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Optics Express

Optical multiple-image authentication method based on Fourier single-pixel imaging and multiple logistic maps

Zeng Tianyu, Liansheng Sui, Zhaolin Xiao, Zhou Yaoling

Published Jul 18, 2023• 13 citations
Publisher

Abstract

As a promising technique, the spatial information of an object can be acquired by employing active illumination of sinusoidal patterns in the Fourier single-pixel imaging. However, the major challenge in this field is that a large number of illumination patterns should be generated to record measurements in order to avoid the loss of object details. In this paper, an optical multiple-image authentication method is proposed based on sparse sampling and multiple logistic maps. To improve the measurement efficiency, object images to be authenticated are randomly sampled based on the spatial frequency distribution with smaller size, and the Fourier sinusoid patterns generated for each frequency are converted into binarized illumination patterns using the Floyd-Steinberg error diffusion dithering algorithm. In the generation process of the ciphertext, two chaotic sequences are used to randomly select spatial frequency for each object image and scramble all measurements, respectively. Considering initial values and bifurcation parameters of logistic maps as secret keys, the security of the cryptosystem can be greatly enhanced. For the first time to our knowledge, how to authenticate the reconstructed object image is implemented using a significantly low number of measurements (i.e., at a very low sampling ratio less than 5% of Nyquist limit) in the Fourier single-pixel imaging. The experimental results as well as simulations illustrate the feasibility of the proposed multiple-image authentication mechanism, which can provide an effective alternative for the related research.

DOI
10.1364/oe.497016

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As a promising technique, the spatial information of an object can be acquired by employing active illumination of sinusoidal patterns in the Fourier single-pixel imaging. However, the major challenge in this field is that a large number of illumination patterns should be generated to record measurements in order to avoid the loss of object details. In this paper, an optical multiple-image authentication method is proposed based on sparse sampling and multiple logistic maps. To improve the measurement efficiency, object images to be authenticated are randomly sampled based on the spatial frequency distribution with smaller size, and the Fourier sinusoid patterns generated for each frequency are converted into binarized illumination patterns using the Floyd-Steinberg error diffusion dithering algorithm. In the generation process of the ciphertext, two chaotic sequences are used to randomly select spatial frequency for each object image and scramble all measurements, respectively. Considering initial values and bifurcation parameters of logistic maps as secret keys, the security of the cryptosystem can be greatly enhanced. For the first time to our knowledge, how to authenticate the reconstructed object image is implemented using a significantly low number of measurements (i.e., at a very low sampling ratio less than 5% of Nyquist limit) in the Fourier single-pixel imaging. The experimental results as well as simulations illustrate the feasibility of the proposed multiple-image authentication mechanism, which can provide an effective alternative for the related research.
Single-pixel imaging (SPI) techniques acquire one-dimensional (1-D) intensities from different projections of the object. Applying SPI to object authentication with optical encryption has the advantages of high security and easy transmission. However, previous image-based schemes have the problem of taking long time to reconstruct image from a large number of measurements. What’s more, perfect reconstruction is not necessary for object authentication. We propose an imageless object authentication strategy using single-pixel detection and sub-Nyquist sampling of Fourier spectrum coefficients. The method consists of three steps: encoding, four-step phase-shifting and authentication. First, we conduct SPI to encode image to 1-D intensities with Fourier basis patterns. Second, we use four-step phase-shifting method to get the Fourier transform of the object (i.e., Fourier spectrum) instead of image reconstruction. Third, calculate the correlation extent between the object and the reference image and then visualize it as a map. If there is only one area that is much higher than other places in the map, the similarity between the image and the reference is high. We have verified the effectiveness of this method by adding noise in simulation. When adding noise or performing at low sampling rate, our scheme still realizes accurate authentication.
An optical image encryption method is proposed based on Fourier single-pixel imaging and iterated phase retrieval algorithm. First, a binary barcode image containing two groups of horizontal strips is randomly generated and used as the target image in the single-pixel imaging process. Second, considering the barcode image as the amplitude constraint, the original plaintext image is encoded to two phase-only masks using a designed phase retrieval algorithm in Fresnel domain, and these masks are applied as secret keys. Finally, the barcode image is encrypted to a series of measurements using two-step phase shift Fourier single-pixel imaging as the ciphertext. Differing other methods, the original image is not directly imaged and encoded into the ciphertext. Even the ciphertext is obtained by a cracker, only the barcode image may be further discovered. Due to two phase-only masks as secret keys, the security level of the cryptosystem can be enhanced greatly. The simulated results verify the feasibility of the proposed method, and this work provides an effective alternative for the related research.
Abstract A novel optical multiple-image authentication scheme based on the phase retrieval algorithm is presented in gyrator domain. According to a plain image, only one phase-only mask is obtained as the encrypted result by using the proposed phase retrieval algorithm, which has a fast convergence rate and good performance on mean square error. Afterwards, the sparsely encrypted distribution is extracted from the phase-only mask by selecting a certain percentage of pixels randomly. Different from other multiple-image authentication system based on space multiplexing, all sparsely encrypted distributions of plain images are finally integrated into the ciphertext by making use of the inter-modulation operation of phase masks, where the decryption process can be performed efficiently without any cross-talk noise and the encrypted capacity is nearly unlimited. Only when the secret keys are correct, the content of the plain images can be authenticated, in which the authentication process can be implemented optically by using the architecture of double random phase encoding. Simulation results are given to demonstrate the feasibility and robustness of the proposed scheme.
In the rapidly evolving field of optical information security, single-pixel imaging (SPI) has emerged as a promising technique for hidden information transmission. However, traditional SPI methods face significant challenges, including the need for excessive modulation patterns and the vulnerability of encrypted information during transmission. Furthermore, the field lacks efficient methods to reconstruct both plaintext and ciphertext images from the same set of single-pixel measurements. Here, we propose a novel and efficient encryption strategy for Fourier single-pixel imaging (FSPI) that addresses these critical challenges. Our approach integrates two key innovations: a two-step Fourier-total variation conjugate gradient descent (F-TVCGD) method and a dual-key decryption mechanism. The F-TVCGD method significantly reduces the number of modulation patterns required for image reconstruction, enhancing efficiency and minimizing data redundancy. Our dual-key mechanism enables the reconstruction of both plaintext and ciphertext images from a single set of single-pixel measurements using different decryption keys, significantly enhancing security without compromising efficiency. The incorporation of Fourier symmetric patterns improves the convergence robustness of the symmetric gradient descent (SGD) algorithm, leading to superior performance under challenging conditions such as sparse sampling and noise attacks. Numerical simulations and optical experiments validate our method's improvements in both accuracy and security compared to traditional approaches. Our findings demonstrate that the proposed F-TVCGD and SGD strategies effectively address the challenges of excessive modulation patterns and information vulnerability in FSPI.
Multi-object optical encryption has emerged as a promising field for enhancing encryption performance and reducing communication overhead, which can ensure the security of single-pixel imaging. However, it faces some critical challenges like low efficiency, reliance on complex system design, high hardware costs, and the difficulty of parallel encryption with independent decryption, hindering practical deployment. In this work, an illumination pattern construction algorithm is proposed to generate projected basis patterns for parallel optical encryption, while a decoupling algorithm is developed to demodulate coupled measurements to recover Hadamard spectrum for each object. Independent decryption is then performed using a random-order Hadamard matrix assigned to each object. The proposed method achieves multi-object parallel encryption and independent decryption using a lightweight optical system, with improved efficiency, lower hardware costs, and smaller ciphertext size compared to conventional methods. In addition, it also exhibits robustness against both cropping and noise attacks. These results indicate potential for practical applications and may contribute to future developments in multi-object optical encryption for single-pixel imaging security.
Single-pixel imaging shows great potential for parallel perception of multiple objects. However, existing methods face information security risks and lack effective user access control. In this Letter, we propose an access-controlled imaging method based on structured single-pixel illumination. The system introduces phase modulation equivalently into the measurement matrix by applying key-controlled spatial displacements to the projection patterns, without requiring additional modulation devices. Meanwhile, an optical projection multiplexing architecture enables linear mixing of multi-object information. During reconstruction, the template decomposition vectors serve as user-specific keys for selective imaging. Experimental results demonstrate high-quality parallel imaging with integrated physical-layer access control, providing a promising solution for secure communication and hierarchical surveillance.