Fig. 13

Illustration of the LUT-based point-backprojector. To determine which sinogram points are backprojected on coefficient \(i \in [0, N_g]\), the matrix \(\mathrm {Pos2}\) (bottom), is accessed at index i, and contains the value \(\mathrm {Pos2}[i] = q_i\). This value \(q_i\) is a position in LUT \(J_2\) (middle), so that \(J_2[q_i] = k_1\) is the index of one sinogram entry being backprojected at index i of the coefficients vector. The process is repeated for \(q_i +1\) until \(q_{i+1}-1\). The corresponding range in \(J_2\) (shaded orange) indicates sinogram indexes that are all backprojected on coefficient index i