An encryption algorithm based on sparse coding and compressive sensing is proposed. Sparse coding is used to find the sparse representation of images as a linear combination of atoms from an overcomplete learned dictionary. The overcomplete dictionary is learned using K-SVD, utilizing non-overlapping patches obtained from a set of images. Compressed sensing is used to sample data at a rate below the Nyquist rate. A Gaussian measurement matrix compressively samples the plain image. As these measurements are linear, chaos based permutation and substitution operations are performed to obtain the cipher image. Bit-level scrambling and block substitution is done to confuse and diffuse the measurements. Simulation results verify the performance of the proposed technique against various statistical attacks.

中文翻译：

---

使用稀疏编码和压缩感知的图像加密

提出了一种基于稀疏编码和压缩感知的加密算法。稀疏编码用于从超完备学习字典中找到作为原子线性组合的图像的稀疏表示。过完备字典是使用 K-SVD 学习的，利用从一组图像中获得的非重叠补丁。压缩感知用于以低于奈奎斯特速率的速率对数据进行采样。高斯测量矩阵对普通图像进行压缩采样。由于这些测量是线性的，因此执行基于混沌的置换和替换操作以获得密码图像。进行比特级加扰和块替换以混淆和扩散测量。仿真结果验证了所提出的技术对各种统计攻击的性能。