中文摘要：

目的依据压缩感知理论具有很好的计算保密性,提出一种基于NSCT和压缩感知的数字图像水印算法,以解决图像的鲁棒性、不可感知性及保密性之间矛盾。方法首先将水印图像分块压缩感知获得测量值,然后再将载体图像NSCT分解,对低频分量Fibonacci置乱后非重叠分块,对每块进行LU分解、奇异值分解,将每个分块的水印测量值按不同的嵌入强度对应嵌入载体奇异值矩阵中,经过一系列逆变换得到含水印图像。结果该算法在水印的嵌入和提取仿真实验结果中峰值信噪比大于40 d B,重建的水印图像与原图像相似度极高,且能抵抗剪切、高斯噪声、椒盐噪声、高斯低通滤波和JPEG压缩等类的攻击。结论该算法既具有很好的鲁棒性又兼有较强的不可见性,具有切实的可行性。

英文摘要：

The work aims to propose a digital image watermarking algorithm based on NSCT and compressive sensing （CS） according to the good computational security of CS theory, so as to solve the conflict between the robustness, imperceptibility and security of images. First, the watermark image was divided into blocks for CS to obtain the measurements. Second, the carrier image NSCT was decomposed. The tow-frequency portion was encrypted through Fibonacci scrambling and divided into blocks. Third, low-frequency sub-bands of each block were subject to LU decomposition and singular value decomposition （SVD）. The measurements of each watermarking block were embedded in carrier＇s singular value matrix with an appropriate embedding strength. The images containing watermark were obtained after a series of inverse transformations. In the process of watermark embedding and extracting simulation experiment results, the PSNR value of the proposed algorithm reached over 40 dB. The reconstructed watermark image was remarkably similar to the original image and had strong robustness against cropping, Gaussian noise, salt and pepper noise, Gaussian low-pass filter and JPEG compression attacks etc. The proposed algorithm has good robustness and strong invisibility, and it is practically feasible.