A Robust Watermarking Scheme Using Sequency-ordered Complex Hadamard Transform

Abstract

This paper presents a robust phase watermarking scheme for still digital images based on the sequency-ordered complex Hadamard transform (SCHT). The transform matrix of the SCHT exhibits sequency ordering which is analogous to frequency in the discrete Fourier transform (DFT). Hence, sequency-based image analysis can be performed for image watermarking while providing simple implementation and with less computational complexity for computation of the transform. As the SCHT coefficients are complex numbers which consist of both magnitudes and phases, they are suited to adopt phase modulation techniques to embed the watermark. In this proposed scheme, the phases of the SCHT coefficients in the sequency domain are altered to convey the watermark information using the phase shift keying (PSK) modulation. Low amplitude block selection (LABS) is used to enhance the imperceptibility of digital watermark, and amplitude boost (AB) method is employed to improve the robustness of the watermarking scheme. Spread spectrum (SS) technique is adopted to increase the security of watermark against various unintentional or intentional attacks. In order to demonstrate the effectiveness of the proposed watermarking scheme, simulations are conducted under various kinds of attacking operations. The results show that the proposed scheme is able to sustain a series of attacks including common geometric transformations such as scaling, rotating, cropping, painting, and common image-processing operations such as JPEG compression, low-pass filtering, sharpening, noising and phase perturbation, etc. Comparisons of the simulation results with the other schemes are also mentioned and the results reveal that the proposed scheme shows better robustness.