# Compressive Ghost Imaging of the Moving Object Using the Low-Order Moments
## 3 Experimental Results  
The experimental demonstration of the proposed method is performed to validate the capability of object-locating and imaging. For comparison, the reproduction of CBGI and the blurred results of the normalized second-order correlation are obtained as well. As a proof-of-concept experiment, the maximum frame rate of our commercial CMOS detector is restricted to be 200 fps. In order to ensure the object to be static in an image period, the speed of the moving object is adjusted by controlling the stepping motor to be reciprocal to the measurement number \(m\) in each image period. For instance, when \(m=300\), the moving speed of object is set to be 0.45 mm/s, and for \(m=600\), the moving speed is set to be 0.225 mm/s. When \(m=300\), the ideal motion status of the object corresponding to different image periods are calculated and shown in Figure 2I. For comparison, the images reconstructed by the normalized GI is also presented in Figure 2 II, which is suffered from the severe motion blur and makes the image illegible. To locate the real trajectory and compensate the displacement of the moving object, the reproduction of CBGI is shown in Figure 2 III. By calculating the cross-correlation function between the blurry images with different displacements, CBGI would locate the relative motion of the moving object when the cross-correlation function reaches its maximum. The image quality of CBGI is gradually improved with the increasing measurement number, and object location can be effectively extracted using the cross-correlation method. However, the reconstructed image quality of CBGI is still suffered from the background noise due to the nature of statistical correlation. Figure 2: Reconstructed images of (**I**) the ideal moving object, (**II**) normalized GI, (**III**) CBGI, (**IV**) CS with the centroid estimation, with the same image period \(m=300\). To improve the reconstructed image quality, and to reduce the necessary measurement number in each image period at the same time, we applied the GPSR algorithm to suppress the background noise, and further improve the object-locating accuracy of centroid estimation. During the experiment, the repeated measurement process is uninterrupted, and when the number of measurements within each image period reach the preset number \(m\), the GPSR algorithm will be activated to reconstruct the image using the \(m\) measurements, and the low-order moments are activated afterwards to extract the motion information of the moving object. The centroid-estimated object location and the CS image reconstructions and are shown in Figure 2 IV. Intuitively speaking, the image quality of CS reconstructions is better than that of second-order correlations, including the CBGI. In order to make a comprehensive comparison of the different methods, the experimental results are quantitatively evaluated to compare the object location accuracy and the reconstructed image quality. At first, the accuracy of the object-locating estimation can be characterized by the rooted-mean-square-error (RMSE), written as  
\[RMSE=\sqrt{\frac{1}{K}\sum_{k=1}^{K}\left[(\vec{e}_{k}-\vec{r}_{k})^{2}\right]} \tag{9}\]  
where \(\vec{e}_{k}\), \(\vec{r}_{k}\) is the vectorized representation of the estimated and the ideal trajectory, respectively. As discussed in Ref. [13], the accuracy of the object-locating procedure could be greatly effected by the measurement number \(m\) in each image period. To get a clearer view, the RMSE of different methods is presented in Figure 3a. Here, we have to mention that, to ensure the object to be static in an image period, the moving speed of the object is also adjusted in this experiment to compensate for different number of measurements. With the increasing measurement number \(m\), the object-locating accuracy of different methods evaluated by RMSE appears to be declining, which is consistent with the inference in Ref. [13].