This paper presents an optically secure image cryptosystem in the compressed-sensing (CS) domain by using a chaos driven nonlinear function. First, the original image is divided into non-overlapping blocks of uniform size, and then the discrete cosine transform (DCT) is used for obtaining sparse representation of these blocks. A logistic map-based circulant sensing measurement matrix is used to compress the sparse representations of the blocks. This partial cipher is further processed for encryption using a nonlinear function based on a dynamic invertible exponential function. The decorrelation of values is done by applying the Arnold 2-D map on the cipher. The seed values to the logistic equation and the parameters of the Arnold map are based on the original image, which makes the proposed algorithm robust in terms of plain text sensitivity. Not only does the algorithm achieve a considerable amount of security, but it also conceals the original image identity by the compression introduced, thereby reducing the storage and transmission cost. The decryption of the cipher is done using a smooth l₀ approximation, giving high-quality reconstruction results. The extensive simulation results and performance analysis illustrates the excellent security and reconstruction results of the proposed scheme in comparison with the existing algorithms.

通过使用混沌驱动的非线性函数，本文提出了一种在压缩感知（CS）域中的光学安全图像密码系统。首先，将原始图像划分为大小一致的非重叠块，然后使用离散余弦变换（DCT）获得这些块的稀疏表示。基于逻辑图的循环感测测量矩阵用于压缩块的稀疏表示。使用基于动态可逆指数函数的非线性函数对该部分密码进行进一步处理以进行加密。值的去相关是通过在密码上应用Arnold二维映射来完成的。Logistic方程的种子值和Arnold映射的参数都基于原始图像，这使得该算法在纯文本敏感度方面具有鲁棒性。该算法不仅实现了可观的安全性，而且还通过引入的压缩隐藏了原始图像的身份，从而降低了存储和传输成本。密码的解密使用平滑方式完成l ₀近似，给出高质量的重建结果。大量的仿真结果和性能分析表明，与现有算法相比，该方案具有出色的安全性和重构结果。