Multi-color-image compression-encryption scheme in the quaternion discrete Fresnel domain

A multiple color images compression-encryption scheme is designed with compressive sensing in the quaternion discrete Fresnel transform. To tackle multiple color images in a holistic manner, the discrete Fresnel transform is extended into the quaternion domain and the images are encrypted with the quaternion discrete Fresnel transform. In this scheme, the RGB color components of plaintext images are simultaneously compressed and encrypted in three mutually independent channels. Then the red, green and blue components are scrambled respectively by a chaos sequence generated by the 2D logistic-sine-coupling map. Each color component matrix is compressed with sparse representation and matrix measurement. Subsequently, the compressed matrices are integrated into the quaternion algebras and re-encrypted by the defined quaternion discrete Fresnel transform. The devised nonlinear cryptosystem originates from the asymmetric phase truncation operation. In decryption, the original color images are reconstructed by the gradient descent with a sparsification algorithm. The proposed multiple color images compression-encryption algorithm is feasible, effective, secure and robust.