Digital watermarking in the fractional Fourier transformation domain

Embedding of a watermark signal is an interesting research and application field in the copyright protection of multimedia signals (images, sounds, movies) [1–4]. The goal is to embed the watermark that is imperceptible in the image, while the copyright holder can detect its existence, by using proper private information—key. Commonly used methods are based on embedding watermark signals in the space or spatial-frequency domain [1]. Recently, watermarking in the combined space/spatial-frequency domain has been defined [5]. In this paper, we will consider image watermarking in the fractional Fourier transformation (FRFT) domain. This approach uses combination of the space and spatial/frequency domains, without introducing the multidimensional Radon-Wigner distribution [5]. The paper is organized as follows. The FRFT is described in Section 2. Watermark embedding in the FRFT domain is considered in Section 3. Numerical examples are given in Section 4.