High-efficiency single-pixel imaging using discrete Hartley transform

Single-pixel imaging technology is popular with invisible wavelengths and low light environments. However, the time-consuming steps hindered the development of single-pixel imaging technology. To improve imaging efficiency, a high-efficiency one-step single-pixel imaging method based on the discrete Hartley transform is proposed. The proposed method does not require a large number of fringe patterns and only requires a real-number calculation. The number of fringe patterns required for the proposed method is only half of that required for the four-step phase-shift Fourier method at the same sampling rate. Although a one-step method, it also uses the idea of differential measurements and adds upsampling processing strategies, which simultaneously improve the signal-to-noise ratio of the recovered image. The simulation shows that the peak signal-to-noise ratio and structural similarity index of the recovered target scene exceed 20 dB and 80%, respectively, when the sampling rate is 30%. Only 20 164 patterns are needed to reconstruct a (256 × 256)-pixel image. After defocusing the gray stripe pattern into a binary pattern, it only takes milliseconds to project these patterns into the target. It can be seen that the experimental results of the proposed method are significantly better than those of the two-step phase-shift method under dramatical noise interference. With the rapid development of advanced equipment, this method will represent significant progress in the real-time reconstruction of single-pixel imaging.