A Gaussian quantum-inspired optimization framework for robust medical image watermarking

The rapid exchange of medical images through telemedicine and cloud-based healthcare systems has increased the need for secure transmission while preserving the diagnostic quality of medical data. Digital image watermarking provides an effective solution by ensuring data authenticity, integrity, and confidentiality without significantly affecting image quality. However, achieving an optimal balance between watermark imperceptibility and robustness remains a challenging task because the embedding strength must be carefully selected. To address this challenge, this paper proposes a robust medical image watermarking framework based on Discrete Wavelet Transform (DWT), Hessenberg Decomposition (HD), Singular Value Decomposition (SVD), and a Gaussian Quantum-Behaved Particle Swarm Optimization (GQBPSO) algorithm for adaptive embedding factor optimization. The watermark is first secured using a scrambling strategy and then embedded into the singular values of the transformed host image. Unlike conventional optimization approaches, the proposed GQBPSO employs Gaussian-guided quantum-inspired particle updates to achieve a better balance between global exploration and local exploitation, enabling adaptive selection of the embedding strength for improved watermark quality. The proposed framework is evaluated on publicly available chest X-ray and diabetic retinopathy datasets under a comprehensive set of image processing, noise, filtering, and geometric attacks. Experimental results demonstrate that the proposed GQBPSO consistently outperforms QPSO and QDPSO in terms of imperceptibility while maintaining competitive robustness. The proposed method achieves a maximum PSNR of 50.166 dB and maintains high Normalized Correlation (NC) values under various attack conditions. These results demonstrate that the proposed framework provides an effective balance between image quality and watermark robustness, making it a promising solution for secure medical image storage and transmission in modern healthcare systems.