Fig. 1. Fourier slice theorem. (a) Projection R(s,θ) when angle between projection direction and horizontal direction is θ; (b) Fourier slice corresponding to angle θ

Fig. 2. Discrete Fourier slice theorem. (a) Discrete Radon projection data in different angles; (b) projection of one-dimensional Fourier transform of discrete Radon projection data in Fourier domain

Fig. 3. Example of Mojette transform for 3×3 image. (a) Projection vector (p,q); (b) Mojette projection data in different projection vector directions

Fig. 4. Diagram of sets of discrete frequency points along different projection directions in Fourier domain

Fig. 5. Discrete frequency points in different projection positions. (a) Frequency points along tangential corresponding to θ=arctan 3; (b) frequency points along tangential corresponding to θ=arctan(5/7)

Fig. 6. Reconstruction results of proposed algorithm. (a)-(d) Original images; (e)-(h) two-dimensional frequency domain of reconstruction images; (i)-(l) reconstruction results of proposed algorithm

Fig. 7. Comparison of reconstruction results of several algorithms. (a)(e)(i) Original images; (b)(f)(j) reconstruction results in Ref. [14]; (c)(g)(k) reconstruction results of proposed algorithm; (d)(h)(l) reconstruction results of SART algorithm

Fig. 8. Image gray values in 28-th row of images in horizontal directions. (a) Image gray value in 1st row of Fig. 7; (b) image gray value in 2nd row of Fig. 7; (c) image gray value in 3rd row of Fig. 7