Image reconstruction for a general circle-plus trajectory

We develop an exact filtered backprojection (FBP) algorithm for a general class of circle-plus trajectories, which consist of two components: C and L. The first component C, which is analogous to a circle of the traditional circle-plus trajectories, is essentially any closed (e.g., not necessarily planar) continuous curve. The second component L is almost any continuous curve. The only condition is that L starts below C and ends above C. The distinctive feature of the new algorithm is that it does not depend on the global properties of L. When the source is located on L, the only thing one needs to know is how C projects onto the corresponding detector. The algorithm is especially convenient for the traditional circle-plus trajectories, which are implemented using a gantry and moving table. In this case we obtain a universal FBP algorithm, which is completely independent of how the table moves during the scan (provided that the main condition on L is satisfied). The results of testing the algorithm on two circle + helix trajectories demonstrate good image quality.