## 2 Related Work  
In the pursuit of robust watermarking systems for telemedicine applications, researchers have explored various methodologies, including spatial and frequency-based approaches, to embed watermarks within medical images. Frequency domain watermarking techniques leverage transforms such as the DCT, the DWT, or SVD to decompose the image into frequency components. These methods offer enhanced robustness against certain types of attacks while preserving image fidelity, making them well suited for applications in telemedicine where image quality is paramount for accurate diagnosis [9]. By embedding the watermark within the frequency domain, researchers aim to achieve a balance between imperceptibility and robustness. Frequency-based methods exploit the properties of these transforms to ensure that the watermark is resilient to common attacks [10] such as compression, noise addition, and geometric alterations. However, frequency domain watermarking techniques may also face challenges, such as increased computational complexity and potential perceptual distortion [11]. Despite these challenges, ongoing research efforts continue to explore novel frequency domain watermarking techniques aimed at bolstering the security and integrity of medical images in telemedicine applications. The Wavelet Transform (DWT) is a mathematical technique used to decompose a signal into frequency components while capturing their locations. Unlike the Discrete Fourier Transform (DFT), which only provides frequency information, the DWT offers additional positional information [12]. This decomposition into frequency bands with spatial information (low-frequency details, high-frequency details at specific locations) makes the DWT particularly valuable for image watermarking. The ability to target specific frequency bands and locations within the image allows for precise watermark embedding, leading to a wide range of possibilities for robust watermarking techniques, as evidenced by the numerous DWT-based watermarking systems [6]. [PERSON] et al. [13] developed a medical image watermarking technique that integrates multiple text and image watermarks. They first applied the DWT to the image, then SVD to the HH, HL, and LH sub-bands. The text watermark is embedded into the singular values of the HH sub-band, while the image watermarks are embedded into the singular values of the LH and HL sub-bands. To enhance security, the watermarked image is then encrypted using hyperchaotic encryption. [PERSON] and [PERSON] [14] used a DWT to transform the blue component of medical images. The LL sub-band is transformed using a fast Walsh-Hadamard transformation. Next, SVD is performed on the acquired blocks. The watermark bits are then incorporated into the singular values of the S matrix. To further protect the watermarked image, it is scrambled using the Arnold transform. In the paper of [PERSON] and [PERSON] [6], a robust watermarking scheme for Digital Imaging and Communications in Medicine (DICOM) images is proposed. To ensure security, the binary watermark is first encrypted with a logistic chaotic map, then embedded into the cover DICOM image by dividing it into blocks. Subsequently, the blocks undergo a first-level DWT to decompose them in the frequency domain. A random set of coefficients within each block is then selected using a secret key. Finally, the encrypted watermark is embedded based on a rank-based criterion within these chosen coefficients. The approach of [PERSON] et al. [15] performed zigzag scanning, then reorganized the coefficients within the Lifting Wavelet Transform (LWT) LL sub-band for watermark integration. The method of [PERSON] et al. [16] prioritized security through a two-step embedding process. The cover image undergoes a DWT decomposition, followed by the selection of specific sub-bands for watermark integration. To enhance robustness, these sub-bands are further transformed using SVD.