A multi-resolution watermarking based on contourlet transform using SVD and QR decomposition

A novel image watermarking algorithm is developed which is based on Contourlet Transform (CT) and Matrix Factorization methods such as Singular Value Decomposition (SVD) technique and QR factorization method. In the proposed scheme, the original image and the watermark image are transformed into subbands by Contourlet Transform. The lowest frequency coefficients of the CT decomposed original image are further factorized using SVD. The image coefficients of the lowest frequency of watermark after CT are decomposed by QR factorization. The QR decomposed coefficients are further factorized by SVD technique. The coefficients of watermark image thus obtained are embedded into the SVD factorized original image values. Inverse SVD and inverse CT are then applied on the modified coefficients of the original image to get the watermarked image. The performance of watermarking algorithm is improved by the combination of CT, SVD and QR factorization. Experimental results show that the proposed algorithm is better than the other contourlet based watermarking technique. It is robust and imperceptible against common signal processing attacks such as scaling, compression and filtering.