A Robust Multi-Transform Watermarking Scheme for Medical Images Using DTCWT, DCT, and SVD

In the context of telemedicine based on medical imaging, unauthorized access to or modification of diagnostic images poses significant medical and legal risks, as it may lead to diagnostic errors and inappropriate treatments [1]. Moreover, the secure transmission and exchange of radiological data between healthcare institutions and medical professionals is a key factor in promoting multidisciplinary collaboration and obtaining specialized consultative expertise [2].

The preservation of healthcare information integrity necessitates adherence to three fundamental pillars: confidentiality, reliability, and availability. Confidentiality encompasses the implementation of comprehensive privacy safeguards and the establishment of stringent access controls to protect sensitive medical data from unauthorized disclosure [3]. Reliability constitutes the assurance of information authenticity and immutability, guaranteeing that data remains uncompromised and forensically verifiable throughout its lifecycle [4]. Availability guarantees that authorized personnel can consistently access vital information, preventing service interruptions that might hinder clinical decisions [5]. Consequently, the implementation of robust mechanisms to safeguard both the integrity and provenance of medical imaging data emerges as an imperative priority within contemporary healthcare infrastructure [6].

Modern healthcare infrastructures rely on multi-layered security architectures that encompass access control protocols, firewalls, anti-malware solutions, intrusion detection systems, steganographic techniques, and cryptographic frameworks. Steganographic methods operate based on information concealment models, prioritizing covert data protection over transparent accessibility. Although cryptographic algorithms are the primary tools for ensuring the integrity of medical data. They possess an inherent vulnerability: once decrypted, the previously protected information becomes susceptible to unauthorized manipulation [7].

In contrast, digital watermarking facilitates image authentication and provenance tracking, enabling detection of unauthorized modifications and source verification. Such functionality holds exceptional significance for safeguarding the fidelity of medical imaging data across all operational phases—spanning initial capture, archival processes, data transfer, and diagnostic evaluation [1]. Digital watermarking technology embeds identifying markers within host images while ensuring negligible and undetectable alterations, thereby preserving visual fidelity. Following embedding, the marked image undergoes transmission to designated receivers who authenticate its legitimacy through watermark extraction and verification processes [8]. Watermarking extraction occurs through blind, semi-blind, or non-blind methods, differentiated by original image dependency. While visible watermarks exist, invisible implementations dominate due to superior security and copyright enforcement. These invisible techniques split between robust (ownership protection) and fragile (tamper detection) applications [9]. Watermarking operates through spatial domain (direct pixel embedding via Local Binary Pattern (LBP) [10]. Least Significant Bit (LSB) [11], Direct Sequence Spread Spectrum (DSSS) [12], Intermediate Significant Bit (ISB) [13], and Pixel Value Differencing (PVD) [14] or frequency domain (coefficient modification post-transformation) [7, 15] techniques. Frequency-domain techniques embed watermarks within transformed image representations rather than raw pixel data [9]. These approaches utilize various mathematical transformations including Redundant Discrete Wavelet Transform (RDWT) [16], Discrete Wavelet Transform (DWT) [15, 17, 18], Discrete Cosine Transform (DCT) [15, 17, 19], Lifting Wavelet Transform (LWT) [7, 20, 21] and Integer Wavelet Transform (IWT) [22, 23]. Operating in the transform domain offers superior embedding efficiency and enhanced resistance to attacks compared to spatial methods. Recent advances have explored hybrid strategies that synergistically combine multiple transforms, resulting in improved visual transparency and strengthened security against malicious attacks [24].

This study aims to create an effective watermarking solution for medical imagery that balances maintaining image fidelity with strengthening protection against different attacks. The proposed approach combines three key transformation methods Dual-Tree Complex Wavelet Transform (DTCWT), Discrete Cosine Transform (DCT), and Singular Value Decomposition (SVD) to build a unified security architecture. The DTCWT provides quasi shift-invariant properties and improved directional discrimination, producing several complex-valued subbands that substantially expand the embedding potential [24]. Meanwhile, the DCT enhances durability against compression-related distortions [25], and the SVD utilizes its geometric stability properties to reinforce resistance across various attack conditions [7]. This integrated multi-transform strategy simultaneously enhances embedding volume, attack tolerance, and visual imperceptibility, thus fulfilling the essential demands of watermarking in medical imaging applications.

3.1 Dual tree complex wavelet transform

Among advanced transformation techniques, DTCWT distinguishes itself by integrating the favorable attributes of both DWT and CWT transforms. This transformation provides exact reconstruction capabilities, efficient computation, near shift-invariance properties, and selective directional filtering mechanisms [34]. Unlike the single-tree architecture of conventional DWT, the DTCWT implements a dual-tree structure that creates two separate coefficient sets, which are then merged to form complex-valued coefficients. In practice, DTCWT employs two separates real DWTs using different filter banks, where one DWT generates the real component of the transform and the other produces the imaginary component [24]. This transform has proven successful in various image processing applications such as classification, denoising, segmentation, enhancement procedures, and watermark insertion. Within watermarking contexts, the quasi shift-invariant property of DTCWT offers significant benefits, enabling embedded information to withstand geometric transformations while maintaining minimal distortion [35]. Moreover, the transform's superior perceptual features, particularly through improved directional analysis of high-frequency components compared to DWT, facilitate the embedding of more imperceptible watermarks. When applied to two-dimensional images, DTCWT generates distinct coefficient structures at each decomposition level, comprising two complex-valued low-frequency subbands and six complex-valued high-frequency subbands. These high-frequency components are derived from six directionally-selective filters oriented at ±15°, ±45°, and ±75° angles [36]. Figure 1 demonstrates how the initial decomposition level of an input image through DTCWT produces this particular collection of subbands. The complex-valued coefficients obtained from this decomposition process can be mathematically expressed as [24]:

Figure 1. The DTCWT's first-level decomposition subbands

${{Z}_{Lev,dir}}=Y_{Lev,dir}^{real}+jY_{Lev,dir}^{im}$    (1)

where, $Lev$ refers to the decomposition level, while $dir$ signifies the directional angles of ±15°, ±45°, and ±75°, which characterize the complex HF components (indexed $dir$ from 1 to 6). The $Y_{Lev,dir}^{real}~$and $jY_{Lev,dir}^{im}$ terms denote the real and imaginary portions, respectively, collected during the DTCWT's dual-tree decomposition [24].

3.2 Discrete cosine transform

Image processing applications, especially JPEG compression systems, rely heavily on a core mathematical procedure known as the Discrete Cosine Transform (DCT). Through its two-dimensional implementation (2D DCT), this technique enables the transformation of M×N spatial image data into its equivalent frequency domain representation according to the mathematical formulation [8]:

$\begin{gathered}T(l, m)=b(l) b(m) \sum_{p=0}^{M-1} \sum_{k=0}^{N-1} t(p, k) \times \cos \left(\frac{(2 p+1) l \pi}{2 N}\right) \times \cos \left(\frac{(2 k+1) m \pi}{2 N}\right)\end{gathered}$    (2)

Within this mathematical framework, t(p, k) denotes the intensity value of a pixel located at position (p, k) in the source image, while the output coefficient at frequency coordinates (u, v) is given by the transformed value. The normalization parameters b(u) and b(v) serve as scaling constants that ensure proper mathematical consistency, established as [37]:

$\begin{aligned} & b(l)=\left\{\begin{array}{cc}\sqrt{\frac{1}{M}} & \text { for } \mathrm{l}=0 \\ \sqrt{\frac{2}{M}} & \text { for } \mathrm{l}=1,2, \ldots, M-1\end{array}\right. \\ & b(m)=\left\{\begin{array}{lc}\sqrt{\frac{1}{N}} & \text { for } \mathrm{m}=0 \\ \sqrt{\frac{2}{N}} & \text { for } \mathrm{m}=1,2, \ldots, N-1\end{array}\right.\end{aligned}$    (3)

Of course, we often need to get the image back, that’s where the 2D-IDCT comes in. It essentially reverses the 2D-DCT process, transforming the frequency data T(l,m) back into the original spatial pixel values t(p,k). You calculate it like this [8]:

$\begin{gathered}t(p, k)=\sum_{l=0}^{M-1} \sum_{m=0}^{N-1} b(l) b(m) T(l, m) \times \cos \left(\frac{(2 p+1) l \pi}{2 N}\right) \times \cos \left(\frac{(2 k+1) m \pi}{2 N}\right)\end{gathered}$    (4)

3.3 Singular value decomposition

A fundamental matrix factorization technique, Singular Value Decomposition (SVD) is widely acknowledged as one of the most powerful linear algebra methodologies. This approach enables the identification of crucial structural characteristics within matrices and finds particularly valuable applications in image analysis and related fields. The core principle involves transforming an original matrix into three distinct matrix components, thereby creating a condensed representation of the source matrix's key elements [30].

Given any matrix (or image) I, SVD decomposes it into three distinct matrices namely U, S, and V which satisfy the relation [38]:

$A=U * S * V^t=\sum_{i=1}^n\left(\sigma_i * u_i * v_i^t\right)$    (5)

Matrix S exhibits a diagonal structure containing the singular values ${{\sigma }_{i}}$ [38]:

$S=\left[\begin{array}{ccc}\sigma_i & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & \sigma_n\end{array}\right]$    (6)

The SVD components include orthogonal matrices U and V, whose columns are the eigenvectors of $I{{I}^{T}}$ and ${{I}^{T}}I$, respectively. These vectors expose the image's key geometric features. The diagonal matrix $S=diag({{\sigma }_{i}}\ldots {{\sigma }_{n}})$ contains the singular values arranged in decreasing order, representing the significance of each corresponding vector [7]. In the context of image processing, particularly for digital watermarking applications, SVD holds a central position. Its advantages encompass the identification of dominant visual components, satisfactory stability, resistance to signal processing transformations, and efficient representation of visual information. Minor adjustments to singular values maintain the perceptual quality of the image. Furthermore, this methodology imposes no dimensional restrictions on the input image matrix [39].

The evaluation of the proposed watermarking approach focuses on imperceptibility, robustness, and comparative analysis. Experiments were conducted on diverse medical imaging types, including X-ray, CT, MRI, and Ultrasound (Figure 4), with all images standardized to 512 × 512 pixels and obtained from different datasets [42, 43]. Institutional logos and other watermark patterns (Figure 5) [7] were embedded at multiple resolutions (256 × 256, 128 × 128, 64 × 64). The experiments were conducted using MATLAB R2022b on a Windows 10 platform equipped with an Intel Core i5 processor (3.2GHz) and 8GB of RAM.

Figure 4. Sample medical imaging modalities: (I) Thoracic1_CT, (II) Spinal_MRI, (III) Chest1_X-ray, (IV) Thoracic2_CT, (V) Lumbar_MRI, (VI) Chest2_X-ray, (VII) Ovarian_Ultrasound, (VIII) Fetal_Ultrasound

Figure 5. Test watermarks

5.1 Gain factor selection

The gain factor α controls the balance between the imperceptibility and watermark robustness: reducing α minimizes image distortion but compromises watermark strength, while increasing α enhances durability but degrades visual quality, as demonstrated in Figure 6. To determine the ideal value, we tested α values from 0.1 to 1.0 in 0.1 increments, measuring mean PSNR and NC values across various medical image types. We established two criteria: (I) visual quality requirements with PSNR ≥ 64dB to maintain diagnostic integrity, and (II) durability requirements with NC ≥ 0.999982 under Gaussian noise conditions (σ² = 0.001). Analysis revealed that only the 0.5-0.6 range met both requirements simultaneously. Values below 0.5 provided inadequate durability, while values above 0.6 produced noticeable quality loss. Consequently, α = 0.6 was chosen as the standard embedding parameter, offering optimal equilibrium between imperceptibility and watermark robustness for medical imaging applications.

Figure 6. (a) PSNR values of the watermarked images in relation to the scaling parameter (α) and (b) Performance of the recovered watermark relative to the scaling parameter α following Gaussian noise (σ²=0.001)

5.2 Imperceptibility analysis

We assess the effectiveness of the proposed scheme in this section by focusing on its main performance attributes: imperceptibility and robustness. Our assessment methodology includes both a qualitative visual review and a rigorous quantitative evaluation. To ensure the watermark does not compromise data confidentiality, it must remain undetectable to the human eye. We adhere to widely accepted quality benchmarks to verify this: an image is considered to have high fidelity when its PSNR is 29dB or greater [44], while an SSIM value of 0.90 or higher is another crucial benchmark for confirming that perceptual quality is maintained [45]. In contrast, significant distortion is present if the PSNR drops below 25dB [44].

Figure 7. Watermarked images with corresponding extracted watermarks (no attack)

Table 1. PSNR and SSIM measurements for diverse watermarked images

Table 2. Assessment of imperceptibility performance across varying parameter settings (host images and watermarks of different dimensions)

Figure 7 demonstrates that both the watermarked image and the extracted watermark retain excellent visual quality, validating the efficiency of the proposed method. PSNR and SSIM measurements for various categories of watermarked medical images are displayed in Table 1, together with NC values for the recovered watermarks. The peak PSNR and SSIM values attained were 64.67 and 1.0000, respectively. These metrics reflect superior visual transparency and strong resemblance between original images and their watermarked versions. Additionally, the elevated NC values (NC=1.0000) validate the extraction algorithm's robust performance.

Imperceptibility results obtained through extensive experimentation using different host images and varied watermarks (W_a-W_e) with multiple dimensions (256×256, 128×128 and 64×64) are presented in Table 2. The findings indicate that the watermarked images and their corresponding extracted watermarks consistently exhibit high visual quality. Moreover, the embedded watermarks remain fully imperceptible, preserving the original image content. Quantitative evaluation further supports this observation, with PSNR values exceeding 57.98dB and SSIM and NC scores greater than 0.9999, thereby confirming the strong invisibility performance of the proposed approach.

5.3 Effect of payload size on watermarked image imperceptibility and robustness

The embedding capacity significantly affects watermarked image quality when tested on eight medical images from different modalities with payloads between 0.1 and 2 BPP. As illustrated in Figure 8 the PSNR decreases steadily from 85dB at 0.1 BPP to 58dB at 2 BPP, showing that image quality reduces as more data is embedded. However, the SSIM remains consistently high, dropping only slightly from 0.99998 to 0.99975, which indicates that the visual appearance and structure of the medical images are well preserved across all modalities tested. The NCC values show initial improvement from 0.1 BPP to around 1.0 BPP before stabilizing above 0.9999975, suggesting good correlation maintenance between original and watermarked images. These findings demonstrate that despite the PSNR reduction, the watermarking method maintains excellent visual quality and structural integrity across different medical imaging types. The results indicate that embedding capacities between 1.0-2.0 BPP provide a practical balance, offering sufficient space for patient data while preserving the diagnostic quality essential for medical applications across various imaging modalities.

Figure 8. Effect of payload size on watermarked image imperceptibility and robustness

5.4 The computational complexity

The computational cost of the presented DTCWT-DCT-SVD watermarking framework primarily stems from the DTCWT, the 2D-DCT, and the SVD. For a host image of size M×M, a single-level DTCWT requires O(M²) operations, while DCT2 on the high-frequency subband adds O (M² log M). The subsequent SVD contributes O(M³) in the worst case, though the effective cost is reduced since it is applied to smaller subband blocks (e.g., 256 × 256). Embedding and extraction involve modifying singular values linearly with the watermark length L, i.e., O(L). Overall, the scheme has a dominant complexity of approximately O(M³).

In practice, the method was implemented in MATLAB R2022b on a desktop computer with an Intel Core i5-6th CPU (3.2GHz) and 8GB RAM. For 512 × 512 medical images, the average embedding time was 1.6035s, while extraction required 1.1405s (Table 3).

These results demonstrate that the DTCWT-DCT-SVD algorithm is highly efficient, provides excellent imperceptibility and robustness, and is well-suited for secure medical image transmission. Further speedups can be obtained via GPU parallelization or optimized compiled languages.

Table 3. Computational duration measurements for medical image samples

5.5 Robustness analysis

In medical imaging applications, where diagnostic precision directly affects patient treatment decisions, ensuring image authenticity and integrity represents a fundamental requirement. Protecting these critical data assets from unauthorized modifications or attacks is therefore essential for maintaining clinical reliability. Once imperceptibility benchmarks are satisfied, thorough robustness validation through systematic attack testing becomes necessary. To establish system robustness, watermark extraction capability is evaluated across a comprehensive attack spectrum. The robustness evaluation encompasses 23 distinct attack scenarios organized into six primary categories. Geometric transformations include rotation, rescaling, directional flipping, cropping, and translation operations. Signal processing attacks involve sharpening, Gaussian LP filtering, Wiener filtering, average filtering, and median filtering techniques. Noise contamination testing employs speckle, Gaussian, and salt-and-pepper noise variants. Compression-based attacks utilize both JPEG and JPEG2000 standards. Image adjustment testing focuses on histogram equalization, while content manipulation assessment includes copy-paste operations. System robustness assessment relies on calculating the (NC) coefficient between the original and extracted watermarks. An NC threshold of 0.75 or above is generally considered acceptable for determining successful watermark recovery [32].

Table 4 details the robustness evaluation for Lumbar_MRI/Wc set to gain factor =0.6, where the system's robustness was tested against various image processing and geometric attacks across three watermark sizes: 256×256, 128×128, and 64×64. The watermarking system demonstrates exceptional robustness with NC values consistently exceeding 0.9999 across all sizes. Perfect recovery (NC = 1.0000) occurs for rotation (2°), rescaling (2), cropping (2%), and sharpening attacks across all watermark sizes. Near-perfect performance (NC ≥ 0.9999) is achieved for speckle noise, Gaussian noise, JPEG 2000 compression, JPEG compression (QF = 50), Gaussian LPF, Wiener filter, and median filter attacks. Geometric attacks show strong resilience, with 45° rotation maintaining NC values of 0.9999-0.99998 across different sizes. Salt and pepper noise demonstrates robust performance with NC values ranging from 0.99995-0.99999. Motion blur and histogram equalization preserve strong performance, with NC values of 0.99991-0.99999 and 0.99991-0.99997 respectively. Average filtering shows the most variation across sizes, with NC values ranging from 0.99993 (64 × 64) to 0.99999 (256×256). Overall, watermark size impact is minimal, with even the smallest 64×64 watermarks maintaining NC values above 0.99991, indicating consistent scale-invariant performance across all payload sizes.

To further evaluate the resilience of the proposed watermarking methodology, supplementary testing with different parameter configurations across various attack scenarios has been performed using the "Thoracic2_CT" host image (512 × 512 pixels) and the "W_e" watermark (256 × 256 pixels). The obtained outcomes are presented in Table 5. Translation (dx = -30, dy = -90), flip direction, and copy-paste operations achieve perfect recovery (NC = 1.0000), demonstrating complete resilience to geometric transformations and content manipulation. Noise attacks show strong performance: Gaussian noise (Var = 0.05) yields NC = 0.99902, salt and pepper noise achieves NC = 0.99944, and speckle noise demonstrates highest resilience with NC = 0.99975. The extracted watermark images confirm successful recovery across all attacks, with the "LTSS" logo remaining clearly visible and recognizable.

Table 4. Watermarking system robustness under various attacks: Lumbar_MRI with W_c at alpha = 0.6

Table 5. Extracted watermark samples under multiple attack types at alpha =0.6

5.6 Comparison of performance with other schemes

To assess the proposed watermarking method's performance, a comparative analysis is conducted against current leading techniques from recent research. The evaluation focuses on highlighting the strengths and weaknesses of our approach compared to existing methods, with particular emphasis on visual quality preservation and robustness against various attacks—critical requirements for effective copyright protection and image verification. Fair comparison is ensured through standardized testing using identical cover images and watermark data across all evaluated methods. The evaluation dataset comprises diverse medical imaging modalities at 512×512 pixel resolution, with embedded watermark (W_c) at 256×256 pixel dimensions.

Table 6 compares PSNR values of the proposed method against four recent watermarking techniques across different medical images. The proposed method achieves consistently superior performance with PSNR values ranging from 64.20-64.67dB across all tested modalities (X-ray, CT, MRI, and US images), representing improvements of approximately 15-21dB over competing methods. The existing techniques show lower performance, with Awasthi and Srivastava [30] achieving 42.90-42.96dB, Latreche et al. [7] demonstrating 42.99-43.04dB, and Chaudhary et al. [46] showing 48.95-49.61dB. This substantial improvement of approximately 15-21dB indicates the proposed method's superior ability to preserve diagnostic image quality while embedding watermarks, demonstrating its effectiveness for medical image watermarking applications where maintaining visual fidelity is critical.

Table 7 presents a robustness comparison between the proposed method and four existing approaches based on Normalized Correlation (NC) values under different attack conditions. NC values closer to 1.0 indicate better watermark recovery after attacks. The proposed method exhibits outstanding robustness, achieving perfect NC values of 1.0000 for most attacks, including rotation, rescaling (factor 2), cropping, sharpening, speckle noise, JPEG compression variants, Wiener filter, and median filter, while maintaining NC values above 0.99999 for rescaling (0.5), salt and pepper noise, Gaussian noise, motion blur, histogram equalization, and Gaussian low-pass filter. This consistent performance indicates excellent resilience against both geometric and signal processing attacks. In contrast, competing methods show significant vulnerabilities to specific attacks. Notably, Awasthi and Srivastava [30] and another variant [30] exhibit sharp performance degradation under histogram equalization (NC ≈ 0.71), while Latreche et al. [7] show reduced performance (NC=0.8571). The existing methods also demonstrate lower performance under rotation attacks, with Awasthi and Srivastava [30] achieving NC values of 0.7502 and 0.7625, compared to the proposed method's perfect 1.0000. Chaudhary et al. [46] show moderate performance where data is available but has limited coverage across attack types (marked as N/A for many scenarios). This comprehensive superiority across diverse attack types validates the proposed framework's enhanced robustness for practical watermarking applications.

Table 6. Comparative PSNR analysis: Proposed scheme vs. Awasthi and Srivastava [30], Latreche et al. [7], and Chaudhary‏ et al. [46]

Table 7. Comparative NC analysis: Proposed scheme vs. Awasthi and Srivastava [30], Boubakeur et al. [7], and Chaudhary‏ et al. [46]