Results of density map

In the previous work, the projection error remained in density maps obtained with DE algorithm when three materials existed on the projection plane. In this work, the TE algorithm was applied to separate the three materials by using the TE monochromatic X-ray beam. The projection error was removed by this method in experimental results. Then, the density map obtained with the proposed TE X-ray beam was similar to the result acquired with photon-counting method.

The linear attenuation coefficients of I, Al, and PMMA for both proposed TE monochromatic X-ray beam and photon-counting method from experimental data were used as a matrix with _Iⁱ, ⁱ_A, and ⁱ_P in equation 3.6 for producing thickness density maps. The obtained phantom images consisting of I, Al, and PMMA were used as log intensity images into T(1), T(2), and T(3), respectively, in equation 3.6 for the proposed TE monochromatic X-ray beams and photon-counting method.

Figure 4.8 showed examples of the experimental images of the phantom at different energies and the reconstructed density maps obtained for the TE method. In figure 4.8 (a), (b), and (c) are thickness density maps of I, Al, and PMMA, respectively, were acquired with proposed TE monochromatic X-ray beam experimentally. Figure 4.8 (d), (e), and (f) are the experimental images of thickness density maps of I, Al, and PMMA with photon-counting method. Figure 4.8 indicates that the densities of I, Al, and PMMA were enhanced from background material obtained by TE monochromatic X-ray beam and photon-counting method.

Figure 4.8 (a) I, (b) Al, and (c) PMMA are obtained with the proposed TE monochromatic X-ray beams with I, Ba, and Gd filters for 50, 60, and 70 kV, respectively. (d) I, (e) Al, and (f) PMMA are the material density maps obtained with the photon-counting method.

The true thickness values of I, Al, and PMMA were 0.50, 0.50, and 2.00 cm, respectively. The three materials I, Al, and PMMA were well separated at each thickness density map obtained with both the proposed TE X-ray beams and photon-counting methods as shown in figure 4.8. The thicknesses densities of I, Al, and PMMA were measured as 0.57, 0.52, and 1.99 cm, respectively, by the proposed TE monochromatic X-ray beams. In the photon-counting method, thickness densities of I, Al, and PMMA were 0.50, 0.51, and 2.05, respectively. The evaluation of thickness density is illustrated in figure 4.9.

Figure 4.9 Thickness density maps of I, Al, and PMMA obtained by the proposed TE X-ray beams and photon-counting methods.

4.4. Discussion

We measured and evaluated the effect of three designed X-ray beams by quantitative indices of mean energy ratio, contrast variation ratio, and exposure efficiency. In addition, density maps were reconstructed using the proposed TE beams and photon-counting methods. Then, the results of density map were evaluated.

Mean energy ratio was estimated for the proposed TE monochromatic X-ray beams and photon-counting methods in equation 3.1. In the simulation results, mean energy ratio is closed to unity for E_1, E_2, and E_3. As shown in the results, mean energy ratio obtained with the proposed TE X-ray beam is nearly balanced when the beams are through Al and PMMA. Therefore, the proposed method contributes to improvement of image contrast according to experimental findings.

Contrast variation ratio was measured at E_1, E_2, and E_3. Contrast variation ratio was calculated as the ratio of the contrast with K-edge filter to contrast without filter.

The improvements of contrast when using filter were 29.00 and 22.00 % for E_1 and E_2, respectively. However, contrast obtained with E_3 declined to 5.00 % because the mean energy of X-ray beam by using filter is higher than that of unfiltered X-ray beam.

Higher energy X-ray beam caused decreasing image contrast. Thus, the monochromatic X-ray beam is effective to improve the image contrast compared to unfiltered X-ray beam.

Exposure efficiency was estimated at E_1, E_2, and E_3. The exposure efficiency acquired with the proposed X-ray beam improved to 35.58 and 50.29 % for E_1 and

E_2, respectively. In E_3, exposure efficiency is decreasing to 14.48 %. Thus, the proposed TE X-ray beam can reduce the exposure dose to the object effectively.

However, the energy spectrum generated by filter having a high K-edge energy is considered to avoid loss of image quality. In this result, monochromatic X-ray beams acquired with low energy K-edge filter improve the contrast and reduce the exposure dose from exposure efficiency.

Prior to reconstructing density map for I, Al, and PMMA, linear attenuation coefficients were decided by measuring the thickness of Al and PMMA blocks with the TE X-ray beam and photon-counting methods. If the X-ray beam is monochromatic, the linear attenuation coefficient is measured accurately [42, 43]. Log intensities for Al and PMMA were increasing in accordance with thickness of the block. Effective linear attenuation coefficients were calculated by using equation 3.1.

From the TE X-ray beam, three materials decomposition was performed for I, Al, and PMMA. Three materials can be decomposed by thickness density maps, which need the information of linear attenuation coefficients of I, Al, and PMMA. Therefore, the linear attenuation coefficients were obtained with attenuation coefficient maps for the proposed method, and the results were compared to the results obtained with the photon-counting method. The resultant thicknesses of I, Al, and PMMA were 0.57, 0.52, and 1.99 cm, respectively, with the proposed TE X-ray beam. In the photon-counting method, thickness densities of I, Al, and PMMA were 0.50, 0.51, and 2.05 cm, respectively. The results of thickness density maps for I, Al, and PMMA indicated that the decomposed image acquired with the proposed method was similar to the

decomposed image obtained with the photon-counting method according to the experimental study.

In this chapter, we investigated the quantitative image metrics of contrast, variation ratio, and exposure efficiency from the TE X-ray beam from the simulation study.

Then, the thickness density maps were acquired with both the proposed and photon-counting methods. Monochromatic beam considering K-edge filter and tube potential can improve the image contrast through contrast variation ratio evaluation. The trend of exposure efficiency is similar to that in simulation results. Thus, a dose reduction effect is expected with the proposed method. Therefore, the triple-energy X-ray beam was well validated with experimental study by verifying quantitative image metrics.