An improved sample projection approach for image watermarking

Very recently, a novel watermarking scheme named sample projection approach (SPA) has been proposed by Akhaee et al. [1] to improve the watermarking performance against gain attacks. The SPA embeds one message symbol into four signal samples by projecting the line segment formed by the four samples on a certain specific codeline. Based on the SPA, this paper presents an improved sample projection approach (ISPA) by introducing a set of modified codelines to decrease embedding distortion and constructing the long line segments to increase robustness. According to our theoretical analysis of document-to-watermark ratio (DWR), the modified codelines result in a lower embedding distortion than the SPAʼs codelines in the same conditions with regard to payload and robustness. We also derive a theoretical expression for the symbol error rate (SER) of the ISPA against additive white Gaussian noise (AWGN) attack. The numerous experiments conducted on both artificial Gaussian signals and the natural images show that the proposed ISPA outperforms the SPA in terms of robustness against attacks.