An image encryption algorithm based on compressed sensing and dual-tree complex wavelet transform

Combined image encryption with the process of compressed sensing (CS) which based on dual-tree complex wavelet transform, we came up with the image encryption algorithm which based on the theory of CS and double random phase encoding (DRPE). Firstly, adopting DT-CWT represent the image sparsely. It can enhance the image edge and texture, it also can attain directional feature information. Secondly, utilizing chaotic system to product chaos sequence as the measurement matrix on the process of CS. At the same time, the values of initial chaotic parameters are the keys. Finally, we selected DRPE on measurements to finish the process of secondary encryption. The values of seeds which are used to generate two random phase masks are the keys of secondary encryption. In the process of decryption, providing the correct values of keys can generate the chaotic measurement matrix and random phase masks to be used for decryption. Orthogonal matching pursuit (OMP) algorithm is employed to reconstruct the original image approximately. Compared with several existing algorithms, this encryption scheme can reconstruct a higher quality image. It has higher robustness and higher sensitivity to the initial keys.