Theoretically exact backprojection filtration algorithm for multi-segment linear trajectory

A theoretically exact backprojection filtration algorithm is proved and implemented for image reconstruction from a multi-segment linear trajectory assuming fan-beam geometry. The reconstruction formula is based on a concept of linear PI-line (L-PI) proposed in our previous work. The proof is completed in two consecutive steps. In the first step, it is proved that theoretically exact image reconstruction can be obtained on an arbitrary L-PI line from an infinite straight-line trajectory. In the second step, it is shown that accurate image reconstruction can be achieved from a multi-segment line trajectory by introducing a weight function to deal with the data redundancy. Numerical implementation and simulation results validate the correctness of our theoretical results.