Abstract. Anatomical and functional information of cardiac vasculature is a key component of future developments in the field of interventional cardiology. With the technology of C-arm CT it is possible to reconstruct intraprocedural 3-D images from angiographic projection data. Current approaches attempt to add the temporal dimension (4D) by ECG-gating in order to distinct physical states of the heart. This model assumes that the heart motion is periodic. However, frequently arrhytmic heart signals are observed in a clinical environment. In addition breathing motion can still occur. We present a reconstruction method based on a 4-D time-continuous motion field which is parameterized by the acquisition time and not the quasi-periodic heart phase. The output of our method is twofold. It provides a motion compensated 3-D reconstruction (anatomic information) and a motion field (functional information). In a physical phantom experiment a vessel of size 3.08 mm undergoing a non-periodic mo...