Quaternion Hadamard Transform and QR Decomposition Based Robust Color Image Watermarking

Abstract

A robust watermarking method depending on Quaternion Hadamard Transform (QHT) and QR decomposition is proposed. The QHT can preserve the relationship among the rgb component and color information. The entire host image is initially processed with Quaternion Hadamard Transform to obtain the QHT transformed image; and then the QHT transformed image is partitioned into $4\\times 4$ sub-blocks. QR decomposition is applied on each sub-block to attain two matrices named as $\\boldsymbol{Q}$ matrix and R matrix. The $\\boldsymbol{Q}$ matrix coefficients are chosen to embed the binary watermark data. A one-bit data is embedded in the second, third and fourth element of the first row of $4\\times 4 \\boldsymbol{Q}$ coefficients. The proposed method s performance is validated using the metrics embedding rate and Normalized cross-correlation (NCC) on different varieties of attacks. The embedding rate is 0.0625, thus the embedding rate of the proposed method is superior to the existing methods. The robustness of the proposed Color Image Watermarking algorithm is validated by testing it with several attacks.