A Direct Proof of Katsevich’s Algorithm in 2D Case

In this work, we propose a direct proof of Katsevich’s algorithm in two-dimensional (2D) case where the proof starts off directly from the 2D fan-beam projection data. Our proof connects the fan-beam data to the Fourier data directly. The geometric meaning in our approach manifests Tuy’s condition. During the proof, we identify that the 2D version of Katsevich’s algorithm is valid for a broader class of scanning trajectories. Also, during the proof, we identity that the so-called filtered backprojection (FBP) algorithm along π-lines comes out of Katsevich’s algorithm very naturally in 2D case.