Two major problems with the current electrocardiogram-gated cardiac computed tomography (CT) imaging technique are a large patient radiation dose (10-15 mSv) and insufficient temporal resolution (83-165 ms). Our long-term goal is to develop new time resolved and low dose cardiac CT imaging techniques that consist of image reconstruction algorithms and estimation methods of the time-dependent motion vector field (MVF) of the heart from the acquired CT data. Toward this goal, we developed a method that estimates the 2D components of the MVF from a sequence of cardiac CT images and used it to "reconstruct" cardiac images at rapidly moving phases. First, two sharp image frames per heart beat (cycle) obtained at slow motion phases (i.e., mid-diastole and end-systole) were chosen. Nodes were coarsely placed among images; and the temporal motion of each node was modeled by B-splines. Our cost function consisted of 3 terms: mean-squared-error with the block-matching, and smoothness constraints in space and time. The timedependent MVF was estimated by minimizing the cost function. We then warped images at slow motion phases using the estimated vector fields to "reconstruct" images at rapidly moving phase. The warping algorithm was evaluated using true time-dependent motion vector fields and images both provided by the NCAT phantom program. Preliminary results from ongoing quantitative and qualitative evaluation using the 4D NCAT phantom and patient data are encouraging. Major motion artifact is much reduced. We conclude the new image-based motion estimation technique is an important step toward the development of the new cardiac CT imaging techniques.