# Compressive Ghost Imaging of the Moving Object Using the Low-Order Moments
## 3 Experimental Results
Besides, compared with CBGI, the RMSE results of CS combined with the centroid estimation converges to a lower limit, which indicates a higher accuracy of object locating in our implementation. The better performance can be explained as, when the moving object is assumed to be sparse, the goal of CS reconstruction is to recover the sparse object from the sensing matrix corrupted by the unsparse noise. Once the background noise is suppressed, the accuracy of the centroid estimation could also be enhanced. Figure 3: Comparing the different object-locating methods on (**a**) the RMSE of the object displacement against the measurement number \(m\) per image period; (**b**) SSIM of the reconstructed images against the total measurement number \(M\). Secondly, the reconstructed image quality is evaluated by the widely-adopted structural similarity index (SSIM) [22], which considers the similarity between the image structures and the differences of image brightness and contrast at the same time. As shown in Figure 3b, the image quality of reconstructed images are both gradually improved with the increasing total measurement number \(M\). The results of the method based on CS combined with the centroid estimation possess a better visual quality than those of the CBGI, and the high performance can be attributed to the characteristics of CS, since it exploits the sparsity prior to suppress the background noise, which not only improve the reconstructed image quality, but also benefit the accuracy of the the centroid estimation. In addition, we also perform our experiment to estimate the rotation angle of a rotating object using the second-order moments of the reconstructed images. The angular speed of the rotating object is also set to be reciprocal to \(m\), e.g., when \(m=200\), the rotating speed of stepping motor is set to be \(10^{\circ}\)/s, and when \(m=400\), the speed is \(5^{\circ}\)/s, and the ideal objects corresponding to different rotations are shown in Figure 4I. For comparison, the normalized GI reconstructions are shown in Figure 4 II with a fixed measurement number \(m=400\) in each image periods, and the images are seemed to be degraded by the rotational motion blur. To tackle this problem, the CBGI method is also applied to estimate the rotation angle \(\phi\). Similarly, CBGI calculates the cross-correlation matrix between two blurry images reconstructed at different image periods and then rotate one of the images to find a maximum correlation. As shown in Figure 4 III, CBGI could effectively estimate the rotation angle of the object, and the reconstructed image quality is increased with the measurement number, while the visual perception is still not satisfactory. From Figure 4 IV, it can be easily observed that the reconstruction quality of the proposed method is better than the other methods under test, especially in the under-sampling cases. Besides, the proposed method could also accurately extract the rotation angle of the object, and effectively compensate the rotational blur caused by the rotating object. The quantitatively comparison of reconstructed image quality and accuracy of rotation estimation by different methods is shown as Figure 5. By comparing the reconstructed images with the ideal rotating object, the RMSE and SSIM are calculated and presented in Figure 5a,b, respectively. In general, the experimental results demonstrate that the rotation angle estimation and reconstructed quality of the proposed method is superior to the performance of CBGI in our implementation. In particular, the reconstructed image quality of the proposed scheme converges to its upper limit in the under-sampling cases, which suggests a great potential of the proposed method applying in the conditions of limited number of measurements. Figure 4: Reconstructed images of (**I**) the ideal rotating object, (**II**) normalized GI, (**III**) CBGI, (**IV**) CS with the rotation angle estimation, with the same image period \(m=400\).