Improving decomposition image quality in dual‐energy chest radiography using two‐dimensional crisscrossed anti‐scatter grid

Abstract

Background

Chest radiography is a widely used medical imaging modality for diagnosing chest‐related diseases. However, anatomical structure overlap hinders accurate lesion detection. While the dual‐energy x‐ray imaging technique addresses this issue by separating soft‐tissue and bone images from an original chest radiograph, scattered radiation remains a significant challenge in decomposition image quality.

Purpose

This work aims to conduct dual‐energy material decomposition (DEMD) in chest radiography using a two‐dimensional (2D) crisscrossed anti‐scatter grid to improve decomposition image quality by effectively removing scattered radiation.

Methods

A 2D graphite‐interspaced grid with a strip density of N = 1.724 lines/mm and grid ratio r = 6:1 was fabricated using a high‐precision sawing process. The grid characteristics were evaluated using the IEC standard fixture. A 2D‐grid‐based DEMD process, which involves the acquisition of low‐ and high‐kV radiographs with a 2D grid, generation of a pairwise decomposition function using a calibration wedge phantom, and decomposition of soft‐tissue and bone images using the decomposition function, was implemented, followed by software‐based grid artifact reduction. Experiments were conducted on a commercially available chest phantom using an x‐ray imaging system operating at two tube voltages of 70 and 120 kVp. The decomposition image quality of the proposed DEMD and conventional dual‐energy subtraction methods was compared for the cases of no grid, software‐based scatter correction, 1D grid (N = 8.475 lines/mm and r = 12:1), and 2D grid.

Results

The 2D grid demonstrated superior scatter radiation removal ability with scatter radiation transmission of 6.34% and grid selectivity of 9.67, representing a 2.6‐fold decrease and a 2.7‐fold improvement over the 1D grid, respectively. Compared to other competitive methods, the 2D‐grid‐based DEMD method considerably improved decomposition image quality, with improved lung structure visibility in selective soft‐tissue images.

Conclusions

The proposed DEMD method yielded high‐quality dual‐energy chest radiographs by effectively removing scattered radiation, demonstrating significant potential for improving lesion detection in clinical practice.

1. INTRODUCTION

Chest radiography is one of the most used medical imaging modalities for screening and diagnosing various chest‐related diseases, such as lung cancer, pneumonia, and bone fracture. ¹ , ² , ³ However, lesions (e.g., lung nodules) located behind the ribs or clavicle are often difficult to detect using chest radiography, mainly because of anatomical structure overlap. A technical approach for reducing the visual complexity of the overlying anatomy is to use three‐dimensional (3D) imaging modalities, such as digital tomosynthesis and computed tomography (CT). ⁴ , ⁵ However, despite the advantages of these modalities, chest radiography is not easily replaced because it is routinely available, dose‐effective, and cost‐effective. ⁶ , ⁷ Another approach involves using the dual‐energy x‐ray imaging (DEXI) technique, which involves capturing x‐ray images at two different tube settings. The two images are then combined to obtain a selective image that highlights either soft‐tissue or bone structures. DEXI is widely utilized in various clinical x‐ray procedures, such as mammography, bone densitometry, CT, and chest radiography, owing to its potential to improve the detection and visualization of lesions when obscured by overlapping tissue structures. ⁸ , ⁹ , ¹⁰ Dual‐energy mammography allows for earlier cancer detection by improving lesion visibility, particularly in dense breast tissue. This advantage decreases false‐negative rates and callbacks for additional diagnostic procedures such as breast biopsy. ¹¹ In osteoporosis assessment, dual‐energy x‐ray absorptiometry provides a highly accurate measurement of bone mineral density while using a considerably lower radiation dose than CT. This approach improves fracture risk assessment with minimal exposure, making it the “gold standard” for osteoporosis diagnosis. ¹² Dual‐energy CT enhances tissue differentiation and material decomposition, reducing the need for multiple scans and enabling virtual non‐contrast imaging. ¹³ Dual‐energy chest radiography suppresses overlying bone structures, improving the detection of lung nodules and calcifications, thus enabling earlier diagnosis of pulmonary diseases and potentially reducing the necessity for follow‐up CT scans. ¹⁴ Thus, the increase in patient dose in DEXI is outweighed by the potential clinical benefit of using this technique.

Although DEXI is a well‐established x‐ray imaging technique, some technical challenges remain, such as misregistration, dual exposure, and scattered radiation, impeding high‐quality, low‐dose DEXI. Misregistration caused by the patient's breathing and movement during a DEXI procedure can degrade decomposition image quality. Recent dual‐energy CT scanners have minimized the misregistration problem by fast acquisition using two x‐ray sources, a fast‐voltage‐switching x‐ray tube, or a dual‐layer detector. ¹⁵ To overcome the limitation of dual exposure in DEXI, specific devices (e.g., dual‐layer detector and photon‐counting detector) have been introduced recently. ¹⁶ , ¹⁷ However, they have not been widely applied in clinical practice because of their high cost. Kis et al. proposed a novel material decomposition algorithm that utilizes a CT‐reconstructed image. ¹⁸ Their algorithm—single‐energy material decomposition—separates soft‐tissue and bone images from single‐exposure x‐rays by measuring the attenuation length of an examined object in a CT‐reconstructed image. More recently, as big‐data technology has become accessible in the medical field, deep‐learning‐based methods have been developed to perform DEXI. ¹⁹ , ²⁰ One advantage of using deep‐learning‐based methods is the facilitation of single‐exposure DEXI with a significantly reduced processing time. However, the image performance strongly depends on the quality and richness of the training data.

Scattered radiation is the dominant cause of DEXI errors, resulting in poor separation of soft‐tissue and bone images. According to Niklason et al., ²¹ the percentage of scattered radiation on chest radiography is typically 60%‒70% in the lungs and 80%‒90% in the mediastinum. Thus, reducing scattered radiation is critical for ensuring high‐quality DEXI. Several scatter reduction methods (by scatter rejection or scatter correction) exist to combat image quality degradation caused by scattered radiation. These methods are generally categorized into hardware‐ and software‐assisted approaches. The hardware‐assisted approach aims to minimize the amount of scattered radiation reaching the detector. For example, anti‐scatter grids can partially block scattered radiation. ²² In practice, 1D grids are more common than 2D grids. However, 1D grids can block scattered radiation in only one direction. Partial beam‐stop arrays can be used to facilitate the direct measurement of scattered radiation. ²³ However, they have drawbacks, such as prolonged data acquisition times, increased radiation dose, and unexpected motion artifacts. The software‐assisted approaches include Monte Carlo (MC) and model‐based methods, or a combination of both. ²⁴ , ²⁵ , ²⁶ While MC methods are accurate in estimating scatter distribution, they are computationally expensive and time‐consuming. Model‐based methods estimate the scattered radiation from a primary signal using a certain convolution kernel. However, the accuracy of the estimated scatter distribution relies heavily on the scatter kernel—which is often difficult to determine in advance.

In a previous study, ²⁷ we investigated a new software‐based scatter correction method based on a simple radiographic scattering model where the intensity of the scattered radiation was directly estimated from a single x‐ray image using a weighted l ¹‐norm contextual regularization framework. We implemented the scatter correction algorithm and conducted a simulation and experiment to demonstrate its viability. Our previous results indicated that the degradation of image quality by scattered radiation was recovered using the software scheme to a certain degree; however, reports on the effects of such a method on image quality remain controversial. Recently, JPI Healthcare Co., ²⁸ Korea, developed a precise 2D graphite‐interspaced anti‐scatter grid (focused and crisscrossed type) by adopting a high‐precision sawing process to maximize its scatter radiation removal ability. Figure 1 shows a schematic of a 2D grid structure and a photograph of the 2D grid used in this study, with the shadows of the grid strips seen in its radiograph. In this study, we employed a 2D grid in dual‐energy chest radiography to effectively remove scattered radiation and, thus, improve the decomposition image quality.

FIGURE 1.

Schematic of a 2D grid structure (top) and a photograph of the 2D grid used in this study (bottom left), with the shadows of the grid strips seen in its radiograph (bottom right).

2. MATERIALS AND METHODS

2.1. Grid fabrication

Figure 2a shows the 2D grid fabrication process implemented by adopting a micro‐controlled sawing machine with a diamond‐coated blade, followed by filling with liquid lead. Figure 2b shows a photograph of the fabricated 2D grid before liquid lead filling. During grid fabrication, accurately aligned grooves were created on a graphite plate using the blade rotating at approximately 20 000 rpm, and liquid lead was then poured into the grooves to form grid strips. The grid consisted of a graphite plate as the interspaced material and lead strips as grid septa. Considering the graphite plate is radiographically more transparent than aluminum (commonly used as an interspaced material in grid fabrication), it maintains a lower radiation dose. The strip density (N) and grid ratio (r) of the fabricated 2D grid were 1.724 lines/mm and 6:1, respectively. A 1D grid with N = 8.475 lines/mm and r = 12:1 was also used for comparison. Both grids were focused on a convergence focal distance of f ₀ = 1500 mm. The specifications of the 1D and 2D grids used in the experiment are listed in Table 1.

FIGURE 2.

(a) 2D grid fabrication process implemented by adopting a micro‐controlled sawing machine with a diamond‐coated blade, followed by filling with liquid lead. (b) Photograph of the fabricated 2D grid before liquid lead filling. (c) IEC standard fixture established for evaluating the grid characteristics. IEC, International Electrotechnical Commission.

TABLE 1.

Specifications of the 1D and 2D grids used in the experiment.

Parameter	2D grid (crisscrossed)	1D grid (linear)
Active area	300 × 300 mm2	300 × 300 mm2
Focal distance (f 0)	1500 mm	1500 mm
Height of lead strips (h)	3.0 mm	1.080 mm
Thickness of lead strips (d)	0.08 mm	0.028 mm
Thickness of graphite interspace (D)	0.50 mm	0.090 mm
Grid ratio (r = h/D)	6:1	12:1
Strip density (N = 1/(D +d))	1.724 lines/mm	8.475 lines/mm

2.2. Grid characteristics

To evaluate the grid characteristics, we established a standard fixture, as shown in Figure 2c, conforming to the International Electrotechnical Commission (IEC) publication 60627 ²⁹ and Technical Report Series (TRS) publication 457, ³⁰ which respectively describe the design and material requirements necessary to measure the performance of general‐purpose anti‐scatter grids and the radiation qualities for calibrating diagnostic dosimeters. The characteristics of the 1D and 2D grids were evaluated in terms of the transmission of primary radiation (T_p ), the transmission of scattered radiation (T_s ), the transmission of total radiation (T_t ), selectivity (Σ), Bucky factor (B), and contrast improvement factor (K) at a tube voltage of 100 kVp (RQR 8 condition) according to each definition. The details of the measurement procedures for these characteristics are described in IEC publication 60627. ²⁹

2.3. Grid artifacts

The critical obstacle remaining for the successful use of anti‐scatter grids in digital radiography is the observation of grid artifacts in x‐ray images, such as shadows of the grid strips themselves and moiré effects. This attribute can degrade the image quality. The shadows of the grid strips frequently appear in x‐ray images when the detector resolution is comparable to or higher than the grid strip spacing. The moiré effect, which occurs when repetitive structures are superposed, is also easily observed in x‐ray images because of the inadequate sampling of the grid strips by the pixel array detector. ³¹ , ³² Numerous studies on methods for removing grid artifacts have been conducted. The moving‐grid technique can be a practical solution to grid line artifacts, wherein a grid moves during exposure to blur the shadows of the grid strips. ³³ However, a major disadvantage of this technique is the required increase in radiation dose to patients from the moving grid. In addition, moving a 2D grid in one direction cannot completely remove its 2D grid artifacts. The frequency‐matching technique between the grid and detector can be a viable solution for obtaining grid‐artifact‐free images. ³⁴ However, complete matching of the grid frequency with that of the detector is impractical because of the grid manufacturing tolerance. The grid angulation technique was also proposed to eliminate the moiré effect in radiography. ³⁵ Through this technique, the moiré frequency component can be placed near the boundary of the Fourier domain by rotating the grid with respect to the sampling direction, after which the moiré effect can be easily alleviated by applying a low‐pass filter.

In this study, to remove the grid artifacts of the 2D grid, as shown in Figure 1 (bottom right), we investigated an effective software‐based grid artifact reduction (GAR) algorithm using an alternative minimization iteration by mixed‐norm and group‐sparsity regularization. ³⁶ The framework of the GAR algorithm is essentially described in Appendix A.

2.4. DEXI methodologies

In general radiography, the intensity I of an x‐ray image can be represented as

$$\begin{array}{ccc}\hfill I_i& =& \int S_i(E)e^{-\underset{l}{\int }\mu (E)\mathrm{dl}}D(E)\mathrm{dE}\hfill \\ & & \approx \int S_i(E)e^{-\left({\mu }_1(E)·t_1+{\mu }_2(E)·t_2\right)}D(E)\mathrm{dE}(i=L,H),\hfill \end{array}$$ (1)

where S(E) denotes the energy spectrum of the x‐ray source; D(E) denotes the detector response function representing the spectral behavior of the detector; and μ ₁(E), μ ₂(E), t ₁, and t ₂ are the linear attenuation coefficients and equivalent attenuation thicknesses of basis materials 1 and 2, respectively. ³⁷ The line‐integrated attenuation index term along the ray path l, ${\int }_l\mu (E)dl$, is theoretically represented by a linear combination of the attenuations of the two basis materials in the diagnostic energy range. In DEXI, polymethyl methacrylate (PMMA) (corresponding to soft‐tissue) and aluminum (Al) (corresponding to bone) are typically used as basis materials owing to their compatibility with most biological tissues. ³⁸

Figure 3 (left axis) shows the mass attenuation coefficients of PMMA, Al, soft‐tissue (ICRU‐44), ³⁹ and cortical bone, indicating that the attenuations between PMMA and soft‐tissue and between Al and bone are considerably close to each other. Two x‐ray images of an examined object were captured by measuring low‐ and high‐kV intensities (I_L and I_H , respectively). Figure 3 (right axis) shows the x‐ray energy spectra calculated at two tube voltages of 70 kVp (with a 1.4‐mm‐thick Al filter) and 120 kVp (with a 1.4‐mm‐thick Al + 0.2‐mm‐thick Cu filter) using SpekPy software (ver. 2.0). ⁴⁰ The effective energies of the low‐ and high‐kV energy spectra were estimated as approximately 38.5 and 62.7 keV, respectively. The specific thicknesses of PMMA and Al (t_PMMA and t_Al ) represent selective soft‐tissue and bone images, respectively.

FIGURE 3.

Mass attenuation coefficients (left axis) of PMMA, Al, soft‐tissue (ICRU‐44), and cortical bone, and the x‐ray energy spectra (right axis) calculated at two tube voltages of 70 and 120 kVp using SpekPy software. The effective energies of the low‐ and high‐kV energy spectra were estimated as approximately 38.5 and 62.7 keV, respectively. Al, aluminum; PMMA, polymethyl methacrylate.

2.4.1. Conventional dual‐energy subtraction

The solution to Equation (1) for t_PMMA and t_Al is not straightforward owing to the energy dependence of the attenuation coefficients. The simplest method to obtain t_PMMA and t_Al is assuming monochromatic x‐rays, represented as an effective energy of polychromatic spectrum, and neglecting the detector response function D(E). This method—called dual‐energy subtraction (DES)—is typically used in clinical dual‐energy chest radiography. In DES, P_L and P_H (on an inverse logarithmic scale) can be represented as

$$\begin{array}{c}{P}_L\equiv \ln \left(\frac{I_{L,0}}{I_L}\right)={\mu }_{eff(PMMA),L}·t_{PMMA}+{\mu }_{eff(Al),L}·t_{Al},\hfill \\ P_H\equiv \ln \left(\frac{I_{H,0}}{I_H}\right)={\mu }_{eff(PMMA),H}·t_{PMMA}+{\mu }_{eff(Al),H}·t_{Al},\hfill \\ I_{L,0}=\int S_L(E)D(E)dE,I_{H,0}=\int S_H(E)D(E)dE,\hfill \end{array}$$ (2)

where I ₀ is the incident x‐ray intensity, and µ_{eff ( PMMA )} and µ_{eff ( Al )} are the linear attenuation coefficients of PMMA and Al, respectively, at an effective x‐ray energy of the polychromatic spectrum. Therefore, the equivalent thicknesses t_PMMA and t_Al are calculated using Equation (2) as follows:

$$\begin{array}{ccc}\hfill t_{PMMA}& =& \frac{P_L-\left(\frac{{\mu }_{eff(Al),L}}{{\mu }_{eff(Al),H}}\right)·P_H}{{\mu }_{eff(PMMA),L}-\left(\frac{{\mu }_{eff(Al),L}}{{\mu }_{eff(Al),H}}\right)·{\mu }_{eff(PMMA),H}},\hfill \\ \hfill t_{Al}& =& \frac{P_L-\left(\frac{{\mu }_{eff(PMMA),L}}{{\mu }_{eff(PMMA),H}}\right)·P_H}{{\mu }_{eff(Al),L}-\left(\frac{{\mu }_{eff(PMMA),L}}{{\mu }_{eff(PMMA),H}}\right)·{\mu }_{eff(Al),H}}.\hfill \end{array}$$ (3)

2.4.2. Proposed dual‐energy material decomposition

In practice, instead of using Equation (3), an approximate solution for t_PMMA and t_Al can be obtained as follows: a set of x‐ray images of a calibration wedge phantom (comprising PMMA and Al with predetermined thicknesses) are obtained at the same tube settings. The calibration wedge phantom is designed to have a maximum PMMA thickness of 60 mm (with 10‐mm steps) and a maximum Al thickness of 6 mm (with 1‐mm steps), ensuring an appropriate intensity range for I_L and I_H . The x‐ray images of the calibration wedge phantom are used to generate a decomposition function in the form of a pairwise lookup table (LUT) using an empirical nonlinear interpolation model (a 10‐parameter cubic model ⁴¹ was used in this study):

$$\begin{array}{ccc}\hfill t_{\mathrm{PMMA}}& =& \sum _{m=0}^3\sum _{n=0}^{3-m}{a}_{m,n}{P}_L^m{P}_H^n(m,n\in \mathbb{Z}),\hfill \\ \hfill t_{\mathrm{Al}}& =& \sum _{m=0}^3\sum _{n=0}^{3-m}{b}_{m,n}{P}_L^m{P}_H^n.\hfill \end{array}$$ (4)

The coefficients {a_m,n, b_m,n } are determined in advance by scanning the predetermined thicknesses of PMMA and Al and measuring I_L and I_H for each combination of these thicknesses. The decomposition function is then applied to the two dual‐energy radiographs to separate soft‐tissue and bone images. Figure 4 shows the simplified diagram of the proposed dual‐energy material decomposition (DEMD) process, involving three main steps: (1) acquisition of low‐ and high‐kV radiographs of an examined object with a 2D grid, (2) generation of a pairwise decomposition function using a calibration wedge phantom under the same tube settings, and (3) decomposition of soft‐tissue and bone images using the decomposition function, followed by software‐based GAR.

FIGURE 4.

Simplified diagram of the proposed DEMD process, involving three main steps: (1) acquisition of low‐ and high‐kV radiographs of an examined object with a 2D grid, (2) generation of a pairwise decomposition function using a calibration wedge phantom, and (3) decomposition of soft‐tissue and bone images using the decomposition function, followed by software‐based grid artifact reduction. DEMD, dual‐energy material decomposition.

2.5. Experimental setup

To verify the efficacy of our approach, we implemented the proposed DEMD algorithm based on Equation (4) using MATLAB (ver. 9.10, R2021a) and conducted experiments on a chest phantom using an x‐ray imaging system (Figure 5). The system comprised an x‐ray tube operating at 70 and 120 kVp, a complementary metal‐oxide‐semiconductor (CMOS) type flat‐panel detector with a pixel size of 139 µm, and a commercially available chest phantom (Lungman, Kagaku Co., Japan) with a large lung volume. The distance between the source and detector was 1500 mm, whereas that between the source and object was 1250 mm. The experimental conditions used in this study are listed in Table 2. A DES‐based algorithm based on Equation (3) was also implemented and used in dual‐energy chest radiography to compare the decomposition image quality. The linear attenuation coefficients of the two basis materials, PMMA and Al, necessary for the DES algorithm were obtained from standard tabulated data from the National Institute of Standards and Technology (NIST) database. ⁴²

FIGURE 5.

X‐ray imaging system and test phantom used in the experiment. The system comprised an x‐ray tube operating at 70 and 120 kVp, a CMOS type flat‐panel detector with a pixel size of 139 µm, and a commercially available chest phantom (Lungman) with a large lung volume. CMOS, complementary metal‐oxide‐semiconductor.

TABLE 2.

Experimental conditions used in this study.

Parameter	Specification
Source‐to‐detector distance	1500 mm
Source‐to‐object distance	1250 mm
X‐ray tube setting	70 and 120 kVp
Focal spot size	0.6 mm
Detector pixel size	0.139 mm
Detector dimension	2000 × 2000
Phantom	Lungman (with a large lung volume)

2.6. Quantitative analysis

We quantitatively evaluated the decomposition image quality for the cases with no grid, software‐based scatter correction, 1D grid, and 2D grid in terms of the image intensity profile, contrast, signal‐to‐noise ratio (SNR), contrast‐to‐noise ratio (CNR), modulation transfer function (MTF), and noise power spectrum (NPS). The contrast is the difference between the values in different parts of the image that enables the distinction of different tissue types:

$$Contrast=\left|P_{ROI}-P_B\right|,$$ (5)

where P_ROI and P_B represent the mean signal intensities within the region of interest (ROI) and background, respectively. The SNR, that is, the ratio of the average image signal in a given ROI and its noise (σ), can be a useful first quantitative measurement:

$$SNR=\frac{P_{ROI}}{{\sigma }_{ROI}}.$$ (6)

The CNR, that is, the ratio of the contrast between the signal in a given ROI and the background, is defined as

$$CNR=\frac{\left|P_{ROI}-P_B\right|}{\sqrt{{\sigma }_{ROI}^2+{\sigma }_B^2}}.$$ (7)

The CNR differs from the SNR in that the CNR is highly dependent on the local contrast. As the CNR increases, the objects are more easily visualized with respect to the background. The MTF, a measure of how well the contrast in an object is transferred to an image, is commonly used to assess the contrast resolution of the image. In this study, MTF measurement was performed using a method for estimating the full‐width‐at‐half maximum (FWHM) of the point spread function (PSF) from sample images. ⁴³ By assuming a Gaussian PSF, the width of the PSF can be determined from a relationship:

$$\ln {\left|F(\mathrm{k})\right|}^2\cong -4{\pi }^2{\sigma }_G^2{\left|\mathrm{k}\right|}^2+\mathrm{constant},$$ (8)

where F(k) is the Fourier transform of the image and σ_G is the standard deviation of the Gaussian PSF. This equation indicates that the Gaussian PSF can be identified as a linear correlation by plotting $\ln {|F(\mathrm{k})|}^2$ as a function of ${|\mathrm{k}|}^2$. The obtained PSF was then transformed into the corresponding MTF. The noise characteristics of the decomposition images were quantified as the normalized NPS, which represents the average area occupied by individual photons per unit area (in mm²):

$$\mathrm{Normalized}\mathrm{NPS}(\mathrm{u},\mathrm{v})=\frac{〈{\left|F\left\{\mathrm{flat}\mathrm{area}(x,y)\right\}\right|}^2〉}{N}{d}^2,$$ (9)

where $⟨{|F\{\mathrm{flat}\mathrm{area}(x,y)\}|}^2⟩$ represents the ensemble average of the squares of the Fourier amplitudes for a selected flat‐intensity area, F represents the Fourier transform, N is the number of image pixels used in the measurement, and d is the detector pixel size.

3. RESULTS

3.1. Evaluation of grid characteristics

Table 3 summarizes the evaluation results of the grid characteristics using the IEC standard fixture. The T_s value of the 2D grid was 6.34%, representing approximately a 2.6‐fold decrease compared to the 1D grid, which indicates that the crisscrossed structure of the 2D grid is more effective than the linear structure of the 1D grid in removing the scattered radiation, as expected. Although the strip density and grid ratio of the 2D grid were much smaller than those of the 1D grid, the selectivity Σ  (= T_p /T_s ) of the 2D grid, which measures the ability of a grid to transmit primary radiation while filtering out scattered radiation, was 9.67, representing approximately a 2.7‐fold improvement over that of the 1D grid. The corresponding contrast improvement factor of the 2D grid was K = 3.95, approximately 1.6 times larger than that of the 1D grid. However, the Bucky factor B (= 1/T_t ) of the 2D grid, which reflects the increased radiation dose required from grid use, was 6.44, representing approximately a 1.5‐fold increase over that of the 1D grid.

TABLE 3.

Evaluation results of the grid characteristics using the IEC standard fixture.

Grid type	Tp	Ts	Tt	Σ	Β	Κ
1D focused	59.72%	16.70%	23.91%	3.58	4.18	2.50
2D focused	61.33%	6.34%	15.53%	9.67	6.44	3.95

Note: Bold values were used to emphasize the characteristics of the 2D focused grid.

Abbreviations: B, Bucky factor; K, contrast improvement factor;T_p , transmission of primary radiation; T_s , transmission of scattered radiation; T_t , transmission of total radiation; Σ, selectivity.

3.2. Generation of decomposition function

Figure 6 shows the x‐ray images of the calibration wedge phantom taken at 70 and 120 kVp and the pairwise decomposition functions interpolated using a 10‐parameter cubic model for PMMA and Al for the cases of no grid, scatter correction, 1D grid, and 2D grid. The slopes of the decomposition functions were gradually less steep for scatter correction, 1D grid, and 2D grid than that of no grid.

FIGURE 6.

X‐ray images of the calibration wedge phantom taken at 70 and 120 kVp (left) and the pairwise decomposition functions interpolated using a 10‐parameter cubic model for PMMA (middle) and Al (right) for the cases of no grid, scatter correction, 1D grid, and 2D grid. Al, aluminum; PMMA, polymethyl methacrylate.

Figure 7 shows the DEMD‐based PMMA and Al images of the calibration wedge phantom separated using the decomposition functions shown in Figure 6. To compare the decomposition performance between the proposed 2D grid and the other scatter reduction approaches, we measured the image intensity profiles along the $\overline{AB}$ (longitudinal) and $\overline{CD}$ (transverse) directions indicated in Figure 7 for PMMA and Al images, as shown in Figure 8. For simplicity, only the intensity profiles of the 40‐mm‐thick PMMA and 4‐mm‐thick Al in the transverse direction are shown.

FIGURE 7.

DEMD‐based PMMA (top) and Al (bottom) images of the calibration wedge phantom separated using the decomposition functions shown in Figure 6. Al, aluminum; DEMD, dual‐energy material decomposition; PMMA, polymethyl methacrylate.

FIGURE 8.

Image intensity profiles measured along the $\overline{AB}$ (longitudinal) and $\overline{CD}$ (transverse) directions indicated in Figure 7 for (a) PMMA and (b) Al images. For simplicity, only the intensity profiles of the 40‐mm‐thick PMMA and 4‐mm‐thick Al in the transverse direction are shown. Al, aluminum; PMMA, polymethyl methacrylate.

3.3. GAR‐based grid artifact reduction

Figure 9 shows the DEMD‐based selective soft‐tissue and bone images of the chest phantom before and after applying the GAR algorithm, with their corresponding Fourier spectra also indicated. The original low‐ and high‐kV images taken with the 2D grid are shown at the far left. The 2D grid shadows that clearly appeared on the soft‐tissue and bone images, owing to the detector resolution (7.194 lines/mm) being much higher than the grid strip density (1.724 lines/mm), were significantly reduced after applying the GAR algorithm, preserving edges and textural features; moiré effect was not clearly observed in the Fourier spectra. The Fourier amplitudes of all grid artifacts were effectively minimized, indicating the robustness of the GAR algorithm in eliminating grid artifacts of a 2D crisscrossed grid.

FIGURE 9.

DEMD‐based selective soft‐tissue (top) and bone (bottom) images of the chest phantom before (middle) and after (right) applying the GAR algorithm, with their corresponding Fourier spectra also indicated. The original low‐ and high‐kV images taken with the 2D grid are shown at the far left. DEMD, dual‐energy material decomposition; GAR, grid artifact reduction.

3.4. Software‐based scatter correction

Figure 10 shows complete sets of original scatter‐degraded images and the estimated scattering and scatter‐corrected images obtained using the software‐based scatter correction algorithm. The DEMD‐based selective soft‐tissue and bone images using the scatter‐corrected images are shown in the fourth column. The degradation of image quality by scattered radiation was recovered to a certain degree using the scatter correction algorithm; however, the image noise was somewhat amplified in the scatter‐corrected images, resulting in a slight improvement of the image's CNR. This observation is explained by the fact that the scatter correction algorithm assumed smooth scatter distributions due to the randomness of scattering events and ignored the existence of high‐frequency scatter noise.

FIGURE 10.

Complete sets of original scatter‐degraded images (first column) and the estimated scattering (second column) and scatter‐corrected (third column) images obtained the software‐based scatter correction algorithm. The DEMD‐based selective soft‐tissue and bone images using the scatter‐corrected images are shown in the fourth column. DEMD, dual‐energy material decomposition.

3.5. Comparison of decomposition image quality

Figure 11 shows the resulting soft‐tissue and bone images of the chest phantom obtained using the DES and DEMD methods for the cases with no grid, scatter correction, 1D grid, and 2D grid. The original low‐ and high‐kV radiographs are shown at the far left. In a comprehensive evaluation, the 2D‐grid‐based DEMD method yielded a significantly enhanced decomposition image quality compared to the DES method, owing to the higher scatter radiation removal ability of the 2D grid and the thickness prior‐based material decomposition approach, demonstrating the efficacy of the proposed approach. In particular, the cardiac shadows in the selective bone image (yellow arrow) were completely suppressed in the 2D‐grid‐based DEMD images while still appearing in other bone images. In addition, the structures of the lung volume (containing simulated tumors and pulmonary vessels) in the soft‐tissue images were more clearly visible for the 2D‐grid‐based DEMD images than for the other soft‐tissue images.

FIGURE 11.

Resulting soft‐tissue and bone images of the chest phantom obtained using the DES and DEMD methods for the cases with no grid, scatter correction, 1D grid, and 2D grid. The original low‐ and high‐kV radiographs are shown at the far left. DEMD, dual‐energy material decomposition; DES, dual‐energy subtraction.

4. DISCUSSION

Scattered radiation is a major limiting factor in DEXI, significantly degrading material decomposition accuracy. Considering scatter contamination affects both low‐ and high‐kV images, it propagates through the decomposition process, leading to signal distortion in material‐selective images. ⁴⁴ Even small amounts of scattered radiation can impair material‐selective cancellations, making accurate decomposition challenging. ⁴⁵ Previous studies indicated that correcting scatter in low‐ and high‐kV images reduced background artifacts and improved image clarity in simulations. ⁴⁶ , ⁴⁷ , ⁴⁸ Unlike software‐based scatter correction, which estimates and removes scatter computationally, a 2D grid physically blocks scattered radiation before it reaches the detector, thereby improving decomposition image quality. However, the specifications of the 2D grid fabricated in this study were limited by the current grid manufacturing capability, producing a lower strip density and grid ratio than the 1D grid. Despite these limitations, the T_p value of the 2D grid remained comparable to that of the 1D grid, and the T_s and Σ values were improved by factors of approximately 2.6 and 2.7, respectively. This result suggests that the 2D grid is more effective for scatter reduction than the 1D grid, as confirmed by the decomposition results from the wedge phantom and chest phantom experiments.

In Figures 7 and 8, the PMMA‐ and Al‐thickness images obtained with the 2D grid showed a more uniform wedge profile than those with no grid, scatter correction, and the 1D grid, indicating that scattered radiation caused dominant DEXI errors, thus demonstrating the viability of using a 2D grid in reducing scatter‐induced decomposition errors in DEXI. Additionally, as highlighted by the yellow arrow in Figure 7, the image quality of the thicker (4‒6 mm) Al‐combination region of the PMMA‐thickness image was relatively poor owing to excessively scattered radiation generated by the thicker Al. This degradation was observed even with software‐based scatter correction. However, when the 2D grid was used, the image quality was improved, confirming its effectiveness in minimizing scatter radiation. For a quantitative comparison, the relative differences in the mean thicknesses of PMMA and Al were evaluated from the intensity profiles shown in Figure 8, with the results summarized in Table 4. The relative differences in the mean thicknesses of PMMA and Al in the transverse direction for the 2D grid were 1.59% and 2.37%, representing approximately 2.2‐fold and 1.3‐fold decreases, respectively, compared to the no‐grid case; the differences in the longitudinal direction were 3.18% for PMMA and 4.14% for Al, representing 1.1‐fold and 1.6‐fold decreases, respectively. These results demonstrate that scatter‐induced errors in DEXI were effectively minimized by the 2D grid, leading to improved decomposition accuracy.

TABLE 4.

Relative differences in the mean thicknesses of PMMA and Al evaluated from the intensity profiles in Figure 8.

Relative difference in the mean thickness		No grid (%)	Scatter correction (%)	1D grid (%)	2D grid (%)
Transverse	PMMA	3.44	2.95	1.75	1.59
	Al	3.01	2.84	2.83	2.37
Longitudinal	PMMA	3.59	3.48	3.34	3.18
	Al	6.69	6.17	6.20	4.14

Note: Bold values indicate the results with the smallest relative difference in the mean thickness.

Abbreviations: Al, aluminum; PMMA, polymethyl methacrylate.

Figure 12 shows enlarged images indicated by boxes A‒D in Figure 11: (a) C‐spine [A] and right lung [B] and (b) cardiac region [C] and L‐spine [D]. The corresponding enlarged low‐kV images are shown at the far left. As shown in Figure 12a, the spinous process (dense material) in the C‐spine region still appeared in the selective soft‐tissue image for both the DES and DEMD methods for the no‐grid case (blue arrows) but nearly disappeared for the 2D‐grid‐based DEMD, indicating high image performance. Similarly, residual rib shadows in the right lung region of the soft‐tissue image were not clearly observed in the 2D‐grid‐based DEMD. As shown in Figure 12b, the cardiac shadows in the bone image were not noticeable (yellow arrow), and the L‐spine was well‐defined (blue arrow) for the 2D‐grid‐based DEMD. Our results aligned well with the previous findings, ⁴⁸ which demonstrated that material decomposition accuracy was improved when nonlinear decomposition methods, such as the proposed DEMD, were applied after effective scatter removal or correction.

FIGURE 12.

Enlarged images indicated by boxes A‒D in Figure 11: (a) C‐spine (top) and right lung (bottom) and (b) cardiac region (top) and L‐spine (bottom). The corresponding enlarged low‐kV images are shown at the far left.

For a quantitative comparison of the decomposition image quality, we measured the contrast, SNR, and CNR from the ROIs of the DEMD images indicated in Figure 11. The evaluation results are summarized in Table 5. The contrast, SNR, and CNR values measured in the C‐spine of the selective soft‐tissue images were 6.22, 30.79, and 3.08 for the 2D‐grid case, representing approximately 1.8‐fold, 1.3‐fold, and 1.5‐fold improvements, respectively, over the no‐grid case; the values measured in the cardiac region of the selective bone images were 4.43, 5.86, and 7.89 for the 2D‐grid case, representing approximately 6.8‐fold, 1.8‐fold, and 5.3‐fold improvements, respectively, over the no‐grid case. The improvements of the scatter correction and the 1D grid in the image quality metrics were relatively slight, compared to the 2D grid, mainly owing to noise amplification by the scatter correction process and the lower scatter radiation removal ability of the 1D grid. However, when using the 2D grid, significant improvement in decomposition image quality was observed. Table 6 shows the CNR improvement factors for the cases of scatter correction, 1D grid, and 2D grid, compared to the no‐grid case. The CNR improvement factors evaluated in the C‐spine and cardiac region were 50.98% and 433.11%, respectively, for the 2D‐grid case. These substantial improvements with the 2D grid were attributed to its effective reduction of scattered radiation, leading to enhanced decomposition accuracy in DEMD images.

TABLE 5.

Quantitative evaluation of the decomposition quality of the DEMD images in Figure 11.

Metric	C‐spine [A]				Right lung [B]				Cardiac region [C]				L‐spine [D]
	NG	SC	1D	2D	NG	SC	1D	2D	NG	SC	1D	2D	NG	SC	1D	2D
Contrast	3.51	4.01	5.69	6.22	3.55	4.34	4.42	6.67	0.65	0.81	1.72	4.43	2.79	2.82	3.32	13.08
SNR	23.49	21.93	27.53	30.79	4.21	4.22	4.39	8.61	3.18	3.01	5.30	5.86	10.01	10.39	18.93	47.51
CNR	2.04	2.05	2.86	3.08	2.23	2.41	2.39	3.81	1.48	1.58	3.13	7.89	5.93	6.51	10.59	35.51

Note: Bold values highlight the metrics with the most significant improvements.

Abbreviations: CNR, contrast‐to‐noise ratio; NG, no grid; SC, software‐based scatter correction; SNR, signal‐to‐noise ratio.

TABLE 6.

CNR improvement factors for the cases of scatter correction, 1D grid, and 2D grid, compared to the no‐grid case.

	C‐spine [A]			Right lung [B]			Cardiac region [C]			L‐spine [D]
	SC	1D	2D	SC	1D	2D	SC	1D	2D	SC	1D	2D
CNR improvement factor (%)	0.49	40.19	50.98	8.07	7.17	70.85	6.76	111.49	433.11	9.78	78.58	498.82

Note: Bold values highlight the metrics with the most significant improvements.

Abbreviations: CNR, contrast‐to‐noise ratio; NG, no grid; SC, software‐based scatter correction.

Figure 13 shows the image intensity profiles measured along the $\overline{AB}$ and $\overline{CD}$ directions indicated in Figure 12b. The L‐spine in the selective bone image was more clearly defined for the 2D‐grid case (red color) than the other cases owing to their incomplete separation of cardiac shadows and abdomen area, which matched the CNR measurement results in Table 5.

FIGURE 13.

Image intensity profiles measured along the $\overline{AB}$ (left) and $\overline{CD}$ (right) directions indicated in Figure 12b. The L‐spine in the selective bone image was more clearly defined for the 2D‐grid case than the other cases.

Figure 14 shows the MTF curves with a Gaussian approximation and normalized NPS curves measured for the DEMD‐based (a) soft‐tissue and (b) bone images in Figure 11. The spatial resolutions evaluated at 10% MTF value for the soft‐tissue images were approximately 2.14, 2.30, 2.36, and 2.42 lines/mm for the cases of no grid, scatter correction, 1D grid, and 2D grid, respectively; the spatial resolutions for the bone images were approximately 2.42, 2.59, 2.70, and 2.81 lines/mm, respectively. The overall spatial resolution performance was improved for the 2D‐grid case, compared to the other cases, indicating the efficacy of the proposed approach. However, the overall noise characteristics were somewhat deteriorated for the 2D‐grid case. The normalized NPS values evaluated at a spatial frequency of 2.0 lines/mm for the soft‐tissue images were approximately 7.9 × 10⁻⁵, 1.1 × 10⁻⁴, 1.5 × 10⁻⁴, and 1.8 × 10⁻⁴ mm² for the cases of no grid, scatter correction, 1D grid, and 2D grid, respectively; the normalized NPS values for the bone images were approximately 1.7 × 10⁻⁵, 2.1 × 10⁻⁵, 9.8 × 10⁻⁵, and 1.6 × 10⁻⁴ mm², respectively. These results suggest that while the 2D grid effectively reduced scattered radiation, it also decreased the total radiation reaching the detector, thereby increasing noise levels. The measured MTF and NPS results are consistent with previous studies on the impact of grids in radiographic imaging. ⁴⁹ Although the previous study did not investigate 2D grids specifically, it reported Bucky factor variations and their impact on MTF and NPS across different grid configurations. The study demonstrated that as the grid ratio increased, scatter rejection was improved while with decreased total transmitted radiation, which in turn influenced spatial resolution and noise characteristics. This relationship aligns with the differences observed among the no grid, 1D grid, and 2D grid cases in our study; more scatter rejection led to MTF enhancement while NPS deterioration owing to reduced total radiation. Despite the increase in noise, the improved contrast due to scatter reduction outweighed the impact of noise amplification, resulting in an overall enhancement in image quality. Compared to the other approaches, the CNR and SNR were improved with the 2D grid, demonstrating its effectiveness in DEMD.

FIGURE 14.

MTF curves with a Gaussian approximation (left) and normalized NPS curves (right) measured for the DEMD‐based (a) soft‐tissue and (b) bone images shown in Figure 11. DEMD, dual‐energy material decomposition; MTF, modulation transfer function.

Despite the improved decomposition image quality achieved using the proposed 2D‐grid‐based DEMD, an important technical limitation remains: increased radiation dose owing to the increased primary x‐ray absorption of the 2D grid. The Bucky factor of the 2D grid was approximately 1.5 times higher than that of the 1D grid. This necessitates grid structure optimization to balance its scatter rejection performance and radiation dose efficiency. Further study will focus on optimizing 2D grid specifications by MC simulations and experiments to maximize scatter rejection while minimizing dose escalation.

5. CONCLUSIONS

This study presents the use of a 2D crisscrossed anti‐scatter grid in dual‐energy chest radiography for improving decomposition image quality. We developed a precise 2D graphite‐interspaced anti‐scatter grid (focused and crisscrossed type) with a strip density N = 1.724 lines/mm and a grid ratio r = 6:1 by adopting a high‐precision sawing process to enhance scatter radiation removal ability and employed it for dual‐energy chest radiography. The crisscrossed structure of the 2D grid was more effective than the linear structure of the 1D grid in removing scattered radiation. The 2D‐grid‐based DEMD method considerably improved decomposition image quality compared to other competitive methods, improving lung structure visibility in selective soft‐tissue images. Consequently, the proposed approach yielded high‐quality dual‐energy chest radiographs by effectively removing scattered radiation, demonstrating significant potential for improving lesion detection in clinical practice. Further study on moiré artifact reduction is necessary to ensure the successful use of the grid in the proposed 2D‐grid‐based DEMD method.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

APPENDIX A. FRAMEWORK OF THE GAR ALGORITHM

A.1.

Figure A.1 shows the simplified framework of the GAR algorithm to remove grid artifacts of a 2D grid. The original (i.e., artifact‐contaminated) image, g(x,y), can be simply described as a sum of the image component (i.e., artifact‐free image), f(x,y), and grid artifact component, a_grid (x,y), as follows:

$$g(x,y)=f(x,y)+a_{grid}(x,y).$$ (A.1)

The image component f is recovered by minimizing the objective function ϕ as the solution to a convex optimization problem f ^*, described as follows

$$\begin{array}{c}{f}^{\ast }=arg\underset{f,a_{grid}}{\min }\varphi ,\hfill \\ \varphi =\frac{1}{2}{‖g-(f+a_{grid})‖}_2^2+{\lambda }_1{‖\mathbf{D}f‖}_{2,1}+{\lambda }_2{‖\Im a_{grid}‖}_{C,1},\hfill \end{array}$$ (A.2)

where $1/2\parallel g-(f+a_{grid}){\parallel }_2^2$ is the data‐fidelity term that quantifies how well the estimated components match the measured data; ${\parallel \mathbf{D}f\parallel }_{2,1}$ and $\parallel \Im a_{grid}{\parallel }_{C,1}$ are the dual regularization terms used to introduce a priori knowledge on the solution; D and $\Im$ denote the forward difference approximation of the gradient and the Fourier transform, respectively; and λ ₁ and λ ₂ are parameters to balance the data‐fidelity and regularization terms. In many image restoration problems, total variation (TV), that is, the l ₁‐norm of the gradient image, is often used as an effective regularization term because derivative images are expected to become sparse in most parts except for image edges and textures. ⁵⁰ , ⁵¹ However, TV alone can lead to unrealistic solutions when performing image restoration with spatially repeated data (e.g., grid artifacts of a 2D crisscrossed grid). To address this limitation, we focused on the fact that the same pattern of the 2D grid artifacts arises iteratively in the original image, and their Fourier components tend to appear sparsely with high peak values over the Fourier space. These properties can be reflected using dual regulation terms based on two‐level mixed norms ⁵² :

$$\begin{array}{ccc}\hfill {‖\mathbf{D}f‖}_{2,1}& =& \sum _{i=1}^N\sqrt{(D_h{f}_i)2+(D_v{f}_i)2},\mathbf{D}\equiv [D_h,D_v],\hfill \\ & & {‖\mathfrak{I}{a}_{\mathrm{grid}}‖}_{C,1}={‖\mathbf{c}‖}_{C,1}=\sum _{i=1}^N{\left|c_i\right|}_C\hfill \\ & =& \sum _{i=1}^N\sqrt{{\left(c_i^R\right)}^2+{\left(c_i^I\right)}^2},\hfill \\ \hfill \mathbf{c}& =& [c_1,c_2,\cdots ,c_N]\in {\mathbb{C}}^N,N=m\times n,\hfill \\ \hfill c_i& =& c_i^R+c_i^{I}j,j\equiv \sqrt{-1},\hfill \end{array}$$ (A.3)

where D_h and D_v denote the forward difference approximation of the horizontal and vertical gradients, respectively; N is the total number of pixels in the image of m × n dimension; and c_i is a complex number at pixel i. Mixed norms are a practical way to explicitly induce a coupling between variables, and the structured sparsity induced by the l _2,1‐mixed norms leads to efficient sparse solutions. The l _{C, 1}‐mixed norm and Fourier transform are also used for Fourier spectral regularization to effectively suppress the 2D grid artifacts, as $\parallel \Im a_{grid}{\parallel }_{C,1}$ in Equation (A.2). The framework simultaneously optimizes two components, f(x,y) and a_grid (x,y), which can be efficiently solved by an alternating iteration for minimization with the alternating direction method of multipliers (ADMM) algorithm. ⁵³

FIGURE A.1.

Simplified framework of the GAR algorithm to remove the grid artifacts of a 2D grid. The framework simultaneously optimizes two components (i.e., image and grid artifact components), which can be efficiently solved by an alternating iteration for minimization with the ADMM algorithm. ADMM, alternating direction method of multipliers; GAR, grid artifact reduction.

Jeon D, Lim Y, Yang H, Park M, Kim K, Cho H. Improving decomposition image quality in dual‐energy chest radiography using two‐dimensional crisscrossed anti‐scatter grid. Med Phys. 2025;52:e17819. 10.1002/mp.17819