2D compressed sensing of encrypted images based on complex-valued measurement matrix

When using untrusted third parties to compress and transmit images in real-life scenarios, it is vital to encrypt them before compression. In order to better address the issues of low security in the original image and poor reconstruction quality of the encrypted image during compressed sensing, this paper proposes a 2D compressed sensing scheme for encrypted images based on complex-valued measurement matrix (2DCS-CVM). Firstly, the SHA-256 algorithm generates keys for the hyperchaotic Lorenz system, and then the chaotic sequences are used to create encrypted images with increased security through subtractive diffusion and global permutation. Secondly, the complex-valued Vandermonde measurement matrix is utilized for 2D compressed sensing on the encrypted image, and the two-dimensional projected gradient with embedding decryption algorithm is used to generate recovered images with improved reconstruction performance. Finally, the measurement matrix's computational complexity and transmission bandwidth are reduced through structural sparsification with sparse random matrices. Simulation results demonstrate that this scheme offers an optimal balance between storage, computational complexity, hardware implementation, and reconstruction performance while providing excellent security and robustness. In order to enhance privacy by encrypting images before compressed transmission, this paper proposes a 2D compressed sensing scheme based on a hyperchaotic Lorenz system and complex-valued Vandermonde measurement matrix. Simulation results demonstrate that the reconstruction performance of this scheme is highly superior to that of the encryption-then-compression scheme proposed recently. The hyperchaotic system for subtractive diffusion and global permutation significantly reduces the correlation of the encrypted image, improving security by key space and robustness.image