Watermarking based on Hessenberg matrix decomposition

Watermerking is a kind of marker covertly embedded in a signal such as audio, video or image data. It is typically used to identify ownership of the copyright of such signal. There are some various ways in watermarking such as using wavelets, Fourier transform or combination of these transforms with matrix decomposition. In this paper, we just use matrix decomposition methods including QR, Hessenberg, Schur, and Singular Value decomposition (SVD). The method consists of two phases. The first one is embedding the watermark image in to the host image. In this stage, we first decompose the matrices corresponding to host and watermark image with one of the known matrix decompositions. Let and be the matrices with highest degree of sparsity in the resulting matrices corresponding to watermark and host images, respectively. Then we compute the matrix , where is a constant factor. Then multiplication of the matrix with the other components of the matrix decomposition corresponding to the host image is considered as the watermarked image which includes a hidden trace of the real owner. After embedding phase, the watermarked image is extracted by an inverse process in the detection phase. We use PSNR and SSIM parameters in order to assess the visual quality and efficiency of the watermarking process. Moreover, the constant should be specified in order to balance between the PSNR corresponding to embedding and detection phases. Numerical experiments are done on some greyscale images in USC-SIPI dataset. Results show that the Hessenberg decomposition has larger PSNR and SSIM values in both embedding and detection phases rather than other matrix decomposition methods. Moreover, watermarked image cannot be extracted in Schur decomposition which in turn shows the weakness of this decomposition. Moreover, numerical experiments reveals improvement and agreement in the PSNR and SSIM parameters, respectively, comparing the most accurate existing methods.