Reversible image-hiding algorithm based on singular value sampling and compressive sensing

Abstract

A reversible image-hiding algorithm based on a novel chaotic system is proposed using compressive sensing (CS) and singular value sampling (SVS) techniques. In the first stage, a novel mathematical model is constructed to extract the plain messages from the secret plain image, and the public-key Rivest–Shamir–Adleman (RSA) algorithm is adopted to encrypt these messages, obtaining the corresponding cipher messages. Then, another mathematical model of key transformation is constructed to transform above messages into the initial keys, which is used to produce a random key stream. In the second stage, the secret plain image is scrambled by a pre-encryption operation, and the corresponding singular values are obtained by singular value decomposition (SVD). Then, these values are partitioned, and zero blocks are identified and removed. Thereafter, the singular values of the blocks with non-zero elements are sampled by CS, with filled by zero elements again. In the third stage, high energy coefficients are removed and replaced by zero elements to obtain new sampling values. Then, the carrier image is processed by discrete wavelet transform (DWT). Next, new sampling values are embedded into the wavelet coefficients, and the inverse DWT is performed. Thus, a new carrier image containing the secrets is obtained. The advantages are: (1) A new chaotic system ImpTDCS is proposed to have a better behavior. (2) A novel model EMM is built to extract plain messages from secret image. (3) Multi-images can be embedded, which can hide more secret information each time. (4) SVD is operated followed by SVS on non-zero blocks, reducing transmission bandwidth. (5) High energy coefficients of SVS are removed before embedding operation, guaranteeing effectively the visual quality of carrier image containing secrets.