An improved QR decomposition for color image watermarking

Beside many other algorithms such as Singular Value Decomposition (SVD), Discreet Cosine Transform (DCT) and Discrete Wavelet Transform (DWT), QR decomposition is known as an effective method for embedding and extracting watermarked image. In QR decomposition, Gram-Schmidt and Householder [10] are the most popular two algorithms. In this paper, QR factorization is executed by exploiting orthogonality of Q matrix and triangularity of R matrix to find out elements of these matrixes. The algorithm of Sun [12] is used for both embedding and extracting. For embedding watermark, Q and R will be calculated separately where computing R is implemented by solving a set of linear equations and calculating Q is base on Gram-Schmidt algorithm [10] via knowing R. In addition, diagonal elements of R matrix are inspected to ensure their validity except the first diagonal one. For extracting watermark, only the first element R(1, 1) of R matrix needs to be computed which is performed by an operation. Experimental results show that the proposed scheme not only has better quality of watermarked image, but also overcomes problems of robustness and computation complexity.