A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution [version 1; peer review: 2 approved with reservations, 1 not approved]

Background The proposed watermarking framework is based on the multi-resolution Walsh-Hadamard Transform (MR-WHT) along with Schur factorization. For embedding, the cover image is converted into a frequency domain using MR-WHT before Schur factorization is applied. Methods The upper triangle's highest stable eigenvalues in the Schur factorization are employed as reliable embedding locations for the watermark. The singular values of these coefficients are updated with the singular values of the watermark, and the matrix array generated by the biggest eigenvalues is further factorised by singular value decomposition using multiple scaling factors and Differential evolution (DE). Later, an inverse SVD, inverse Schur, and inverse multiresolution Walsh-Hadamard transform is executed to obtain a watermarked image. Results The simulation results show that the proposed method is imperceptible and robust against existing watermarking algorithms used in the literature.