基于二维耦合映像格子模型的图像压缩加密方案

二维耦合映像格子(two-dimensional coupled map lattice,2D CML)模型具有很复杂的动力学行为，它的最大李雅普诺夫指数(maximum Lyapunov exponent,MLE)是由局部混沌映射函数决定。选择具有较大的李雅普诺夫指数(Lyapunov exponent,LE)的分段logistic函数(piecewise logistic map,PLM)作为模型的局部映射函数。通过独立性假设实验，验证2D CML模型在一定条件下拟服从独立同分布。在并行压缩感知条件下，基于2D CML模型产生压缩测量矩阵，使用测量矩阵对原始图像的每一列并行压缩采样。对采样图像进行处理和多轮扩散，实现对图像的加密，并对加密后的图像性能进行实验分析。实验表明，基于2D CML模型的图像压缩加密方案具有较好的加密性能和应用前景。

Image compression and encryption scheme based on the two-dimensional coupled map lattice model

Two-dimensional coupled map lattice (2D CML) model has quite complex dynamic behavior. Its maximum Lyapunov exponent (MLE) is only determined by the local chaotic map. Therefore, a piecewise logistic map (PLM) with much larger Lyapunov exponent (LE) value is selected as the local mapping function of the 2D CML model. According to the independence hypothesis experiment, it is proved that the 2D CML model is intended to obey independent and identical distribution under certain conditions. With the parallel compressed sensing, a compressed sensing measurement matrix is generated by the 2D CML model, and the original image is sampled by compressed sensing measurement matrix. The image is encrypted by processing and multi-round diffusion of the sampled image, and the performance of the encrypted image is analyzed experimentally. Experiments show that the image compression encryption scheme based on 2D CML model has good encryption performance and application prospects.