Scatter correction for contrast-enhanced digital breast tomosynthesis with a dual-layer detector

Abstract.

Purpose

Contrast-enhanced digital breast tomosynthesis (CEDBT) highlights breast tumors with neo-angiogenesis. A recently proposed CEDBT system with a dual-layer (DL) flat-panel detector enables simultaneous acquisition of high-energy (HE) and low-energy (LE) projection images with a single exposure, which reduces acquisition time and eliminates motion artifacts. However, x-ray scatter degrades image quality and lesion detectability. We propose a practical method for accurate and robust scatter correction (SC) for DL-CEDBT.

Approach

The proposed hybrid SC method combines the advantages of a two-kernel iterative convolution method and an empirical interpolation strategy, which accounts for the reduced scatter from the peripheral breast region due to thickness roll-off and the scatter contribution from the region outside the breast. Scatter point spread functions were generated using Monte Carlo simulations with different breast glandular fractions, compressed thicknesses, and projection angles. Projection images and ground truth scatter maps of anthropomorphic digital breast phantoms were simulated to evaluate the performance of the proposed SC method and three other kernel- and interpolation-based methods. The mean absolute relative error (MARE) between scatter estimates and ground truth was used as the metric for SC accuracy.

Results

DL-CEDBT shows scatter characteristics different from dual-shot, primarily due to the two energy peaks of the incident spectrum and the structure of the DL detector. Compared with the other methods investigated, the proposed hybrid SC method showed superior accuracy and robustness, with MARE of $\sim 3.1\%$ for all LE and HE projection images of different phantoms in both cranial-caudal and mediolateral-oblique views. After SC, cupping artifacts in the dual-energy image were removed, and the signal difference-to-noise ratio was improved by 82.0% for 8 mm iodine objects.

Conclusions

A practical SC method was developed, which provided accurate and robust scatter estimates to improve image quality and lesion detectability for DL-CEDBT.

1. Introduction

Contrast-enhanced digital breast tomosynthesis (CEDBT) provides 3D contrast enhancement of breast lesions.^1–4 In the imaging procedure, the breast is compressed in cranial-caudal (CC) or mediolateral-oblique (MLO) view $\sim 2\min$ after intravenous administration of iodinated contrast agents. High- and low-energy (HE and LE) projection images of the compressed breast are acquired at different angles within a limited angular range and used to reconstruct quasi-3D volumes. As the attenuation difference between breast tissue and iodine is more pronounced at HE than at LE, weighted subtraction between HE and LE images removes the breast tissue background, making contrast-enhanced tumors stand out in the dual-energy (DE) images.⁴

CEDBT is currently implemented with a dual-shot (DS) technique, in which HE and LE projection images are acquired sequentially with two separate exposures.^2–5 The acquisition time interval can be up to 120 s in CEDBT,⁶ which would suffer from more severe patient motion artifacts than contrast-enhanced digital mammography (CEDM).^7–11 More recently, multi-layer flat-panel detectors (FPD) have attracted a lot of attention in spectral imaging applications.^12–14 In our previous study, a direct-indirect dual-layer (DL) FPD has been designed for CEDBT [Fig. 1(a)].¹⁵ The DL-CEDBT enables the simultaneous acquisition of spatially aligned HE and LE projection images with a single exposure. This technique provides comparable breast tissue background cancellation and enhances iodine object detectability when compared with DS-CEDBT.¹⁵

Fig. 1.

(a) Imaging geometry of DL-CEDBT and (b) its parameters. (c) Energy spectrum of the incident x-ray beam. (d) Energy spectra of x-rays absorbed by the FL a-Se and BL CsI.

Due to a lack of anti-scatter grids in DBT, scattered radiation degrades image quality (i.e., introduces cupping artifacts) and reduces lesion contrast.¹⁶ In DS-CEDBT, scattered radiation for HE images is even more severe than that for LE and exacerbates the inaccuracy of iodine quantification in reconstructed slices.^17–20 In DL-CEDBT, the x-ray spectrum and the DL detector structure make a significant difference in scatter properties and their effect on image performance.^21,22 This necessitates x-ray scatter characterization and correction that is specific for DL-CEDBT.

Substantial effort has been devoted to scatter correction (SC) using methods based on Monte Carlo (MC) simulation,^23,24 kernel-based convolution,^25–27 empirical interpolation,¹⁸ deep learning,^19,28 and primary modulators.^29,30 The MC method provides reliable SC results but is not practical in clinical settings due to its high computational cost.²³ Huang developed a single-kernel iterative convolution method, which leads to an overestimation of scatter contribution from the peripheral breast region with thickness roll-off.²⁷ Lu¹⁸ proposed an empirical method, which uses a polynomial interpolation of measured scatter outside the breast region to estimate scatter within the breast. Duan¹⁹ developed a deep-learning SC method for both CC and MLO views in a prototype DS-CEDBT and demonstrated high accuracy and speed. Pinto²⁸ applied a deep-learning model method for CC view in a regular DBT system. For a DLFPD-based radiography system, Wang used a primary modulator with a “checkerboard” pattern of semitransparent blockers to encode the primary signal and enable scatter estimation and material decomposition simultaneously.^29,30 To the best of our knowledge, no software-based SC algorithm has been developed for DLFPD-based systems.

This paper proposes a software-based practical SC method for a DL-CEDBT system.¹⁵ It utilizes a two-kernel convolution method to account for the reduced scatter contribution from the peripheral breast region due to thickness roll-off. It also incorporates the empirical interpolation method to consider the scatter contribution from the open field of plates [the breast compression plate, the detector cover plate, and the front layer (FL)]. To implement SC, scatter point spread function (PSF) kernels were generated using MC simulations. Projection images and ground truth scatter maps of anthropomorphic digital breast phantoms were simulated to evaluate the performance of the proposed hybrid method and other SC methods.

2. Methods

2.1. Imaging Geometry of DL-CEDBT

The imaging geometry is shown in Fig. 1(a), and the parameters are listed in Fig. 1(b). The incident spectrum is 49 kV with a tungsten (W) target and a $150\mu \mathrm{m}$ thick silver (Ag) filter, which results in two energy peaks, one below and the other above the K-edge of iodine [Fig. 1(c)]. A $200\mu \mathrm{m}$ thick amorphous selenium (a-Se) detector (deposited on a $700\mu \mathrm{m}$ thick glass substrate) is used as the front layer (FL), which predominately captures LE x-rays and provides LE projection images. A $400\mu \mathrm{m}$ thick cesium iodide (CsI) scintillator is used as the back layer (BL), which absorbs the HE x-rays that transmit through the FL and provides HE projection images. The energy spectra of x-rays absorbed by the FL a-Se and BL CsI are shown in Fig. 1(d).¹⁵ A portion of the HE x-rays is absorbed by the FL a-Se, leading to HE photon contamination in LE projection images. This contamination decreases energy separation between HE and LE, thereby degrading lesion detectability.³¹ The contamination can be removed using an analytical algorithm developed in our previous work.³¹ In this work, we focus on SC and do not involve HE contamination removal.

MC simulations were performed using VICTRE MCGPU.³² Attenuation coefficients for materials were generated using PENELOPE 2006.³³ The incident x-ray spectrum was simulated using the TASMIP model.³⁴ To analyze the effect of HE photon contamination, the LE and HE components (${\mathrm{LE}}_{\mathrm{FL}}$ and ${\mathrm{HE}}_{\mathrm{FL}}$) detected by FL were simulated separately and then combined to generate the LE projection images ($\mathrm{LE}={\mathrm{LE}}_{\mathrm{FL}}+{\mathrm{HE}}_{\mathrm{FL}}$). The mean glandular doses (MGD) delivered to phantoms ranged from 1.0 to 1.6 mGy, lower than in clinical settings.^4,35 The simulated detector has an $85\mu \mathrm{m}\times 85\mu \mathrm{m}$ pixel pitch. Pixel binning ($16\times 16$) was performed to simulated projection images, which minimizes quantum noise while maintaining low-frequency scatter information.

2.2. Monte Carlo Simulations of DL-CEDBT

2.2.1. Scatter point spread functions

LE and HE scatter PSF kernels were simulated with different glandular fractions (0%, 50%, and 100%), compressed breast thicknesses (from 0 to 9 cm with an increment of 1 cm), and projection angles (0 deg to 24 deg in 2 deg increment). Narrow pencil beams were directed at the center of uniform phantoms. Images underwent pixel binning ($16\times 16$) and normalization to the signals of primary x-rays to produce scatter PSF kernels. Linear interpolation or extrapolation was used to produce kernels of thicknesses and projection angles not simulated, such as 5.5 cm at 25 deg.

2.2.2. Scatter maps of anthropomorphic digital breast phantoms

Raw (scatter-present) and primary (scatter-free) projection images were simulated for anthropomorphic digital breast phantoms using half-cone beams. Scatter maps were produced by subtracting the primary from the raw projection images and were used as ground truth to evaluate the performance of SC methods. Six phantoms, labeled P1 through P6, were generated using VICTRE with a voxel size of $0.2\times 0.2\times 0.2{\mathrm{mm}}^3$ and then compressed in both CC and MLO views.³² Figure 2(a) shows a phantom compressed in CC view with a uniform thickness in the central area and thickness roll-off in the peripheral area. The phantom possesses a realistic breast shape, composition, and texture. For the phantom in MLO view, as shown in Fig. 2(b), an elliptical cone-shaped pectoral muscle and an inframammary fold are inserted.^36,37 Figure 3(a) shows the compressed breast thicknesses assigned for each phantom according to the breast area at the chest wall.^38,39 Phantoms have higher compressed thicknesses in the MLO view than in the CC view due to the involvement of the pectoral muscle.^40,41 Figure 3(b) shows the breast glandular fractions ranging from 5.8% to 30.0%, which cover the range typically seen in clinical exams.^42,43

Fig. 2.

Digital anthropomorphic phantom compressed in (a) CC and (b) MLO views, showing a realistic breast shape, composition, and texture. 3D renderings and axial slices are displayed.

Fig. 3.

(a) Compressed breast thicknesses and (b) glandular fractions for phantoms P1 through P6.

2.3. Hybrid Scatter Correction Method for DL-CEDBT

2.3.1. Two-kernel iterative convolution strategy for the central region

In the single-kernel SC method, the raw image is assumed to be the primary estimate. This overestimated primary signal, when convolved with a scatter PSF kernel, leads to an overestimation of scatter.^25,27,44 In the iterative convolution method, despite the initial overestimation of scatter, subtracting it from the raw image updates the primary signal to an underestimated but more accurate value for the next iteration. Each iteration further refines the primary and scatter estimates, reducing the overestimation compared with the single-kernel SC method.^25,27 However, the kernel also causes overestimation, as it is determined based on the compressed breast thickness ($T$). This kernel accurately represents scatter in the central region but overestimates scatter in the peripheral region due to the thickness roll-off.

We propose a two-kernel iterative convolution method. In addition to the kernel for the central region ($T$), one more kernel is added to represent the average thickness in the peripheral region. For this average thickness, we chose $0.5T$ as a reasonable estimate. Figure 4 shows the workflow of this method. The projected breast area is automatically segmented into a central region with a uniform compressed thickness and a peripheral region with thickness roll-off.⁴⁵ Two kernels, associated with $T$ and $0.5T$, are convolved separately with the respective regions, yielding individual estimates of scatter contribution from each region of the breast. Summing the two produces the estimate of scatter from the entire breast. Iteration stops when the absolute difference between consecutive estimates falls below ${10}^{-6}$ times the average pixel intensity in the region of the raw projection image. This criterion ensures that the scatter estimate converges with an accuracy of 99.99% relative to the target.

Fig. 4.

Workflow of the 2-kernel iterative convolution strategy in the breast area. LE projection image of phantom P1 in CC view at $-25\mathrm{deg}$ is shown as an example.

2.3.2. Interpolation strategy for the peripheral region

The two-kernel strategy does not consider scatter originating from the open field of plates which could be significant for the peripheral region,²⁴ leading to scatter estimation inaccuracy. To address this issue, we introduce 2D interpolation⁴⁶ to estimate scatter in the peripheral region (Fig. 5). The scatter estimated by the two-kernel iterative convolution method for the central region and scatter measured in the background region are treated as known data. To measure scatter in the background region, a blank scan is acquired without the breast,¹⁸ and its primary component is calculated by iterative convolution with the kernel for 0 cm breast thickness. Subtraction of the primary component from the raw projection image provides the scatter in the background region.

Fig. 5.

Workflow of the interpolation strategy for the peripheral region from the scatter estimate in the central region and the scatter measurement in the background region (dashed box). LE raw projection image of phantom P1 in CC view at 0 deg is shown as an example.

To account for the asymmetry in scatter at oblique projection angles ($\theta$), the central region used for interpolation is shifted toward the tube movement direction by a displacement ($D$), as shown in Fig. 6(a). $D$ is calculated using $\frac{T\theta }{10\times 25}L$, where $L$ is the distance between the boundaries of the breast area and the central region. Both distance parameters, $D$ and $L$, are measured in pixels. The maximum reference values of 10 cm for $T$ and 25 deg for $\theta$ are used in the denominator. Therefore, for 25 deg projection images of a 10 cm thick breast, $D$ equals $L$. For thin phantoms with small $T$ and mild scatter asymmetry, $D$ is small [Fig. 6(b)].

Fig. 6.

Central region shifted by a displacement $D$, toward the tube movement direction (the right of the figure) for projection images ($\theta =25\mathrm{deg}$) of (a) the 7.8 cm thick phantom P6 and (b) the 3.7 cm thick phantom P1 in CC view. $L$ is the pixel gap between the boundaries of the breast area and the central region.

2.4. Performance Evaluation

2.4.1. Scatter correction accuracy

The proposed SC method was implemented in MATLAB and applied to all LE and HE raw projection images at 25 angles for each breast phantom using an Intel Core i5-10400F processor. The accuracy for SC was evaluated using mean absolute relative error (MARE) between scatter estimates ($S_{\mathrm{Est}}$) and ground truth ($S_{\mathrm{GT}}$) calculated over the entire breast area as

$$\mathrm{MARE}=\frac{1}{N}\sum |S_{\mathrm{Est}}-S_{\mathrm{GT}}|/S_{\mathrm{GT}},$$ (1)

where $N$ is the number of pixels within the breast area.

To investigate the impact of two-kernel and interpolation separately, we implemented methods $A$, $B$, and $C$, as listed in Table 1, in addition to the proposed method $D$.

Table 1.

Three other methods implemented for comparison with the proposed hybrid method.

Method	Description
$A$	Single-kernel iterative convolution method
$B$	Single-kernel iterative convolution combined with interpolation method
$C$	Two-kernel iterative convolution method
$D$ (proposed)	Two-kernel iterative convolution combined with interpolation method

2.4.2. Image quality and lesion detectability in scatter-corrected images

A 5.7 cm thick digital breast phantom [Fig. 7(a)] with 25% glandular fraction was employed to evaluate the effect of SC methods on image quality and lesion conspicuity. One-half of the phantom has an anthropomorphic breast tissue background, whereas the other half is uniform. Iodine objects with different sizes (2, 3, 5, and 8 mm in diameter and depth) and concentrations (1, 2, 3, and $5\mathrm{mg}/\mathrm{ml}$) are inserted at different locations. Figure 7(b) shows the raw and primary LE and HE images simulated for CEDM with 1.6 mGy MGD.³⁵

Fig. 7.

(a) A 5.7 cm thick digital breast phantom with iodine objects of different sizes, concentrations, and locations. (b) Raw and primary LE and HE images of the phantom. The boundaries between central and peripheral regions are clear in the uniform breast tissue due to the low resolution of the phantom.

Methods $A$ and $D$ were applied to produce scatter-corrected images. LE and HE images were affine-registered according to the magnification factor of the imaging geometry.^14,15 Logarithmic transformation and weighted subtraction were then performed to generate DE images, with weighting factors determined by the compressed breast thickness.^4,47,48 Note that for the raw images with scatter, the weighting factor was refined to achieve the best cancellation of normal breast tissue background. For quantitative evaluation, the signal difference-to-noise ratio (SDNR) of iodine objects in DE images was calculated and used as the figure of merit:⁴⁹

$$\mathrm{SDNR}=\frac{|{\overline{\mu }}_{\mathrm{obj}}-{\overline{\mu }}_{\mathrm{bkg}}|}{{\overline{\sigma }}_{\mathrm{bkg}}},$$ (2)

where ${\overline{\mu }}_{\mathrm{obj}}$ is the mean intensity in the ROI of an iodine object, ${\overline{\mu }}_{\mathrm{bkg}}$ is the mean intensity of four background ROIs surrounding the object, and ${\overline{\sigma }}_{\mathrm{bkg}}$ is the average of the standard deviations in the background ROIs.

3. Results

3.1. Scatter Point Spread Function

Figure 8(a) shows the scatter PSFs for different glandular fractions, demonstrating negligible impact, similar to findings in regular DM and DBT.^24,42 This minimal impact of breast composition supports the use of these kernels for heterogeneous phantoms with varying densities across different regions.⁵⁰ In DL, LE scatter PSFs have lower amplitudes and greater widths than HE, whereas in DS [Fig. 8(b)], the LE scatter PSF exhibits a similar amplitude and narrower width compared with HE.¹⁹ Figure 8(c) shows the contributions from ${\mathrm{LE}}_{\mathrm{FL}}$ and ${\mathrm{HE}}_{\mathrm{FL}}$ components of the x-ray spectrum absorbed by FL to the LE scatter PSF in DL. It shows that the dominant source of scatter is from ${\mathrm{HE}}_{\mathrm{FL}}$, which explains the greater width of DL LE scatter PSFs shown in Fig. 8(a).

Fig. 8.

(a) LE and HE scatter PSFs for different glandular fractions in DL ($T=5.0\mathrm{cm}$, $\theta =0\mathrm{deg}$). (b) LE and HE scatter PSFs in DS. (c) Contributions from ${\mathrm{LE}}_{\mathrm{FL}}$ and ${\mathrm{HE}}_{\mathrm{FL}}$ components of absorbed x-rays to the LE scatter PSFs in DL.

Figure 9 shows the dependence of scatter PSFs on breast thicknesses and projection angles in DL. As shown in Fig. 9(a) for LE and Fig. 9(b) for HE, scatter PSF amplitude increases with breast thickness. The amplitude of PSF without the breast (i.e., 0 cm thickness) is much higher for HE than that for LE. For HE, the amplitude is about 50% of that with a 2 cm thick breast, while for LE, it is only around 2%. This is due to scattered x-rays from FL that are detected by the BL, which also explains why the HE scatter PSFs have higher amplitudes than LE shown in Fig. 8(a). Figures 9(c) and 9(d) show the asymmetry in PSFs at oblique angles, which is more severe for thicker breasts.

Fig. 9.

Dependence of LE and HE scatter PSFs on (a)–(b) breast thicknesses ($\theta =0\mathrm{deg}$), (c)–(d) projection angles in DL. The x-ray tube moves toward the right of the figure.

3.2. Scatter Maps of Anthropomorphic Digital Breast Phantoms

Figure 10(a) shows the ${\mathrm{LE}}_{\mathrm{FL}}$ component detected by the FL in LE raw and primary projections, and the scatter map for the 6.3 cm thick phantom P4 in CC view at 0 deg. The ${\mathrm{LE}}_{\mathrm{FL}}$ scatter map shows a sharp increase near the outer edge of the breast, similar to that observed in regular LE images.^19,24 This increase is due to the scatter contribution from the open field of plates and is especially pronounced for thick breasts.²⁴ Figure 10(b) shows the ${\mathrm{HE}}_{\mathrm{FL}}$ component detected by the FL in LE projections and scatter map. Due to the higher probability of Compton scatter and greater penetration, the ${\mathrm{HE}}_{\mathrm{FL}}$ scatter map has a much higher intensity than the ${\mathrm{LE}}_{\mathrm{FL}}$, thereby minimizing the impact of ${\mathrm{LE}}_{\mathrm{FL}}$ on the LE scatter map. Figure 10(c) shows the LE projections and the corresponding scatter map. As ${\mathrm{HE}}_{\mathrm{FL}}$ scatter is the dominant source, the LE scatter map features a gradual reduction in intensity from the central region to the periphery.

Fig. 10.

(a) ${\mathrm{LE}}_{\mathrm{FL}}$ component and (b) ${\mathrm{HE}}_{\mathrm{FL}}$ component in the (c) LE raw and primary projections, and scatter map of the 6.3 cm thick phantom P4 in CC view ($\theta =0\mathrm{deg}$). Scatter maps are displayed using the same colormap (jet) limits, with red for higher values and blue for lower values. The dotted outlines indicate the boundaries of the breast area.

Figure 11 shows LE and HE scatter maps of different phantoms. For the 3.7 cm phantom P1 shown in Fig. 11(a), the two scatter maps have comparable intensity levels, and both feature a gradual reduction in intensity due to the dominance of HE scattered photons. The HE scatter map shows higher noise than LE, which is due to the smaller number of x-rays incident on and absorbed by the BL, as illustrated in Fig. 1(d). Figure 11(b) shows scatter maps for the 6.3 cm phantom P4. This thick breast results in high attenuation of scattered photons, reducing the number detected, particularly for LE. That is one reason why the LE scatter map shows a lower intensity level than HE. In the HE scatter map, scattered photons from the breast are also attenuated, leading to a relative increase in the scatter contribution from the FL. These effects are more pronounced for thicker breasts, as shown in Fig. 11(c) for the 7.8 cm breast P6.

Fig. 11.

LE and HE scatter maps for the phantoms (a) P1 (3.7 cm), (b) P4 (6.3 cm), and (c) P6 (7.8 cm). The same colormap limits are used for each individual phantom. Red indicates higher values, and blue indicates lower values. The dotted outlines indicate the boundaries of the breast area.

Figure 12 shows the raw and primary projection images at 0 deg and the corresponding scatter map for the 5.6 cm thick phantom P3 in MLO view. In both raw and primary images, the signal intensity behind the pectoral muscle is lower than that behind breast tissues, due to the higher x-ray attenuation of the muscle. Despite the differences in breast shape between the MLO and CC views, the scatter maps retain a gradual intensity change across the entire breast area, in which the accuracy for SC was evaluated.

Fig. 12.

(a) LE and (b) HE raw and primary projection images of the 5.6 cm thick phantom P3 in MLO ($\theta =0\mathrm{deg}$) and scatter maps shown with same colormap (jet) limits. Red indicates higher values, and blue indicates lower values. The dotted outlines indicate the boundaries of the breast area.

3.3. Scatter Correction for DL-CEDBT

3.2.1. Scatter correction accuracy

Scatter correction was completed within 26 s for all projection images of each phantom. Figure 13(a) shows the scatter estimates using different SC methods for the 6.3 cm thick phantom P4 in CC view. Compared with the ground truth shown in Fig. 13(b), method $A$ exhibits the most severe overestimation. Although methods $B$ and $C$ reduce the overestimation, method $D$ achieves the closest agreement with the ground truth, as seen with the relative error maps in Fig. 13(c). Method $A$ overestimates scatter by 11.0% across the entire breast area. Method $B$ provides higher accuracy in the peripheral region but retains severe overestimation in the central region. Method $C$ improves accuracy in the central region but suffers from underestimation around the breast edge. Method $D$ shows excellent agreement with the ground truth across the entire breast area, achieving MARE of 1.7% in the central region, 3.2% in the periphery, and 2.2% overall. The asymmetry observed in the scatter maps and relative error maps is primarily due to the asymmetrical breast shape.

Fig. 13.

Comparison of scatter estimates using different methods ($A$, $B$, $C$, and $D$) for LE projection image ($\theta =0\mathrm{deg}$) of the 6.3 cm thick phantom P4. (a) Estimated scatter maps and (b) ground truth shown with the same colormap (jet) limits, where red indicates higher values and blue indicates lower value. (c) Relative error maps and MARE of scatter estimates compared with the ground truth.

Figures 14(a)–14(d) show the MARE of scatter estimates using different SC methods, where the median, 25th percentile, 75th percentile, and outliers are provided for all 25 LE projection images of each phantom in CC view. As shown in Fig. 14(a) for method $A$, the median MARE increases with breast thickness, ranging from 3.2% [interquartile range (IQR), 2.4% to 4.0%] for the 3.7 cm thick phantom P1 to 23.7% (IQR, 19.2% to 30.7%) for the 7.8 cm thick phantom P6. Method $B$ [Fig. 14(b)] provides lower MARE (median and IQR) compared with method A but exhibits the same dependence of median MARE on breast thickness. Method $C$ [Fig. 14(c)] provides a lower median MARE than method $A$, but it still suffers from large IQRs for thicker breast phantoms. As shown in Fig. 14(d), method $D$ provides the highest accuracy for LE scatter estimates, with a median MARE below 5.0% with an IQR below 1.5% for all phantoms. For HE scatter estimates, Figs. 14(e)–14(h) show the similar phenomena. Methods $A$ and $B$ show a significant dependence on breast thickness. Although methods $B$ and $C$ improve upon $A$, method $D$ provides the highest accuracy for HE scatter estimates, with a median MARE below 5.0% with an IQR below 1.5% for all phantoms.

Fig. 14.

Boxplots of MARE for different SC methods, showing the median, 25th and 75th percentiles, and outliers across 25 projection images of each phantom in CC view. The top row shows methods (a) $A$, (b) $B$, (c) $C$, and (d) $D$ for LE scatter estimation. The bottom row shows methods (e) $A$, (f) $B$, (g) $C$, and (h) $D$ for HE scatter estimation.

Figure 15 shows the average MARE (± standard deviation) across all phantoms for different SC methods. As shown in Fig. 15(a) for LE projections in CC view, method $A$ yields the highest MARE of 13.1% ($\pm 8.2\%$). Although methods $B$ and $C$ decrease MARE, method $D$ achieves the lowest MARE of 3.4% ($\pm 0.9\%$). As shown in Fig. 15(b) for HE in CC, MARE is 9.2% ($\pm 4.7\%$) with method $A$, decreasing with methods $B$ and $C$, and reaching 2.8% ($\pm 0.1\%$) with method $D$. For MLO shown in Figs. 15(c) and 15(d), the decreasing trend in MARE from method $A$ to $D$ is similar to that for the CC view. With method D, MARE is 3.0% ($\pm 0.8\%$) and 3.1% ($\pm 0.9\%$) for LE and HE across different phantoms in MLO. Our additional trials using the second kernel with $0.45T$ and $0.55T$ for method $D$ both show an average MARE below 3.4% across all phantoms. This highlights the effectiveness of using $0.5T$ for the second kernel and the robustness of method $D$ to variations in this thickness.

Fig. 15.

MARE of different SC methods for all phantoms, where average and standard deviation (error bar) are shown across (a) LE projection images in CC view, (b) HE projection images in CC view, (c) LE projection images in MLO view, and (d) HE projection images in MLO view.

3.2.2. Image quality and lesion detectability in scatter-corrected images

Figure 16(a) shows the DE image obtained from raw LE and HE images, exhibiting cupping artifacts. Figure 16(b) shows the DE image obtained from primary images, which is free from cupping artifacts and can be used as the reference for evaluating SC. As a single weighting factor was used in DE subtraction across the entire breast area, there is residual breast tissue in the peripheral region due to thickness roll-off. Figure 16(c) shows the DE image obtained from scatter-corrected images using method $A$, which has reduced cupping artifacts. With method $D$, as shown in Fig. 16(d), the cupping artifacts in the DE image are eliminated. Figure 16(e) shows the profiles in DE images. Compared with the raw image, both methods $A$ and $D$ reduce cupping artifacts, whereas method $D$ provides a better match with the primary image and better contrast.

Fig. 16.

Comparison of DE images calculated from (a) raw images, (b) primary images, and scatter-corrected images using methods (c) $A$ and (d) $D$, and (e) smooth profiles along the yellow dashed line. The same window center and width are used for panels (b)–(d).

Figure 17 shows the SDNR of iodine objects in raw, primary, and scatter-corrected DE images. As shown in Fig. 17(a) for 8 mm iodine objects in uniform background, method $A$ improves SDNR by an average of 49.6% (17.3%, 117.3%) compared with the raw image, whereas method $D$ achieves a higher improvement of 82.0% (24.8%, 202.0%). For 5 mm iodine objects shown in Fig. 17(b), method A does not improve SDNR, whereas method D provides an improvement of 8.6% (0.7%, 20.7%). Compared with raw images, primary images and scatter-corrected images with methods $A$ and $D$ demonstrated maximum improvements for objects with the lowest iodine concentration due to its low contrast. Also, the improvement of SDNR was limited by the residual noise of scattered radiation signals, which may be solved with further investigation of noise reduction.^27,51 For iodine objects in the nonuniform background [Fig. 17(c)], SDNR increases approximately linearly with iodine concentrations, and the trend of different methods is similar to Fig. 17(a). Method $D$ provides superior linearity, achieving an $r$-squared value ($r^2$) of 98.3%, compared with method $A$ with an $r^2$ of 96.0%.

Fig. 17.

Comparison of SDNR of iodine objects in DE images calculated from raw images, primary images, and scatter-corrected images using methods $A$ and $D$. (a) 8 mm and (b) 5 mm iodine objects in uniform background, and (c) 8 mm iodine objects in non-uniform background.

4. Discussions

4.1. Monte Carlo-Simulated Scatter Properties for DL-CEDBT

The scatter PSFs in Figs. 8 and 9 show that the characteristics of scatter in DL are different from that in DS^19,24 due to the use of DLFPD and the K-edge filter, which generates two energy peaks in the incident spectrum. Because a portion of the HE component of x-rays is absorbed by the FL detector, the scatter characteristics of the LE image are dominated by the HE photons (Fig. 8). In addition, scattered x-rays from the FL detector are detected by the BL detector, leading to an increase in scattered radiation in DL HE images (Fig. 9). These unique characteristics necessitate a dedicated SC method for DL-CEDBT. The effects of glandular fractions, compressed breast thicknesses, and projection angles are consistent with those reported for regular DM or DBT.^24,52 These indicate the importance of accurate breast thickness and projection angle measurements in implementing kernel-based SC methods.

Through Figs. 10 and 11, scatter maps in both LE and HE projection images show a gradual intensity change over the breast area and little presence of breast texture, indicating the rationale of using 2D interpolation for SC in the peripheral region. Moreover, for MLO with the pectoral muscle, the overall scatter distribution does not change (Fig. 12), suggesting that both MLO and CC views could use the same SC method.

4.2. Scatter Correction for DL-CEDBT

The proposed SC method achieves high accuracy, with MARE of $\sim 3.1\%$ across the entire breast area, outperforming other investigated methods (Fig. 13). This improvement results from combining the strengths of the two-kernel iterative convolution method and the interpolation of measured scatter in the background. The former strategy improves the accuracy in the central region using appropriate kernels to represent breast regions with different thicknesses. The latter improves the accuracy in the peripheral region by incorporating the measured scatter in the background region.

Figure 14 demonstrates the robustness of the proposed method for all projection angles of different breast phantoms. For thicker breasts, the substantial thickness roll-off in the peripheral region leads to severe overestimation of scatter using the single-kernel approach [Fig. 14(a)], which can be improved with the use of two kernels [Fig. 14(c)]. Furthermore, the MARE IQR also increases with breast thickness using kernel-based methods without interpolation [Figs. 14(a) and 14(c)]. This is due to the increased asymmetry at oblique projection angles for thicker breasts. The asymmetry does not alter the gradual change of scatter intensity, and thus, the interpolation method provides higher consistency of SC for different projection angles [Figs. 14(b) and 14(d)]. Therefore, the proposed method can provide accurate SC for oblique projections of all breast thicknesses. Figure 15 demonstrates that the proposed SC method can be used reliably for both LE and HE, and in both CC and MLO views, making it practical for SC in DL-CEDBT.

Through Figs. 16 and 17, we have demonstrated the potential of the SC method to reduce cupping artifacts and improve lesion detectability and quantification in DE images, which is superior to the single-kernel convolution method.

The proposed SC method can be rapidly adapted in clinical settings. Scatter PSFs can be pre-calculated, validated, and refined using experimentally measured scatter-to-primary ratios.^18,19 Blank scans can be experimentally acquired. In addition, the SC method can be easily accelerated with more powerful parallel computing.

5. Conclusions

In this work, we proposed a practical SC method for DL-CEDBT based on pre-calculated scatter PSFs and experimentally acquired blank scans. The accuracy and robustness of the proposed SC method were demonstrated for LE and HE projection images of different anthropomorphic breast phantoms in both CC and MLO views. It has the potential for rapid adoption in clinical settings to improve image quality and lesion detectability for DL-CEDBT.

Biographies

Xiangyi Wu is a PhD student at Stony Brook University. Her research interests focus on dual-layer detector-based breast imaging, including system optimization and the development of image processing techniques, to improve image quality and lesion detectability for CEDM and CEDBT.

Wei Zhao is a professor of radiology at Stony Brook University. She received her PhD in medical biophysics from the University of Toronto in 1997. Her current research interests include the optimization of imaging system geometry and flat-panel detector performance for DBT and dual-energy contrast-enhanced imaging applications, as well as the development of a-Se-based indirect flat-panel detectors with avalanche gain for low-dose imaging applications. She is a member of SPIE.

Biographies of the other authors are not available.

Disclosures

No conflict of interest to disclose.

Code and Data Availability

The data used in this article are simulated using a publicly available tool, VICTRE. Both the code and the data are available upon reasonable request to the authors.