Image encryption-compression method via encryption based sparse decomposition

This paper proposes an image compression and encryption scheme based on sparse decomposition and chaotic system. The proposed approach contains three steps. In the first step, the original image is encrypted and converted to a meaningless image via the perturbation of the image phase in the Fourier transform and chaotic scrambling. This step improves the accuracy of image reconstruction based on sparse decomposition. In the second step, the encrypted image is compressed with a measurement matrix generated from a chaotic system. Then the compressed image is mapped and quantized. Finally, DNA XOR operation and chaotic scrambling are used to increase security. This step reduces the correlation among pixels and maximizes the entropy of the encrypted image. The two first steps present a problem of encryption-based sparse decomposition (ESD). The ESD problem is solved via the Half Quadratic Splitting approach in the decryption process. The proposed image reconstruction approach is based on sequential encryption, image denoising, and projection on the feasible set. The convergence of the ESD solver is investigated analytically. The simulation results show that the proposed method improves image reconstruction performance. The Peak Signal to Noise Ratios of the proposed approach are approximately in the range of 29 to 40 dB for compression ratios higher than 0.25. The ESD approach outperforms some other reconstruction approaches. The Security analysis based on different measures, such as obtaining near-zero correlation among adjacent pixels and maximum entropy of nearly 8, indicates the effectiveness of the proposed approach.