Secure frequency-domain image compressed sensing with matrix-inversion-free recovery

Image encryption should be performed prior to image compression in many real-world ap-plications. This results in the requirement of compressing the encrypted image. Compressed sensing (CS) is an attractive tool for compressing encrypted images. Unfortunately, most existing CS-based image encryption-then-compression (ETC) schemes face several critical challenges, such as low security, high-complexity sampling and recovery. Therefore, this paper presents a secure frequency-domain image CS scheme with matrix-inversion-free (MIF) recovery for ETC applications to address the above challenges. More specifically, the bilateral permutation and nonzero entry diffusion encryption operations are utilized to encrypt the frequency -domain image orderly. Surprisingly, the above two encryption operations do not compromise recovery performance with proper parameters. Then, the encrypted frequency-domain image is simultaneously compressed and sampled with low complexity by an untrusted bandwidth -constrained channel provider. Additionally, we design an accompanying access password as a defence layer, and it can further enhance security. Finally, an extension orthogonal matching pursuit (OMP) recovery algorithm is investigated by avoiding pseudo-inverse and multiple encryption and decryption to reduce computational complexity, named MIF OMP (MIFOMP). Theoretical analyses and simulation results demonstrate the proposed scheme can achieve high security, low-complexity sampling and recovery, and satisfy the expected recovery performance.