The U(2) Fourier group for rectangular pixellated images

Kurt Bernardo Wolf, Natig M. Atakishiyev

The Fourier group U(2) F is the maximal compact group of the group of linear canonical transformations on configuration space. When we finitely quantize the two-dimensional harmonic oscillator we turn this space into an array of N 2 points arranged along either Cartesian or polar coordinates, as a square or a circle, that model pixellated screens. We investigate the action of U(2) F on these two N 2 -dimensional spaces, which become a homogeneous space for this group action.

Luis Edgar Vicent

Tianyu ZENG, Liansheng Sui, Cong Du +2 more

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.

Д.Т. Мухамедиева, Р.А. Собиров, N. M. Turgunova +1 more

Rui Wang, Yuanjin Yu, Jiali Zheng +1 more

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.

Fei Yan, Shan-Shan Zhao, Salvador Elías Venegas-Andraca +1 more