A Watermarking Method Utilizing SVD

In the field of information protection, a watermarking method based on the Singular Value Decomposition (SVD) algorithm can be effectively applied. Singular Value Decomposition is a fundamental matrix factorization technique widely used in various domains including image processing and data dimensionality reduction. By leveraging the SVD algorithm, we can implement watermark embedding and extraction processes to safeguard data security and integrity. The implementation typically involves decomposing the host matrix (e.g., image data matrix) into three components using the SVD operation: U, S, and V matrices. The watermark information is embedded by modifying the singular values in the S matrix, which represent the fundamental geometric properties of the data. For extraction, the inverse SVD process is performed to recover the embedded watermark while maintaining minimal distortion to the original data. Key functions in implementation would include: 1. svd() function for matrix decomposition 2. Custom algorithms for singular value modification 3. Reconstruction techniques using matrix multiplication of U, modified S, and V transpose This approach provides robust watermarking with good resistance to common signal processing operations due to the stability of singular values.