Optical multiple-image authentication method based on Haar matrix based computational ghost imaging and l _<i>1</i> -l _<i>2</i> minimization

Recently, with the rapid popularization and widespread application of digital content, especially in the field of images, videos and multimedia data, the demand for verifying their security and authenticity has increased dramatically. This growth in demand stems from the risk that digital content can be easily tampered with, forged, or accessed without authorization, which has promoted the research on efficient and robust security authentication methods. An optical multiple-image authentication method based on computational ghost imaging and ℓ₁ - ℓ₂ minimization is proposed, where illumination patterns used in the imaging process are generated based on the Haar matrix. Different from the traditional methods to directly encrypt multiple images into the noisy ciphertext, this method improves the cognition and perceptibility of the authentication process by embedding the encoded information into the carrier image. First, multiple original images are composited using space multiplexing and the inverse Haar transform, and scrambled using Arnold transform. Second, the obtained fused image is converted to the sparse measurements using computational ghost imaging. Further, these measurements are scrambled with the help of a chaotic sequence generated with Chen system, and evenly divided into two sets. Finally, two sets of measurements are embedded into two sub-images decomposed from the carrier images using the Haar wavelet transform, respectively. After the inverse transform, the marked carrier image is obtained. The embedded positions in two sub-images are determined based on other two sequences of Chen system. In the authentication process, the visual quality of reconstructed results can be significantly improved through ℓ₁ - ℓ₂ minimization. Even at a very low sampling ratio (i.e., 2%), the authentication process can be successfully accomplished. To our knowledge, it is first to embed sparse measurements into two high-frequency sub-images of the carrier image, which can guarantee high robustness against the sharpen filter and expand the information loading capability. Therefore, this research work can bring the potential application value to the field of image verification.