The singular value decomposition ghost imaging (SVDGI) is proposed to enhance the fidelity of computational ghost imaging (GI) by constructing a measurement matrix using singular value decomposition (SVD) transform. After SVD transform on a random matrix, the non-zero elements of singular value matrix are all made equal to 1.0, then the measurement matrix is acquired by inverse SVD transform. Eventually, the original objects can be reconstructed by multiplying the transposition of the matrix by a series of collected intensity. SVDGI enables the reconstruction of an N-pixel image using much less than N measurements, and perfectly reconstructs original object with N measurements. Both the simulated and the optical experimental results show that SVDGI always costs less time to accomplish better works. Firstly, it is at least ten times faster than GI and differential ghost imaging (DGI), and several orders of magnitude faster than pseudo-inverse ghost imaging (PGI). Secondly, in comparison with GI, the clarity of SVDGI can get sharply improved, and it is more robust than the other three methods so that it yields a clearer image in the noisy environment.

An optical identity authentication scheme based on the elliptic curve digital signature algorithm (ECDSA) and phase retrieval algorithm (PRA) is proposed. In this scheme, a user’s certification image and the quick response code of the user identity’s keyed-hash message authentication code (HMAC) with added noise, serving as the amplitude and phase restriction, respectively, are digitally encoded into two phase keys using a PRA in the Fresnel domain. During the authentication process, when the two phase keys are presented to the system and illuminated by a plane wave of correct wavelength, an output image is generated in the output plane. By identifying whether there is a match between the amplitude of the output image and all the certification images pre-stored in the database, the system can thus accomplish a first-level verification. After the confirmation of first-level verification, the ECDSA signature is decoded from the phase part of the output image and verified to allege whether the user’s identity is legal or not. Moreover, the introduction of HMAC makes it almost impossible to forge the signature and hence the phase keys thanks to the HMAC’s irreversible property. Theoretical analysis and numerical simulations both validate the feasibility of our proposed scheme.

A multiple-image authentication method with a cascaded multilevel architecture in the Fresnel domain is proposed, in which a synthetic encoded complex amplitude is first fabricated, and its real amplitude component is generated by iterative amplitude encoding, random sampling, and space multiplexing for the low-level certification images, while the phase component of the synthetic encoded complex amplitude is constructed by iterative phase information encoding and multiplexing for the high-level certification images. Then the synthetic encoded complex amplitude is iteratively encoded into two phase-type ciphertexts located in two different transform planes. During high-level authentication, when the two phase-type ciphertexts and the high-level decryption key are presented to the system and then the Fresnel transform is carried out, a meaningful image with good quality and a high correlation coefficient with the original certification image can be recovered in the output plane. Similar to the procedure of high-level authentication, in the case of low-level authentication with the aid of a low-level decryption key, no significant or meaningful information is retrieved, but it can result in a remarkable peak output in the nonlinear correlation coefficient of the output image and the corresponding original certification image. Therefore, the method realizes different levels of accessibility to the original certification image for different authority levels with the same cascaded multilevel architecture.

In recent years, low-cost high-quality non-line-of-sight (NLOS) imaging by a passive light source has been a significant research dimension. Here, we report a new, to the best of our knowledge, reconstruction method for the well-known “occluder-aided” NLOS imaging configuration based on an untrained deep decoder network. Using the interaction between the neural network and the physical forward model, the network weights can be automatically updated without the need for training data. Completion of the optimization process facilitates high-quality reconstructions of hidden scenes from photographs of a blank wall under high ambient light conditions. Simulations and experiments show the superior performance of the proposed method in terms of the details and the robustness of the reconstructed images. Our method will further promote the practical application of NLOS imaging in real scenes.