images against all attacks.

Fig. 9
figure 9

Robustness representation of all images under various attacks.

Full size image
Table 3 Simulation Parameters Specifications.
Full size table

The imperceptibility of the W* and HMI is evaluated using PSNR and SSIM. PSNR is used to demonstrate how much watermarked different attacks disrupt images. The higher the PSNR value, the less distortion we have, and the good PSNR results show that the algorithm works fine on many results. The results of PSNR against no attack and listed attacks are plotted in Fig. 10. A W* without attack has a baseline PSNR of 49.86. Different attacks are added individually, and changes in PSNR concerning each type reflect the influence level of such attacks on the quality of the watermarked images. PSNR for noise-based attacks has shown enormous deterioration of image quality. On the other hand, JPEG compression and JPEG2000 compression attacks achieve PSNR of 44.20,48.50, respectively, which is trivial because the watermarking algorithm is highly resistant due to this standard operation. Histogram equalisation is the method that results in the worst image quality, with a PSNR value of 16.62. Thus, there is scope for improvement in Histogram equalisation.

Fig. 10
figure 10

Imperceptibility representation of all images under various attacks.

Full size image

The SSIM is a measure used to compare two HMI to W* based on their structural, luminance, and contrast similarities. The results from Table 4 indicate that the watermarking scheme maintains high structural similarity, ensuring strong imperceptibility in most attack scenarios. The consistently high SSIM values (close to 1.00) across various datasets such as brain, breast, COVID, landscapes, lung, CT scan, and pneumonia show that the embedded watermark introduces imperceptible distortion in the perception of images, thus ensuring better perceptual quality. The watermarking scheme also demonstrates robustness against impairments like median filtering, sharpening, compression, and Gaussian low-pass filtering, with only a slight decrease in perceptual invisibility. However, noise-based distortions present a challenge, with the propounded method showing the best results among all other models, achieving acceptable SSIM values of 0.76 and 0. The results in Fig. 11 highlight the need for additional fine-tuned implementations to address noise-related artifacts in domains such as medical images, despite the watermarking method’s overall satisfactory performance. In summary, the watermarking scheme offers good imperceptibility with potential for improvement in specific attack situations.

Table 4 Results of Robustness (NC) for all Host medical images against all attacks.
Full size table
Fig. 11
figure 11

SSIM representation of all images under various attacks.

Full size image

The UACI is a metric used to measure the average intensity of differences between a watermarked image and its attacked version, specifically in terms of pixel values. A higher UACI value indicates a more significant change in pixel intensities, which suggests a more robust attack and greater image distortion. The Fig. 12 provided shows the UACI results for common attacks like salt and pepper noise, median filtering, JPEG compression, and speckle noise on different types of HMI. The results indicate that speckle noise causes the most significant intensity changes, especially for COVID-19 and COVID-19 images, with UACI values reaching up to 1.63. On the other hand, salt and pepper noise causes minimal intensity changes across all image types, with UACI values mostly below 0.06, suggesting it is a relatively mild attack. This analysis helps us understand how sensitive different images are to various attacks. UACI values are crucial indicators of how well the watermark withstands these distortions.

Fig. 12
figure 12

UACI representation of all images under various attacks.

Full size image

The Number of Pixels Change Rate (NPCR) is a metric used in digital image watermarking to measure the percentage of pixel differences between an original and attacked image. Higher values indicate more significant changes introduced by the attack. The NPCR results in the Fig. 13 show varying levels of pixel alteration across different image types when subjected to common attacks such as salt and pepper noise, median filtering, sharpening, and compression. The speckle noise attack produces the highest NPCR values, particularly for "COVID-1" and "COVID-2" images, with NPCR reaching 88.62% and 93.20%, indicating substantial pixel changes. On the other hand, salt and pepper noise results in the lowest NPCR values across all images, generally around 0.09–0.11%, demonstrating that it causes minimal pixel disturbance. Other attacks, like median filtering and JPEG compression, show moderate to high NPCR values, particularly affecting “breast” and "lung CT scan" images, making these attacks more disruptive in terms of pixel alterations. This analysis highlights the robustness of the watermarking system against different types of attacks, with speckle noise and JPEG compression causing the most substantial pixel changes.

Fig. 13
figure 13

NPCR representation of all images under various attacks.

Full size image

The results are compared and presented in Table 5, which highlights the robustness comparison with other algorithms.

Table 5 Sample watermark images, attack type and their respective extracted watermark.
Full size table

Further results are also explored by evaluating the Algorithm’s capacity. Capacity is evaluated to understand the Proportion of embedded data.

Capacity = (No. of watermark bits Embedded/total num of bits in host image) *100

Here, the total number of bits in the host image is 512*512, and the number of embedded watermark bits is 64*64. So, the capacity will be evaluated as 1.56% (Table 6).

Table 6 Robustness comparison with other algorithms.
Full size table

Results are also explored in terms of computational time, and analysis is shown in Fig. 14.

Fig. 14
figure 14

Computational analysis of algorithms.

Full size image

Conclusion

In this article, a novel hybrid transformation-based watermarking algorithm is propounded. The algorithm specifically secured the watermark by scrambling, and then the watermark was decomposed using SVD. The necessity of any new watermarking algorithm is to have a balance between Robustness and imperceptibility. The propounded algorithm has successively achieved the desired balance. This paper is experimented with the robustness and imperceptibility of a digital watermarking scheme using DWT, HMD, SVD, and Arnold Transform applied to the medical images used as host medical images and a binary watermark. The results show that the propounded method effectively preserves Imperceptibility (PSNR and SSIM) and Robustness (NC) against attacks, including filtering, compression, and noise addition. In addition to it, algorithm also perform better and give competitive results for UACI and NPCR. However, the watermarking scheme shows vulnerability to aggressive attacks such as Gaussian noise and histogram equalization, indicating potential areas for enhancement. Further, future work considering more attacks can better analyse the algorithm. Adjusting watermarking parameters using optimization techniques can improve the results. Amalgamating machine learning and deep learning models while watermarking the host medical image can significantly improve robustness and imperceptibility. In future following works can be done:

  • Optimization algorithms can be employed to optimize the strength factor value and results can be compared.

  • The deep learning algorithms can be implemented to extract the watermark image.

  • The work can also be implemented on large datasets to prove its practical applicability.

  • Embedding can be done on robust pixel location values to improve the robustness against multiple attacks.