Color image encryption based on discrete trinion Fourier transform and compressive sensing

To protect visual content in color images, this paper presents an encryption method by employing discrete trinion Fourier transform and compressive sensing. Firstly, each color image is precoded into a trinion matrix for holistically processing. The discrete trinion Fourier transform is performed to construct an enducing matrix. With measurement matrices generated by 3D Lorenz chaotic map, complex-type compressed sensing is then utilized to obtain sparse coefficients. Followed by Josephus scrambling and inverse discrete trinion Fourier transform, the ciphertext can be obtained. The plain-text images can be restored perfectly and the maximum PSNR value is more than 280dB. Additionally, the proposed cryptosystem shows high-level sensitivity, which is evidenced by NPCR and UACI values beyond 99.9998% and 33.3337%, respectively. Compared with several existing methods, the proposed algorithm exhibits stronger resistance against Gaussian noise.