Random Permutation-Based Block Compressed Sensing for Image Encryption-then-Compression Applications

Compressed sensing (CS) proposed recently has been demonstrated very effective for data Encryption-then-Compression (ETC) applications. However, when applying CS to two-dimension (2D) images, how to protect the privacy of digital images while keeping efficiency becomes a challenge. To solve this problem, we propose a random permutation-based block CS (BCS) strategy for ETC applications in this paper. In the proposed method, the CS sampling is performed on each small block of the image. In this way, the efficiency can be guaranteed. For security consideration, random permutation is employed to encrypt each small block of the image. For signal reconstruction, a modified smoothed projection-based Landweber (SPL) algorithm which embeds inverse random permutation into classical SPL algorithm is proposed, where inverse random permutation is used for decrypting. Several simulation results demonstrate the effectiveness of the proposed method.