Image compression-encryption scheme combining 2D compressive sensing with discrete fractional random transform

Most of the existing image encryption algorithms based on compressive sensing are too complex to operate. An image compression-encryption scheme with simple operation is presented based on 2D compressive sensing and discrete fractional random transform (DFrRT). To accomplish compression and encryption simultaneously, the original image is expressed in a 2D discrete cosine domain and measured by the measurement matrices in two orthogonal directions during the encryption process, where the matrices are constructed with Logistic chaos map to control the row vectors of Hadamard matrix. Then the intermediate resulting image is re-encrypted by taking discrete fractional random transform. Decryption process includes the inverse operation of the DFrRT and the reconstruction process with the Newton Smoothed l0 Norm (NSL0) algorithm in sequence. Simulation results verify the security and the effectiveness of this scheme by taking advantages of both compressive sensing and DFrRT.