中文摘要：

研究脊波变换域稳健性数字水印嵌入问题，提出一种新颖的自适应乘性数字水印嵌入算法。将图像分块后对每块进行脊波变换，使变换系数能够分段线状表示图像中的边缘奇异性；通过分析脊波系数对不同纹理程度图像的分布特点，估计块内的噪声可见性。水印自适应嵌入到块内具有能量最大方向的脊波系数，并根据嵌入水印图像的视觉感知质量和分块能量最大方向不能改变的约束要求估计水印嵌入的强度缩放参数。水印的盲检测使用相关检测器。理论分析和实验结果表明所提出的水印算法具有较高的稳健性和不可见性。

英文摘要：

This paper addresses the issue of how to embed watermarks in ridgelet domain and proposes a novel adaptive and muhiplicative watermarking algorithm based on ridgelet transform. In order to obtain a sparse representation of the image, especially for straight edge singularity, the image is first partitioned into small blocks and the ridgelet transform is applied for each block. Through analyzing the distribution of the texture in ridgelet coefficients of each block, the noise visible function is proposed to guarantee the adaptive capability of the watermark embedding. Followed by the multiplicative rule, the watermark sequence is embedded into the ridgelet coefficients in the highest energy direction of each block. Also the watermark strength scaling factor is estimated by the requirements of visual quality of watermarked image and without any change to the highest energy direction of each block. Then the embedded watermark can be blindly detected by the correlation coefficients between the watermarked image and the water-mark sequence. Experiments show that the proposed algorithm can achieve a better tradeoff between the robustness and transparency.