High x-ray radiation dose is a major public concern with the increasing use of multidetector computed tomography (CT) for diagnosis of cardiovascular diseases. This issue must be effectively addressed by dose-reduction techniques. Recently, our group proved that an internal region of interest (ROI) can be exactly reconstructed solely from localized projections if a small subregion within the ROI is known. In this article, we propose to use attenuation values of the blood in aorta and vertebral bone to serve as the known information for localized cardiac CT. First, we describe a novel interior tomography approach that backprojects differential fan-beam or parallel-beam projections to obtain the Hilbert transform and then reconstructs the original image in an ROI using the iterative projection onto convex sets algorithm. Then, we develop a numerical phantom based on clinical cardiac CT images for simulations. Our results demonstrate that it is feasible to use practical prior information and exactly reconstruct cardiovascular structures only from projection data along x-ray paths through the ROI.