## 1 Introduction  
Ghost imaging (GI), also known as correlated imaging (CI), has been extensively researched as a novel imaging method in recent years [1; 2; 3; 4; 5]. GI acquires object information by utilizing two spatially correlated optical beams. One beam known as the object beam crosses an object, and the reflected (or transmitted) signal is detected by a single-pixel bucket detector. The other beam, known as the reference beam, never interacts with the object and is detected by a spatially resolving detector. By calculating the correlation between the two beams, the image of the object can be recovered, and neither of them can restore the image of the object alone [6; 7]. The demonstration of GI using entangled photons was explained as a quantum phenomenon firstly [8; 9]. Subsequently, pseudothermal light sources and thermal light sources used in GI have also been proven effective [10; 11; 12]. Then, as a variant of the standard two-detector pseudothermal GI, computational ghost imaging (CGI), which simplifies the double optical paths to a single optical path and precomputes the reference patterns, further enhances the application of GI [13; 14; 15; 16]. Recently, several papers have been devoted to studying GI in imaging moving objects. The condition of GI to imaging a moving object was firstly given by the second-order correlation function through quasistatic approximation [17]. Later, it was proven that Fourier-transform ghost diffraction has the ability to overcome the influence of the system's shaking [18]. Then, the methods to overcome the decline of GI resolution caused by the tangential or axial movement of moving objects relative to the imaging system were discussed [19; 20]. Meanwhile, background-subtracted images of moving targets were reconstructed by using compressive sensing (CS) and complementary modulation techniques [21]. By tracking the target position or motion trajectory captured by the under-sampled image,the moving object's deblurred image can be gradually obtained [22, 23]. With the prior knowledge of the motion, a method of setting the object as static and inversely transforming the illumination mode to image a moving object was proposed [24]. To compensate for the limited rate of structured illumination, structured illumination based on the light-emitting diode (LED) was designed to capture images of moving objects [25, 26]. As CGI requires a certain number of measurements in one image, to reconstruct the image of a moving object with high quality, the object is always assumed to be relatively static during the measurement period. From the above works, we can see that there are two ways to improve the performance of imaging the moving object in CGI. One method is to design an optimization algorithm to reduce the number of measurements during the relative static period of the object as much as possible. Another way is to improve the performance of the devices in CGI to produce more speckle patterns and enable more detection in a small period. However, these schemes all need a high sampling bucket detector that performs the detection of the relatively static object in each measurement. In our previous work, we proposed a new scheme that uses a slow bucket detector to image an object with fast periodic moving/state-changed [27]. However, more speckle patterns and measurement times are required, resulting in an excessively long sampling time. Since traditional GI uses random speckle patterns, the number of measurements required to obtain a good reconstruction of an \(N\)-pixel image is much greater than \(N\)[28]. Subsequently, compressive ghost imaging (CSGI) was proposed to obtain better imaging performance from fewer than \(N\) measurements by exploiting the sparsity of the object, at the expense of computational time for the reconstruction [29, 30]. In this paper, we propose a method that uses a slow bucket detector to image objects with fast periodic moving/state-changes based on CSGI, and we call it MIPO-CSGI.