# Compressive Ghost Imaging of the Moving Object Using the Low-Order Moments
## 4 Discussions  
The effectiveness of the proposed method relies on the assumption that, during a limited number of measurements, the moving object can be regarded as immobile [7; 13]. So we can infer that, if the object is moving fast and the sampling rate of the camera is low, the number \(m\) of the measurements to meet our assumptions would be limited to a very small value. In reverse, if we have a camera with a moderately high sampling rate, we would have a much greater tolerance for the moving speed of the object. Moreover, in our experiment, we consider that the frame rate of the camera is limited to 200 fps, so the number of measurements \(m\) to satisfy our assumption is also finite. If the number of measurements in each image period is not set properly, it may result to an inadequate sampling or some additional motion blur.  
For example, as shown in Figure 7I,II, when the speed of the horizontal translational moving object is set to be 0.65 mm/s, and the frame rate of the camera is 200 fps, the reconstructed image quality first increase with the number of measurements, and then decrease due to the appearance of the motion blur. Similarily, in Figure 7 II,IV, when the rotating speed of the moving object is set to be \(10^{\circ}\)/s, the behavior of the reconstructed image quality against the number of measurements appears a similar upward and then downward trend. It also suggests the importance to choose a proper \(m\) when  
Figure 6: The influence of the penalty parameter \(\tau\) on (**a**) the object translation estimation accuracy evaluated by the RMSE; (**b**) the reconstructed image quality of the translating object evaluated by the SSIM; (**c**) the object rotation estimation accuracy; (**d**) the image quality of the rotating object, under different measurement number \(m\) per image period.  
the sampling rate of the camera is not high enough. Once the sampling device is fast enough, it will be more tolerant to the choice of \(m\).  
Although, there are already many outstanding deblurring methods developed to solve the motion blur in conventional imaging. It is worth noticing that, in the conventional \"single-snapshot\" direct imaging, the translational motion blur is usually modeled as a convolution of a clear image with a shift-invariant blur kernel, e.g., the point spread function. The commonly used methods to solve this kind of problem is applying some additional image priors, such as the global gradient distribution of the clear images [25]. Moreover, handling the rotational motion blur could be an even more difficult task, since the blur kernel is spatially variant in size, shape and values among pixels. To solve the problem, some research regards the spatially variant kernel as a weighted sum of several spatially invariant kernels [26], and makes the problem solvable. However, the motion blur model is quite different in GI, since it relies on the random modulation of the light source and only point a non-resolvable bucket detector to the object, thus the blur kernel cannot be directly and accurately analyzed. Therefore, there still exists some obstacles to be solved when introducing the noted motion deblurring algorithms into the GI scenario.