A Single-Pixel High-Precision Imaging Technique Based on a Discrete Zernike Transform for High-Efficiency Image Reconstructions

Single-pixel imaging (SPI) has attracted increasing attention in recent years because of its advantages in imaging systems. However, a low reconstruction quality and a long reconstruction time have hindered the development of SPI. Hence, in this study, we propose a Zernike SPI (ZSPI) technique to reduce the number of illumination patterns and reconstruction time whilst retaining robustness. First, the ZSPI technique was theoretically demonstrated. Phase-shifting Zernike moment projections were used to illuminate the target and an inverse Zernike transform was used to reconstruct the desired image. In order to prove the feasibility, numerical simulations were carried out with different sample ratios (SRs) ranging from 0.1 to 0.3; an acceptable reconstruction appeared at approximately 0.1. This result indicated that ZSPI could obtain satisfactory reconstruction results at low SRs. Further simulation and physical experiments were compared with different reconstruction algorithms, including noniterative, linear iterative, and nonlinear iterative methods under speckle modulation patterns at a sample of 0.1 in terms of different targets. The results revealed that ZSPI had a higher imaging quality and required less imaging time, particularly for low-frequency targets. The method presented in this study has advantages for the high-efficiency imaging of low-frequency targets, which can provide a new solution for the SPI method.