基于Arnold逆变换的图像置乱恢复算法

RESTORATION ALGORITHM OF IMAGE SCRAMBLING BASED ON ARNOLD INVERSE TRANSFORMATION

针对Arnold变换图像置乱恢复,目前常用的方法有利用Arnold变换的周期性和利用反变换两种。提出一种新的基于Arnold逆变换的置乱恢复方法,该方法将Arnold变换矩阵的逆矩阵作为置乱恢复过程中的变换矩阵,同时,把二维逆变换推广到了m维的情形,并在此基础上,统一了Arnold变换和Arnold逆变换的形式。实验对三种方法的性能进行了比较,结果表明,对于已应用Arnold变换进行预处理的置乱图像,算法无须计算变换周期,无须讨论方程式即可快速实现图像的置乱恢复。

The restoration with Arnold transformation for image scrambling, currently there are two common used methods ： utilising the ey- clicity of Arnold transformation and utilising the inverse transformation. A new restoration algorithm for scrambling based on Arnold inverse transformation is proposed in this paper, it takes the inverse-matrix of Arnold transform matrix as the transform matrix using in the process of restoring the scrambled images. And the two-dimensional inverse transform is extended to the m-dimensional cases. On this basis, the forms of Arnold transform and inverse transform are uniformed. The experiment has been done to compare the performances of these three methods, the results show that for the scrambled images pre-treated by Arnold transform, applying the algorithm in this paper to them can quickly achieve the scrambling restoration without the need of calculating the transformation and discussing the equations.