Efficient Fourier single-pixel imaging based on weighted sorting

Fourier single-pixel imaging (FSI) has attracted increased attention in recent years with the advantages of a wide spectrum range and low cost. FSI reconstructs a scene by directly measuring the Fourier coefficients with a single-pixel detector. However, the existing sampling method is difficult to balance the noise suppression and image details within a limited number of measurements. Here we propose a new sampling strategy for FSI to solve this problem. Both the generality of the spectral distribution of natural images in the Fourier domain and the uniqueness of the spectral distribution of the target images in the Fourier domain are considered in the proposed method. These two distributions are summed with certain weights to determine the importance of the Fourier coefficients. Then these coefficients are sampled in order of decreasing importance. Both the simulations and experiments demonstrate that the proposed method can capture more key Fourier coefficients and retain more details with lower noise. The proposed method provides an efficient way for Fourier coefficient acquisition.

Fractional Fourier single-pixel imaging

Single-pixel imaging technology has a number of advantages over conventional imaging approaches, such as wide operation wavelength region, compressive sampling, low light radiation dose and insensitivity to distortion. Here, we report on a novel single-pixel imaging based on fractional Fourier transform (FRFT), which captures images by acquiring the fractional-domain information of targets. With the use of structured illumination of two-dimensional FRFT base patterns, FRFT coefficients of the object could be measured by single-pixel detection. Then, the object image is achieved by performing inverse FRFT on the measurements. Furthermore, the proposed method can reconstruct the object image from sub-Nyquist measurements because of the sparsity of image data in fractional domain. In comparison with traditional single-pixel imaging, it provides a new degree of freedom, namely fractional order, and therefore has more flexibility and new features for practical applications. In experiments, the proposed method has been applied for edge detection of object, with an adjustable parameter as a new degree of freedom.

Compressive optical image encryption

An optical image encryption technique based on compressive sensing using fully optical means has been proposed. An object image is first encrypted to a white-sense stationary noise pattern using a double random phase encoding (DRPE) method in a Mach-Zehnder interferometer. Then, the encrypted image is highly compressed to a signal using single-pixel compressive holographic imaging in the optical domain. At the receiving terminal, the encrypted image is reconstructed well via compressive sensing theory, and the original image can be decrypted with three reconstructed holograms and the correct keys. The numerical simulations show that the method is effective and suitable for optical image security transmission in future all-optical networks because of the ability of completely optical implementation and substantially smaller hologram data volume.