Robust Watermarking in Multiresolution Walsh-Hadamard Transform

In this paper, a newer version of Walsh-Hadamard Transform namely multiresolution Walsh-Hadamard Transform (MR-WHT) is proposed for images. Further, a robust watermarking scheme is proposed for copyright protection using MRWHT and singular value decomposition. The core idea of the proposed scheme is to decompose an image using MR-WHT and then middle singular values of high frequency sub-band at the coarsest and the finest level are modified with the singular values of the watermark. Finally, a reliable watermark extraction scheme is developed for the extraction of the watermark from the distorted image. The experimental results show better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks.

💡 Research Summary

The paper introduces a novel multiresolution version of the Walsh‑Hadamard Transform (MR‑WHT) and employs it together with Singular Value Decomposition (SVD) to create a robust image watermarking scheme. The MR‑WHT is constructed by applying the one‑dimensional Walsh‑Hadamard Transform sequentially along rows and columns, then recursively decomposing the result into four sub‑bands (LL, LH, HL, HH) at each level, thereby providing a hierarchical frequency representation similar to wavelet decompositions.

The watermark embedding process works as follows: the host image is transformed by an L‑level MR‑WHT; the HH sub‑band from the coarsest (largest scale) and the finest (smallest scale) levels are selected; each selected HH sub‑band undergoes SVD, yielding orthogonal matrices U and Vᵀ and a diagonal singular‑value matrix Σ. The watermark image (typically 64×64 gray‑scale) is also decomposed by SVD to obtain its singular values Σ_w. Instead of altering the largest singular values (which heavily affect visual quality) or the smallest ones (which are highly sensitive to noise), the algorithm modifies the middle singular values of Σ by adding a scaled version of the corresponding watermark singular values: Σ′(p) = Σ(p) + α·(Σ_w(p) – μ_Σ_w), where p denotes a middle index and α is a strength factor. The modified Σ′ together with the original U and Vᵀ reconstructs a modified HH sub‑band; inverse MR‑WHT finally yields the watermarked image.

Extraction mirrors the embedding steps: both the possibly attacked watermarked image and the original host image are subjected to the same MR‑WHT and SVD; the middle singular values of the HH sub‑bands are retrieved, and the watermark is reconstructed by inverse SVD. The similarity between the extracted watermark and the original is measured by the correlation coefficient.

Experiments use 512×512 standard gray‑scale test images (Payaso, Yacht, Zelda) and three 64×64 watermark images (Peacock, Cup, IEEE CS). The watermarked images achieve Peak Signal‑to‑Noise Ratios between 46 dB and 49 dB, indicating negligible visual distortion. Robustness is evaluated against a comprehensive set of attacks: 100 % Gaussian noise, 13×13 Gaussian blur, 100 % salt‑and‑pepper noise, JPEG compression (CR = 100), deletion of 20 rows and 20 columns, pixelation, cropping leaving only 2.5 % of the area, vertical and horizontal flipping, sharpening, and geometric wrapping. Correlation coefficients after attacks are generally above 0.9; even the most severe attacks (row/column deletion) retain coefficients around –0.86, still allowing detection.

The authors claim three main contributions: (1) the introduction of MR‑WHT as a multiscale, computationally efficient transform for watermarking; (2) the strategic use of middle singular values in high‑frequency HH sub‑bands to balance imperceptibility and robustness; (3) extensive quantitative validation across a wide range of common and adversarial image manipulations. Limitations include the empirical selection of the strength parameter α and the middle‑index p, lack of analysis for color images or video streams, and the absence of tests against geometric transformations such as rotation or scaling.

In conclusion, the proposed MR‑WHT‑SVD watermarking scheme demonstrates strong resistance to both intentional attacks and unintentional degradations while preserving image quality, making it a promising candidate for practical digital rights management in imaging applications.