Image Encryption Scheme Based on Multiscale Block Compressed Sensing and Markov Model

Many image encryption schemes based on compressed sensing have the problem of poor quality of decrypted images. To deal with this problem, this paper develops an image encryption scheme by multiscale block compressed sensing. The image is decomposed by a three-level wavelet transform, and the sampling rates of coefficient matrices at all levels are calculated according to multiscale block compressed sensing theory and the given compression ratio. The first round of permutation is performed on the internal elements of the coefficient matrices at all levels. Then the coefficient matrix is compressed and combined. The second round of permutation is performed on the combined matrix based on the state transition matrix. Independent diffusion and forward-backward diffusion between pixels are used to obtain the final cipher image. Different sampling rates are set by considering the difference of information between an image’s low- and high-frequency parts. Therefore, the reconstruction quality of the decrypted image is better than that of other schemes, which set one sampling rate on an entire image. The proposed scheme takes full advantage of the randomness of the Markov model and shows an excellent encryption effect to resist various attacks.