Two-Dimensional Compressed Sensing Using Two-Dimensional Random Permutation For Image Encryption-Then-Compression Applications

Block compressed sensing with random permutation (BCS-RP) has been shown to be very effective for image Encryption-then-Compression (ETC) applications. However, in the BCS-RP scheme, the statistical information of the blocks is disclosed, because the encryption is conducted within each small block of the image. To solve this problem, a two-dimension compressed sensing (2DCS) with 2D random permutation (2DRP) strategy for image ETC applications is proposed in this letter, where the 2DRP strategy is used for encrypting the image and the 2DCS scheme is used for compressing the encrypted image. Compared with the BCS-RP scheme, the proposed approach has two benefits. Firstly, it offers better security. Secondly, it obtains a significant gain of peak signal-to-noise ratio (PSNR) of the reconstructed-images.