Abstract
This paper proposes a novel method for embedding a digital watermark based on adaptive selection of ring radii in the spectral domain of the Discrete Fourier Transform (DFT). The method involves dynamically forming embedding zones based on the energy profile of the image, which improves the watermark's robustness against frequency-domain distortions. To compensate for geometric attacks, auxiliary synchronization information is embedded using the Dual-Tree Complex Wavelet Transform (DTCWT). Theoretical modeling demonstrates that the proposed approach retains high effectiveness under JPEG compression, blurring, noise addition, rotation, and scaling, including in biomedical image contexts. The method exhibits strong imperceptibility (PSNR > 38 dB) and high watermark recovery accuracy (NCC > 0.8, BCR > 80%) even under combined attacks, validating its applicability for digital content protection systems.