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A robust image watermarking scheme in the ridgelet transform domain is proposed in this paper. Due to the use of the ridgelet domain, sparse representation of an image which deals with line singularities is obtained. In order to achieve more robustness and transparency, the watermark data is embedded in selected blocks of the host image by modifying the amplitude of the ridgelet coefficients which represent the most energetic direction. Since the probability distribution function of the ridgelet coefficients is not known, we propose a universally optimum decoder to perform the watermark extraction in a distribution-independent fashion. Decoder extracts the watermark data using the variance of the ridgelet coefficients of the most energetic direction in each block. Furthermore, since the decoder needs the noise variance to perform decoding, a robust noise estimation scheme is proposed. Moreover, the implementation of error correction codes on the proposed method is investigated. Analytical derivation of bit error probability is also carried out and experimental results prove its accuracy. Simulation also shows outstanding robustness of the proposed scheme against common attacks, especially additive white noise and JPEG compression.
Kalantari et al. (Fri,) studied this question.