Fig. 1. Projection process under two-dimensional X-ray parallel beams

Fig. 2. Flow chart of algorithm

Fig. 3. Sample images. (a) Sample 1; (b) sample 2

Fig. 4. Attenuation coefficients of sample 1. (a) Attenuation coefficients of base materials; (b) relative difference in attenuation coefficient of base material

Fig. 5. Projection results under different voltages. (a) Projections; (b) grayscale line graphs at middle horizontal position of projections

Fig. 6. Reconstruction results under different voltages. (a) Reconstruction images; (b) line graphs of attenuation coefficients at middle horizontal positions of reconstructed images

Fig. 7. Decomposition projection results of BSM-BE model in the 7^th, 9^th, and 11^th spectral intervals. (a) Projections; (b) grayscale line graphs at middle horizontal positions of separated projections

Fig. 8. Decomposition projection results of improved model in the 7^th, 9^th, and 11^th spectral intervals. (a) Projections; (b) grayscale line graphs at middle horizontal positions of separated projections

Fig. 9. Reconstruction results of BSM-BE model in 7^th, 9^th, and 11^th spectral intervals. (a) Reconstruction images; (b) line graphs of attenuation coefficients at middle horizontal positions of reconstructed images

Fig. 10. Reconstruction results of improved model in the 7^th, 9^th, and 11^th spectral intervals. (a) Reconstruction images; (b) line graphs of attenuation coefficients at middle horizontal positions of reconstructed images

Fig. 11. Differential line charts of attenuation coefficients of reconstructed images of different models and theoretical attenuation coefficients. (a) 7^th spectral interval; (b) 9^th spectral interval; (c) 11^th spectral interval

Fig. 12. Change curves of average attenuation coefficient of magnesium with energy

Fig. 13. Change curves of average attenuation coefficient of aluminum with energy

Fig. 14. Reconstruction results of direct reconstruction, BSM-BE model, and improved model. (a) Reconstruction images; (b) line graphs of attenuation coefficients at middle horizontal positions of reconstructed images