Optical multiple-image authentication based on computational ghost imaging using a parametric slant-Hadamard matrix

An optical multiple-image authentication method is proposed based on computational ghost imaging (CGI) and multiple domain transforms. Unlike other single-pixel imaging methods, where illumination patterns are generated using the Hadamard matrix, the parametric slant-Hadamard matrix is applied to ensure smoother low-frequency illumination patterns and gradually slanted structures even at middle-high frequencies, rather than the abrupt binary edges observed in Hadamard patterns. Therefore, the visual quality of reconstructed images can be improved significantly. Original images to be authenticated are encoded as sparse information using CGI and then embedded in the cover image. To improve the imperceptibility of hidden information and resistance against different attacks, the cover image is processed with multiple domain transforms, namely, decomposing the cover image with discrete wavelet transform (DWT) to get the low-frequency coefficient matrix, eliminating the redundancy of this matrix with discrete cosine transform (DCT), obtaining the singular value matrix by decomposing the DCT coefficient matrix using singular value decomposition (SVD). The embedding positions in the singular value matrix are determined by binary masks generated by the Logistic map. Before obtaining the marked cover image, the modified singular-value matrix is scrambled with the Arnold transform. In the authentication process, original images can be reconstructed with high visual quality at full sampling rate. Moreover, the existence of an original image can be efficiently verified using the nonlinear correlation map. To the best of our knowledge, the goal of authenticating original images can be achieved at a very low sampling rate, i.e., 1%, because the parametric slant-Hadamard matrix is used to generate illumination patterns in CGI. In addition, security is greatly enhanced by considering the parameters of the Logistic map and the iteration number of the Arnold transform as secret keys.