A visually secure image encryption scheme based on semi-tensor product compressed sensing

•The proposed scheme integrates image processing and image encryption techniques.•The proposed scheme applies the new matrix quadrature method of STP to CS, which can greatly save the storage space of measurement matrix.•The proposed scheme employs visually secure image encryption technology into the system, the final encrypted image can be visually aligned with the normal image.•This study gives a new perspective for further research on visual security encryption algorithms. In traditional compressed sensing (CS), the measurement matrix always faces problems such as large data storage, high memory usage and a large amount of data calculation. To reduce the storage space of the measurement matrix, improve memory usage and reduce the amount of data, this paper proposes a CS strategy based on a semitensor product (STP). The STP is employed to sample a sparse matrix from the measurement matrix, and Arnold scrambling is used to increase the security of the secret image. Furthermore, a visual security strategy for the secret image is employed to transform it into a visually meaningful image. The simulations show that the proposed visual security strategy based on STP-CS can not only greatly reduce the storage space occupied by the measurement matrix but also maintain high reconstruction quality compared with the traditional CS model while ensuring visual security quality.