FS-VMADW: a frequency–spatial vision mamba framework for dual watermarking of medical MRI images

Abstract Secure transmission and copyright protection of medical images require watermarking methods that preserve image quality and enable reliable payload recovery. However, the currently available deep watermarking architectures either encode only a single watermark or use convolutional networks with inherently restricted receptive fields, which limits their ability to capture long-range anatomical dependencies in medical images. Moreover, spatial modeling alone does not explicitly capture the frequency characteristics that influence watermark imperceptibility and robustness. This work proposes FS-VMADW - a Frequency-Spatial Vision Mamba Dual Watermarking architecture for abdominal MRI security. The proposed encoder combines the Vision Mamba spatial branch with a four-direction selective scan of state-space models applied with linear complexity, along with a two-stage Haar Discrete Wavelet Transform frequency branch, which are fused with a gating module generating location-specific weighting of spatial and frequency feature maps. Two independent spread-spectrum carriers encode two 64-bit binary watermarks, while an adaptively generated Vision Mamba mask controls their embedding. A two-phase training curriculum mitigates the gradient conflict between imperceptibility and extraction fidelity by decoupling the two objectives across successive training phases. Experiments on the CHAOS abdominal MRI benchmark demonstrate PSNR = 42.37 dB, SSIM = 0.9557, NC = 0.9511, BER = 0.0491, and BitAcc = 0.9509 under clean conditions. Controlled backbone comparisons further show that Vision Mamba outperforms CNN and Transformer alternatives, while the addition of DWT provides further improvements in both imperceptibility and watermark recovery. These results demonstrate that long-range spatial modeling and multi-scale frequency information provide complementary benefits for dual watermarking of medical images.