Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform

Most of the existing image encryption techniques bear security risks for taking linear transform or suffer encryption data expansion for adopting nonlinear transformation directly. To overcome these difficulties, a novel image compression-encryption scheme is proposed by combining 2D compressive sensing with nonlinear fractional Mellin transform. In this scheme, the original image is measured by measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the nonlinear fractional Mellin transform. The measurement matrices are controlled by chaos map. The Newton Smoothed l0 Norm (NSL0) algorithm is adopted to obtain the decryption image. Simulation results verify the validity and the reliability of this scheme.