6. Optimization parameter

Mono\_p\_img ¼ f CaCO<sup>3</sup>

76 Medical Imaging and Image-Guided Interventions

5. DT system

5.1. DT overview

5.2. DE-DT acquisition

that of conventional DT.

val, 1 mm).

<sup>∗</sup> μ r 

CaCO3

monochromatic processing, and MLEM, were implemented in MATLAB.

tively (antiscatter grid, focused type; grid ratio, 12:1).

ð Þþ E f PMMA

where Mono\_p\_img is the virtual monochromatic projection image, and [μ/r]caco3(E), [μ/ r]PMMA(E), and [μ/r]epoxy(E) are the mass attenuation coefficients of each material. The generated virtual monochromatic X-ray projection image was reconstructed by using each algorithm for energies of 60, 80, 100, 120, and 140 keV. The real projection data acquired on a DT system were used for reconstruction. All image reconstruction calculations, including DE material decomposition processing and reconstruction, as well as FBP, SART, SART-TV, virtual

The DT system (SonialVision Safire II; Shimadzu Co., Kyoto, Japan) comprised an X-ray tube [anode: tungsten with rhenium and molybdenum; real filter: inherent; aluminum (1.1 mm), additional; aluminum (0.9 mm), and copper (0.1 mm)] with a 0.4 mm focal spot and 362.88 � 362.88 mm amorphous selenium digital flat-panel detector (detector element, 150 � <sup>150</sup> <sup>μ</sup>m2

The source-to-isocenter and isocenter-to-detector distances were 924 and 1100 mm, respec-

Collimator motion was synchronized by measuring the misalignment of the low-voltage (60 kV) and high-voltage (120 kV) images at a constant tube motion. A large energy gap between low and high tube potential kVp imaging yields better material decomposition [28–33]. We selected the abovementioned kV values because this study aimed to improve contrast and artifact reduction during DT acquisition while maintaining an imaging performance similar to

Pulsed X-ray exposures and rapid switching between low and high tube potential kVp values were used for DE-DT imaging. Linear system movement and a swing angle of 40� were used when performing tomography, and 37 low- and high-voltage projection images were sampled during a single tomographic pass. We used a low voltage, and each projection image was acquired at 416 mA. A 9.4 ms exposure time was used for low-voltage (60 kV) X-rays at 416 mA, and a 2.5 ms exposure time was used for high-voltage (120 kV) X-rays. To generate reconstructed tomograms of the desired height, we used a 768 � 7684 matrix with 32 bits (single-precision floating number) per image (pixel size, 0.252 mm/pixel; reconstruction inter-

<sup>∗</sup> μ r 

PMMA

ð Þþ E f epoxy

<sup>∗</sup> μ r 

epoxy

ð Þ E (17)

).

The experiments were performed according to the scheme shown in Figure 3. A range of optional parameters have been identified for IR algorithms. Among these parameters, some are important for determining algorithmic behavior. In this study, we compared the root-meansquare error (RMSE) and mean structural similarity (MSSIM; reconstructed volume image from the previous iterations between the current iteration) to optimize the iteration numbers (i).

The RMSE was defined in this study as follows:

$$RMSE = \sqrt{\frac{\sum\_{i=1}^{n} \left(\hat{y}\_k - y\_k\right)^2}{n}} \tag{18}$$

where yk is the observed image [current reconstructed image (in-focus plane)], y ∧ <sup>k</sup> is the referenced image [previous reconstructed image (in-focus plane)], and n is the number of compounds in the analyzed set.

The MSSIM of local patterns of luminance- and contrast-normalized pixel intensity were compared to determine the structural similarity (SSIM) index of contrast preservation. This image quality metric is based on the assumed suitability of the human visual system for extracting structure-based information [34].

Figure 3. For DT acquisition, the phantom was arranged parallel to the x–y detector plane.

Figure 4. The RMSE characteristics caused by the differences in the number of iterations of each IR algorithm. (60 and 120kVp; polychromatic, 60, 80, 100, 120, and 140 keV; virtual monochromatic).

The SSIM index between pixel values x and y was calculated as follows:

$$\text{SSIM}(\mathbf{x}, y) = [l(\mathbf{x}, y)]^\alpha \cdot [\mathbf{c}(\mathbf{x}, y)]^\beta \cdot [\mathbf{s}(\mathbf{x}, y)]^\gamma \tag{19}$$

It was feasible to maintain a steady convergence of polychromatic IR images for inconsistency after the fourth iteration and a convergence of monochromatic IR images for inconsistency

Figure 5. The MSSIM characteristics caused by differences in the number of iterations of each IR algorithm. (60 and

State-Of-The-Art X-Ray Digital Tomosynthesis Imaging http://dx.doi.org/10.5772/intechopen.81667 79

The contrast derived from the contrast-to-noise ratio (CNR) in the in-focus plane (15 mm φ; CaCO3, 175 mg/ml, and 100 mg/ml) was also evaluated as a quantitative measure of the reconstructed image quality. In DT, the CNR is frequently used to estimate low-contrast

> CNR <sup>¼</sup> <sup>μ</sup>Feature � <sup>μ</sup>BG σBG

where μFeature is the mean object pixel value, μBG is the mean background area pixel value, and σBG is the standard deviation of the background pixel values. The latter parameter includes the

(21)

after the fifth iteration (Figures 4 and 5).

detectability and was defined in this study as follows:

120kVp; polychromatic, 60, 80, 100, 120, and 140 keV; virtual monochromatic).

7. Evaluation

where l is the luminance, c is the contrast, and s is the structure. Subsequently,

$$\alpha = \beta = \gamma = 1.0$$

The MSSIM was then used to evaluate the overall image quality:

$$\text{MSSIM}(\mathbf{X}, Y) = \frac{1}{M} \sum\_{j=1}^{M} \text{SSIM}\left(\mathbf{x}\_i, y\_j\right) \tag{20}$$

where X and Y are the reference [previous reconstructed image (in-focus plane)] and objective [current reconstructed image (in-focus plane)] images, respectively; xi and yj are the image contents at the jth pixel; and M is the number of pixels in the image.

Figure 5. The MSSIM characteristics caused by differences in the number of iterations of each IR algorithm. (60 and 120kVp; polychromatic, 60, 80, 100, 120, and 140 keV; virtual monochromatic).

It was feasible to maintain a steady convergence of polychromatic IR images for inconsistency after the fourth iteration and a convergence of monochromatic IR images for inconsistency after the fifth iteration (Figures 4 and 5).

#### 7. Evaluation

The SSIM index between pixel values x and y was calculated as follows:

120kVp; polychromatic, 60, 80, 100, 120, and 140 keV; virtual monochromatic).

78 Medical Imaging and Image-Guided Interventions

The MSSIM was then used to evaluate the overall image quality:

contents at the jth pixel; and M is the number of pixels in the image.

where l is the luminance, c is the contrast, and s is the structure. Subsequently,

MSSIM Xð Þ¼ ;<sup>Y</sup> <sup>1</sup>

α ¼ β ¼ γ ¼ 1:0

Figure 4. The RMSE characteristics caused by the differences in the number of iterations of each IR algorithm. (60 and

M X M

where X and Y are the reference [previous reconstructed image (in-focus plane)] and objective [current reconstructed image (in-focus plane)] images, respectively; xi and yj are the image

j¼1

SSIM xð Þ¼ ; <sup>y</sup> ½ � l xð Þ ; <sup>y</sup> <sup>α</sup> � ½ � c xð Þ ; <sup>y</sup> <sup>β</sup> � ½ � s xð Þ ; <sup>y</sup> <sup>γ</sup> (19)

SSIM xi; yj � �

(20)

The contrast derived from the contrast-to-noise ratio (CNR) in the in-focus plane (15 mm φ; CaCO3, 175 mg/ml, and 100 mg/ml) was also evaluated as a quantitative measure of the reconstructed image quality. In DT, the CNR is frequently used to estimate low-contrast detectability and was defined in this study as follows:

$$\text{CNR} = \frac{\mu\_{\text{Feature}} - \mu\_{\text{BG}}}{\sigma\_{\text{BG}}} \tag{21}$$

where μFeature is the mean object pixel value, μBG is the mean background area pixel value, and σBG is the standard deviation of the background pixel values. The latter parameter includes the photon statistics, the electronic noise from the results, and the structural noise that could obscure the object. The sizes of all regions of interest (ROIs) used to measure the CNR were adjusted to an internal signal (ROI diameter; eight pixels).
