Encryption in ghost imaging with Kronecker products of random matrices

By forming measurement matrices with the Kronecker product of two random matrices, image encryption in computational ghost imaging is investigated. The two-dimensional images are conveniently reconstructed with the pseudo-inverse matrices of the two random matrices. To suppress the noise, the method of truncated singular value decomposition can be applied to either or both of the two pseudo-inverse matrices. Further, our proposal facilitates for image encryption since more matrices can be involved in forming the measurement matrix. Two permutation matrices are inserted into the matrix sequence. The image information can only be reconstructed with the correct permutation matrices and the matrix sequence in image decryption. The experimental results show the facilitations our proposal. The technique paves the way for the practicality and flexibility of computational ghost imaging.