# Binary Ghost Imaging Based on the Fuzzy Integral Method
## 3 Experiment Results and Comparative Analysis  
The experiment conducted based on the schematic of the BGI system as Figure 1 verifies the feasibility of the proposed algorithm. In the experiment, a pulse laser (NPL52B) is chosen as the laser source. The center wavelength and the pulsed average power of the laser are 520 \(\pm\) 10 nm and 12 mW, respectively. The laser illuminates a ground glass, which is slowly rotated by a stepping motor. A 50%-50% BS (BS031) is behind the RGG to split the light into object and reference paths. In the object path, a transmission spatial light modulator (SLM) is placed following the BS. The computer sends the image of target to the SLM to mimic transmission object. The effective active pixel number of SLM is 1024 \(\times\) 1024 and the resolution of target image is set to 128 \(\times\) 128. The diameter of focusing lens is 50 mm and the focus length of the lens is 100 mm. Light transmitted through the target is recorded by a single pixel detector (DET36A2). The detector is connected to a data acquiring card (NI-PXI-5154) to measure the total light intensity. The data acquiring card has 2 GHz bandwidth and the sampling frequency is 5 GHz/s. In the reference path, a CCD (MV-CA050-20 UM/UC) is used to record the speckle distribution. The distance between the CCD and BS should equal to that between the SLM and BS. The recorded speckle distributions are all binarized in the computer with the proposed binary method. The intensity distribution information of the target can be obtained by the correlation operation between the binarization speckle and the total light transmitting through the target. In the experiment, binary images are chosen as the target, whose pixel values are either 0 or 1. The resolution of the targets is 128 \(\times\) 128. The selected two binary image targets are a Chinese character and panda. The total number of measurements is set to 10,000 and the hyper-parameters \(w\) and \(\alpha\) are set to 16 and 0.095, respectively. Meanwhile, the reconstruction result of the proposed method is compared with DGI, MBGI, OBGI, and PPBGI. The images in the first row of Figure 4 are the speckle distributions utilized in the reconstruction processing of different methods. The speckle distribution in the first column is recorded by the CCD camera. The speckle distributions of other columns are obtained by different binarization methods. The reconstruction results of different methods are shown in the second and third rows. As the reconstruction results shown in Figure 4, reconstruction results with MBGI and OBGI, which utilize the global binarization method, have the worst image quality. The reconstructed Chinese character and panda image are blurry, with very low resolution and high noise. The reconstruction result of DGI is better than those of MBGI and OBGI. Although the resolution of reconstructed result is still low and the visual effect is still blurred, the noise in the background is reduced to a certain level. From the perspective of visual effect, the reconstructed results of PPBGI and FIBGI, which utilized the local adaptive binarization method, have the best reconstruction effects. Both methods have higher imaging resolutions and clearer target details than the other three methods. Compared with the PPBGI method, the proposed method is better. The edges of the reconstructed image by the PPBGI method are still blurred, and some details of the reconstructed image are distorted. In order to compare the reconstruction quality of different methods quantitatively, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are calculated as follows:  
\[PSNR=10\times\log_{10}(\frac{MAX_{1}^{2}}{MSE}), \tag{15}\]  
\[SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+c_{1})(2\sigma_{xy}+c_{2})}{(\mu_{x}^{2}+\mu_ {y}^{2}+c_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+c_{2})}. \tag{16}\]  
Figure 4: The binarized speckle distributions and the reconstruction results with different methods. The total number of measurements is 10,000.