Statistical Analysis of the Orthogonality Between Imagesand Pseudo-random Sequences
基于统计数学的伪随机序列与图像正交性分析

In digital image watermarking and image encryption, researchers often require a pseudo random sequence which is statistically orthogonal to an image. The white noise sequences, such as m sequence, are often used in these situations. But our study shows they are not optimum on orthogonal property. To get a better orthogonality, we studied the cross correlation of unartificial images and pseudo random sequences by means of statistical mathematics method. The second order expectation of the cross correlation value was determined in both space and frequency domains. The expression suggests that sequences which are high pass in frequency domain, like Run Length Limited (RLL) sequences, have better orthogonal character with unartificial images than white noise sequences which are widely used at present. The conclusion and the validity of our mathematical model were also proved by the result of statistical experiments. In order to generate 2D RLL sequences rapidly, we developed a simple and convenient algorithm. The experiments that confirmed 2D RLL sequences have better orthogonality with natural images than m sequences.