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.

Computational ghost imaging with hybrid transforms by integrating Hadamard, discrete cosine, and Haar matrices

A scenario of ghost imaging with hybrid transform approach is proposed by integrating Hadamard, discrete cosine, and Haar matrices. The measurement matrix is formed by the Kronecker product of the two different transform matrices. The image information can be conveniently reconstructed by the corresponding inverse matrices. In experiment, six hybridization sets are performed in computational ghost imaging. For an object of staggered stripes, only one bucket signal survives in the Hadamard-cosine, Haar-Hadamard, and Haar-cosine hybridization sets, demonstrating flexible image compression. For a handmade windmill object, the quality factors of the reconstructed images vary with the hybridization sets. Sub-Nyquist sampling can be applied to either or both of the different transform matrices in each hybridization set in experiment. The hybridization method can be extended to apply more transforms at once. Ghost imaging with hybrid transforms may find flexible applications in image processing, such as image compression and image encryption.