Color image encryption with semi-tensor product compressive sensing and quaternion discrete fractional Krawtchouk transform

A color image encryption scheme is investigated by integrating the semi-tensor product compressive sensing (STP-CS) with the quaternion discrete fractional Krawtchouk transform (QDFrKT). To process the color components of plaintext image as a whole, the discrete fractional Krawtchouk transform (DFrKT) is popularized into the quaternion domain and the color image is secured by the QDFrKT. The image matrices are compressed with the discrete wavelet transform (DWT) and the STP measurement matrix. Then the compressed matrices represented by quaternion algebra are re-encrypted by the double random phase encoding and the quaternion DFrKT. Subsequently, the nonlinear hyperchaotic Lorenz system is applied to pixel diffusion to obtain the encrypted image. The proposed reconstruction algorithm based on the grouping iterative reweighted least squares (GIRLS) can resume the decryption image with high precision. The efficiency, security and robustness of the image compression encryption algorithm for color images are evaluated.