Robustness has played extremely important role in the multiple applications of digital watermarking technology. The reason lies in its influence on the watermarking system’s practicability. As one of the most difficult kinds of digital signal processing for a digital watermark to survive, geometric distortions have become a central problem in digital image watermarking research. Therefore, resigning a greatly robust digital image watermarking approach which can withstand geometric distortions is still a quite challenging work. On account of Bessel K-form (BKF) probability density function (PDF), this paper proposes an optimal synchronization correction-based digital image watermarking method which can resist geometric distortions. This approach consists of watermark embedding, synchronization correction and watermark extraction. Using the quantization index modulation (QIM), the watermark is inserted into the original host images in the nonsubsampled shearlet transform (NSST) domain by adjusting the selected blocks’ low-frequency NSST coefficients. The BKF PDF describes the NSST coefficients’ statistical features. Besides, the BKF statistical model parameters can be used in constructing a compact image characteristic space. Utilizing the compact image feature, the least squares support vector regression (LS-SVR) synchronization correction is performed to estimate the geometric distortions parameters. After LS-SVR synchronization correction, the inverse QIM is performed to recover blindly the inserted watermark. Simulation results demonstrate that the presented digital image watermarking method not only has good imperceptibility performance, but also can well resist challenging common signal processing operations as well as geometric distortions, which can be superior to the most advanced approaches.

中文翻译：

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基于Bessel K -form PDF的基于同步校正的鲁棒数字图像水印方法

鲁棒性在数字水印技术的多种应用中起着极其重要的作用。原因在于它对水印系统的实用性的影响。作为数字水印生存中最困难的数字信号处理之一，几何失真已成为数字图像水印研究中的核心问题。因此，放弃一种可以承受几何失真的非常健壮的数字图像水印方法仍然是一项颇具挑战性的工作。鉴于贝塞尔K型（BKF）概率密度函数（PDF），本文提出了一种基于最佳同步校正的数字图像水印方法，可以抵抗几何失真。该方法包括水印嵌入，同步校正和水印提取。使用量化索引调制（QIM），通过调整所选块的低频NSST系数，将水印插入非下采样的来回波变换（NSST）域中的原始宿主图像中。BKF PDF描述了NSST系数的统计特征。此外，BKF统计模型参数可用于构建紧凑的图像特征空间。利用紧凑的图像特征，执行最小二乘支持向量回归（LS-SVR）同步校正以估计几何变形参数。LS-SVR同步校正后，执行反QIM以盲目恢复插入的水印。仿真结果表明，所提出的数字图像水印方法不仅具有良好的感知性能，