Image Compression and Encryption Scheme Based on Compressive Sensing and Fourier Transform

An image compression and encryption scheme based on compressive sensing (CS) and Fourier transform is proposed to achieve image encryption and compression with reconstruction robustness and high security. Making use of the property of CS, encryption and compression are combined. In order to avoid the security limitations of revealing the energy information of the plaintext from ciphertext and reusing of measurement matrix to improve security, chaos system and two-dimensional fractional Fourier transform (2D-FRT) are used to perform encryption. Moreover, double random phase encryption based on 2D-FRT can avoid the loss of reconstruction robustness in diffusion encryption. The test results indicate that the proposed method has high security, good compression performance and reconstruction robustness.