A novel optical image encryption method based on Fourier single-pixel imaging using a deception strategy

As an advanced technology, Fourier single-pixel imaging can be used to obtain the spectral information of a target image by utilizing active illumination with sinusoidal patterns. Nevertheless, in order to ensure the integrity of image restoration, it is inevitable to generate a large number of illumination patterns to record light intensity values reflected from the target image in the imaging process. In this paper, a novel optical image encryption method is proposed based on Fourier single-pixel imaging and phase retrieval algorithm. To reduce the number of illumination patterns, a barcode image composed of horizontal strips is randomly generated and used as the target image in the imaging process. Due to the sparse distribution of its Fourier spectrum, less number of spatial frequencies are measured. Thus, less number of sinusoidal patterns are generated to collect light intensity values. The ciphertext is a real-valued sequence through integrating these collected values. Moreover, a new phase retrieval algorithm with high convergence speed is designed under the framework of double random phase coding in Fresnel domain. Considering the barcode image as the constraint, the plaintext image is encoded to two phase-only masks that can be served as the secret keys. The main advantage of this method is that the security can be enhanced by applying a deception strategy for eavesdroppers, namely there is no direct relationship between the encryption process of the plaintext image and the generation process of the ciphertext sequence. Even an eavesdropper knows that the ciphertext sequence is obtained using the Fourier single-pixel imaging, only the barcode image can be reconstructed using correlation algorithm, and the content of the plaintext image is not leaked at all. Through simulated and optical experiments, the feasibility and robustness of the proposed method have been demonstrated, and the plaintext image can be recovered at a lower sampling ratio, i.e., only approximate one-quarter of the spatial frequencies are recorded. To our best knowledge, it is first time to implement an image encryption using the deception mechanism, which can provide a new perspective for using Fourier single-pixel imaging in the field of optical information security.