Blind digital watermarking method in the fractional Fourier transform domain

•We propose a blind watermarking method which can embed visually recognizable image.•It uses FRFT to share the peculiarities of both spatial and frequency domain watermarking methods.•It can realize the blind extraction of watermark without any information of the original image.

In this paper, we proposed a novel blind digital image watermarking algorithm based on the fractional Fourier transform (FRFT), which is a generalization of the ordinary Fourier transform and its output has the mixed time and frequency components of the signal. The original image is segmented into non-overlapping blocks for watermarking, and each block is transformed by the two dimensional fractional Fourier transform with two fractional orders. Then each pixel value of binary watermark is embedded by modifying the back-diagonal FRFT coefficients of each image block at the same location with a random array. After perform an inverse two dimensional fractional Fourier transform, we can obtain the watermarked image and the transform orders can be consider as the encryption keys in this method. A series of attacking experiments are performed on the proposed method. The experiments results show that the proposed algorithm not only is of good imperceptibility and security and is very robust to JPEG compression noise attacks and image manipulation operations, but also can provide protection even under compound attacks.