# Experimental Investigation of Anisotropic Diffusion Applied in Ghost Imaging Reconstruction
## 3 Experiments and Discussion  
To verify the effectiveness of our method, a series of experiments were performed using the setup shown in Figure 1. Given that IPGI has a fine ability of image reconstruction, the number of experimental samples was small, less than 6400 groups. In the first set of experiments, we choose a binary transmission aperture \"Zhong\" (shown in Figure 3a)as the reconstructed object, the distance L\({}_{1}\) (L\({}_{1}\) = L\({}_{2}\)) was 200 mm, the focal length f of the lens was 150 mm and the speckle transverse size was 40 \(\upmu\)m. CCD1 and CCD2 were identical devices (Stingray F-504B, AVT, Stadtroda, Germany), however, their roles in the experiment are completely different: CCD1 is used to gather the sum of light field distribution when the object beam has been modulated, while CCD2 is used to record the light field distribution of the reference beam at the surface of the measured object. For a simple illustration, the method of combining anisotropic diffusion with IPGI is abbreviated as AD-IPGI. The peak signal-to-noise ratio (PSNR) is introduced as a quantitative measurement of the similarity between the reconstructed image and the original image, to evaluate the method more objectively. It is defined as:  
\[PSNR=10\times\log_{10}\left[\frac{\left(2^{8}-1\right)^{2}}{MSE}\right], \tag{12}\]  
where \(2^{8}-1\) indicates that the maximum pixel value of the grayscale image, the range of pixel values is from 0 to 255, and MSE represents the mean square error between the original image and the reconstructed image. As shown in Figures 4 and 5, with the increase of measurement times, the visual effects of the reconstructed images of IPGI and AD-IPGI are synchronously enhanced, their PSNR also respectively rises to varying degrees, but the PSNR of IPGI rises slowly, and there is so much background noise in its reconstructed images, even some information of the imaging object \"Zhong\" is submerged by the background noise with the sampling time of 600. Instead, we can see an obvious enhancement of both the visual effect and the PSNR of the reconstructed image of AD-IPGI over that of IPGI at the same sampling times. The noise of AD-IPGI results is reduced and the imaging quality is increased greatly after the anisotropic diffusion process. The edges can be well preserved in reconstructed images of AD-IPGI, even at the measurement time of 600. The experimental results show the effectiveness of our method. Our method performs better in experiments with smaller speckle transverse size. This is because the size of noise points and speckle are similar in ghost imaging experiments, and the isolated smaller noise points in the original images can be removed more effectively by anisotropic diffusion, making the constructed noise disturbance closer to the actual noise with the edges well preserved. In the second set of experiments, we chose imaging object \"Slits\" (shown in Figure 3b) as the reconstructed object. The experimental parameters depicted in Figure 1 are as follows: L\({}_{1}\) = L\({}_{2}\) = 150 mm, f = 250 mm, and the speckle transverse size is 19.5 \(\upmu\)m. Experimental results are shown in Figures 6 and 7, where the reconstruction images of IPGI are filled with massive background noise. Some imaging information may be masked by the background noise at fewer measurement times, such as the detail loss of  
Figure 3: The reconstructed objects: (**a**) imaging object “Zhong” (80 \(\times\) 80 pixels), (**b**) imaging object “Slits” (80 \(\times\) 80 pixels, slit width a = 30 \(\upmu\)m, slit height h = 300 \(\upmu\)m, and center-to-center separation d = 60, 120, 180, and 240 \(\upmu\)m). the two stripes on the right side in the IPGI result; the detail loss is serious at 500 groups of data. Under the same conditions, AD-IPGI has better performance on \"Slits\" imaging. As shown in Figure 6, AD-IPGI reduces the noise and strengthens the visual effects effectively.