Robust Watermarking Algorithm for Medical Images Based on Non-Subsampled Shearlet Transform and Schur Decomposition

With the development of digitalization in healthcare, more and more information is delivered and stored in digital form, facilitating people's lives significantly. In the meanwhile, privacy leakage and security issues come along with it. Zero watermarking can solve this problem well. To protect the security of medical information and improve the algorithm's robustness, this paper proposes a robust watermarking algorithm for medical images based on Non-Subsampled Shearlet Transform (NSST) and Schur decomposition. Firstly, the low-frequency subband image of the original medical image is obtained by NSST and chunked. Secondly, the Schur decomposition of lowfrequency blocks to get stable values, extracting the maximum absolute value of the diagonal elements of the upper triangle matrix after the Schur decomposition of each low-frequency block and constructing the transition matrix from it. Then, the mean of the matrix is compared to each element's value, creating a feature matrix by combining perceptual hashing, and selecting 32 bits as the feature sequence. Finally, the feature vector is exclusive OR (XOR) operated with the encrypted watermark information to get the zero watermark and complete registration with a third-party copyright certification center. Experimental data show that the Normalized Correlation (NC) values of watermarks extracted in random carrier medical images are above 0.5, with higher robustness than traditional algorithms, especially against geometric attacks and achieve watermark information invisibility without altering the carrier medical image.