A robust and secure watermarking algorithm based on DWT and SVD in the fractional order fourier transform domain

The present paper aims to develop and validate a robust and secure watermarking algorithm. Firstly, the algorithm transforms the cover image and the watermark image separately by FRFT to obtain the amplitudes of both the cover image and watermark image, and then the two-level DWT transformation only carries out for the amplitude of the cover image. Secondly, the algorithm applies the SVD to the low-frequency sub-band of the second level DWT of the cover image and the amplitude of the watermark image. Thirdly, a new matrix is constructed based on the singular values from both the cover and watermark images to embed watermark information. Lastly, the algorithm takes the preliminary numerical calculation to determine an appropriate transformation order of FRFT for the cover image and to provide an outstanding balance between the imperceptibility and robustness in the proposed watermarking scheme. Moreover, it guarantees the security of watermarking scheme by the transformation order of FRFT. Experimental results demonstrate that the proposed watermarking scheme provides better performance in imperceptibility and resistance against traditional signal processing and geometric attacks, especially in image rotation, image cropping, average filtering, median filtering, and Gaussian filtering in comparison with the existing methods in the literature.