Coronary artery imaging with multi-slice helical computed tomography is a promising noninvasive imaging technique. The current major issues include the insufficient temporal resolution and large patient dose. We propose an image reconstruction method which provides a solution to both of the problems. The method uses an iterative approach repeating the following four steps until the difference between the two projection data sets falls below a certain criteria in step-4: 1) estimating or updating the cardiac motion vectors, 2) reconstructing the time-resolved 4D dynamic volume images using the motion vectors, 3) calculating the projection data from the current 4D images, 4) comparing them with the measured ones. In this study, we obtain the first estimate of the motion vector. We use the 4D NCAT phantom, a realistic computer model for the human anatomy and cardiac motions, to generate the dynamic fan-beam projection data sets as well to provide a known truth for the motion. Then, the halfscan reconstruction with the sliding time-window technique is used to generate cine images: f(t, r). Here, we use one heart beat for each position r so that the time information is retained. Next, the magnitude of the first derivative of f(t, r) with respect to time, i.e., |df/dt|, is calculated and summed over a region-of-interest (ROI), which is called the mean-absolute difference (MAD). The initial estimation of the vector field are obtained using MAD for each ROI. Results of the preliminary study are presented.