DUAL energy X-ray radiography [1] can be used to separate

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 1, FEBRUARY 2006 133 A Scatter Correction Using Thickness Iteration in Dual-Energy Radiography S. K. Ahn, G. Cho, and H. Jeon Abstract In dual-energy radiography with area detectors, a scattered signal causes dominant error in the separation of different materials. Several methods for scatter correction in dual energy radiography have been suggested, yielding improved results. Such methods, however, require additional lead blocks or detectors, and additional exposures to estimate the scatter fraction for every correction. In the present study we suggest a scatter correction method that uses a database of fractions and distributions of the scattered radiation. To verify the feasibility of this method we conducted a MCNP simulation for a two-material problem, aluminum and water. The generation of the scatter information for different thicknesses of an aluminum-water phantom has been simulated. Based on the uncorrected signals, the thickness of each material can be calculated by a conventional dual-energy algorithm. The scatter information of the corresponding thickness from the database, a look-up table, is then used to correct the original signals. The iteration of this scatter correction reduced relative-thickness error from 32% to 3.4% in aluminum, and from 41% to 2.8% in water. The proposed scatter correction method can be applied to two-material dual-energy radiography such as mammography, contrast imaging, and industrial inspections. I. INTRODUCTION DUAL energy X-ray radiography [1] can be used to separate soft and dense-material images in medical and industrial applications. It can be performed successfully with a line-scanning system because of its scatter-free nature. With area detectors, however, scattered radiation also contributes to the signal. This undesired behavior of scattered X-ray photons in radiography causes serious degradation of the contrast in the observed images. This results in poor separation of soft and dense-material images in dual-energy radiography. As the scatter fraction increases, the thickness is underestimated. As such, a dual-energy algorithm does not work well. According to previous studies [2], the percentage of scattered photons is typically 60% to 70% in the lungs and 80% to 95% in the mediastinum in a standard PA chest radiograph. Anti-scatter grids can reduce these scatter fractions to 20% to 30% in the lungs and 40% to 60% in the mediastinum. Several methods [3] [6] for scatter correction in dual-energy radiography have been suggested, yielding improved results. These software post-processing methods are mostly based on convolution filtering. However, these approaches require additional lead blocks or detectors, and also additional exposures to estimate the scatter fraction for each correction. Furthermore, Manuscript received November 15, 2004. This work was supported by the itrs, Innovative Technology Center for Radiation Safety, Korea. The authors are with the Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology, Daejon, Korea 305-701 (e-mail: skahn76@kaist.ac.kr; gscho@kaist.ac.kr; shiloh1@kaist.ac.kr). Digital Object Identifier 10.1109/TNS.2005.862974 Fig. 1. Schematic of the aluminum-water phantom simulated with MCNP and the resultant low- and high-energy images. The phantom has four steps of aluminum (0.1/0.2/0.3/0.4 cm) overlapped at the top and four steps of water (1/2/3/4 cm) at the bottom. The incident X-ray has a top-down parallel direction covering the whole top surface, and the detection pixel array is located immediately under the phantom. The low-energy spectrum is 70 kvp filtered by 10 mm Al, and the high-energy spectrum is 150 kvp filtered by 20 mm Cu. previous studies used only one or two convolution kernels even though the scatter point spread functions have different shapes as a function of object thickness. The present study suggests a new scatter correction method for use in dual-energy radiography. Using a dual-energy algorithm, we can roughly estimate the object thickness, which can assign the unique scatter-spread function for a more precise correction. In this study, we assumed that the object is composed of aluminum and water only, and that this composition is known. All resultant image and scatter point spread functions are simulated with MCNPX. Image separation by the dual-energy algorithm and its scatter correction method are described in Section II, and quantitative results obtained by simulations are discussed in detail in Section III. II. MATERIALS AND METHODS Fig. 1 provides a description of the aluminum-water phantom and the simulation geometry for the dual-energy radiography, and the resultant low- and high-energy images. The phantom has four steps of aluminum (0.1/0.2/0.3/0.4 cm) overlapped at the top and four steps of water (1/2/3/4 cm) at the bottom. The incident X-ray has a top-down parallel direction over the whole top surface, and the detection pixel array is located immediately under the phantom. The simulation tool was MCNPX code version 2.4.0 [7], and photoelectric, Rayleigh and Compton scattering were taken into consideration. The detection array has 24 24 pixels and the pixel size is 0.5 0.5 cm. To obtain statistically confident results with a reasonable simulation time, 0018-9499/$20.00 2006 IEEE

134 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 1, FEBRUARY 2006 Fig. 2. Separated images of (left) the aluminum step and (right) the water step by a dual-energy algorithm without any scatter correction. Due to scatter effects, the thickness maps are seriously distorted and the water thickness is especially underestimated. the pixel size is much larger than that utilized in a real situation. There is no influence of pixel size on the correction. X-ray spectra were generated by a SRS78, a diagnostic X-ray spectra generator [8]. The low-energy spectrum is 70 kvp filtered by 10 mm Al, and the high-energy spectrum is 150 kvp filtered by 20 mm Cu. These simulation conditions, including the phantom, X-ray spectra and the detection conditions, are the same for all simulations in this work. The gray level in the images is not an absolute value, but rather it is equalized by maximum and minimum values in each image. For these images, we applied the dual-energy algorithm to separate the two materials, and the suggested scatter correction method to improve dual-energy imaging. The detailed procedure is described below. A. Dual-Energy Algorithm With monoenergetic X-ray sources, there is an exact solution of thickness because of perfect linearity between logarithmic signals and attenuation coefficients. With broad spectra sources, however, an exact solution does not exist because of the nonlinear relationship arising from broad energy and attenuation coefficients. Therefore, the thickness should be estimated by an empirical model, and this is the situation in general dual-energy radiography. This situation is worsened if there is scattered radiation in the signals. Using a dual-energy algorithm, we can separate aluminum and water in the images. Fig. 2 shows the separated thickness maps and the aluminum-only and the water-only images. In the thickness maps, there are serious distortions due to scatter effects, and the water thickness is especially underestimated. These aluminum and water thickness images are used as the seed-thickness in the scatter correction, which assigns a unique scatter point spread function from the look-up table. B. Generation of the SPSFs and the Look-Up Table The characteristics of the scatter point-spread functions (SPSFs) have been studied by several research groups. Their results from Monte Carlo simulations and experiments showed that the spatial distribution of the SPSF is rotationally symmetric [9]. Therefore, we have simulated a quarter of SPSFs and built whole SPSFs with the assumption they are symmetric. The quarter-spsfs in a dimension of 24 24 are expanded into whole-spsfs in 47 47, and this dimension is diminished into 39 39 by cutting out the near-zero section. Therefore, the final SPSFs have 39 39 pixels with 0.5 0.5 cm pixel size.

AHN et al.: SCATTER CORRECTION USING THICKNESS ITERATION 135 Fig. 4. Pixel value of the central pixel (primary signal), scatter signal, and their ratio SPR as a function of pixel size. We can see that the SPR is decreasing with larger pixel size (detection pixel is the circle with various radiuses) and the relationship between the SPR and the pixel-size depends on the object thickness. and various combinations of thickness of aluminum and water, comprise the look-up table (LUT) (Fig. 5). Fig. 3. (a) Schematic of the MCNP simulation for generation of scatter-spread functions and (b) some of results. We assumed the center pixel value is the primary intensity, and the others are scattered. In the simulation, the aluminum and water thicknesses are varied from 0.0 to 0.4 cm and 0 to 5 cm, respectively. A schematic of the MCNP simulation for generation of SPSFs is shown in Fig. 3. The X-ray beam is pencil-shaped. Only the center pixel has primary X-ray intensity, and the others have scattered X-rays. In the simulation, the aluminum thickness is varied at 0.0/0.1/0.2/0.3/0.4 cm, and the water thickness at 0/1/2/3/4/5 cm. Therefore, 30 different SPSFs are generated for low-energy and 30 SPSFs for high-energy. 5 cm-thick water has been simulated because the estimated thickness for the correction is thicker than the real thickness in the early part of iteration, even though the thickest water step is 4 cm in the example image. The bottom graph in Fig. 3 shows one set of results, displaying six different shapes of SPSF for low-energy with 0.4 cm fixed aluminum thickness and various water thicknesses. Due to the assumption of a primary signal from the pixel value of the central pixel and finite size of the pixel, the primary signal includes the scattered photons in a simulation. These effects are shown in Fig. 4. In the graph, the simulated primary signal (pixel value of the central pixel) and scatter signal, and their ratio (scatter-to-primary ratio), are given as a function of the pixel size. Several other simulations show that SPR is also a function of object thickness. Therefore, a correction for pixel size effects is needed. We corrected SPSFs with the absolute primary intensities, which are estimated by fitting the SPRs as a function of pixel size with 2-order exponential decay functions. The corrected final SPSFs, which are for low- and high-energies C. Generation of Scatter Images Using the LUT and the estimated thickness, low- and highenergy scatter-only images are generated. These scatter-only images are an integration of the pixel values in SPSFs on a pixel by pixel basis (Fig. 6). SPSFs are selected by seed-thickness of aluminum and water. The scatter-corrected images are obtained by subtraction of these scatter-only images from the original low- and high-energy images. D. Scatter Correction Algorithm The procedure of the suggested scatter correction method (Fig. 7) is as follows. 1. Estimation of object thickness using a dual-energy algorithm without scatter correction: These thickness images, which have large error, are seed-thicknesses for scatter images (described in Section II-A). 2. For each pixel, generation of scatter images by integration of scatter point spread functions from the look-up-table: Thickness of each pixel is used for the appropriate scatter point spread functions (described in Sections II-B and II-C). 3. Scatter correction of original low- and high-energy images: Scatter-corrected images are obtained by subtraction of scatter from original images (described in Section II-C). 4. Estimation of new object thickness with corrected lowand high-energy images: These estimated thicknesses give more correct results than the first seed-thickness. The result is used as the new seed-thickness for the iterative correction. 5. Comparison of scatter-only images: After generation of new scatter-only images with the results from step 4, the difference between the previous scatter-only and the new scatter-only images can be obtained.

136 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 1, FEBRUARY 2006 Fig. 5. LUT for the scatter correction. The LUT consisted of low- and high-energy scatter point spread functions of various combination of thickness of aluminum and water. Fig. 6. Algorithm for the generation of scatter-only images. Using the LUT and estimated thickness (seed-thickness), low- and high-energy scatter-only images are generated. 6. Iterate process 2 through 5 : Continue steps 2 through 5 with newly estimated thickness images as new seed-thickness until the difference becomes less than the pre-set error. This scatter correction process converges into some finite error of scatter signals if the SPR is less than 1 [10]. In this Fig. 7. Algorithm of the scatter correction method in dual-energy radiography. The dual-energy processing and the generation of scatter images were described in Sections II-A and II-C. work, the object is not thick enough for the SPR to be greater than 1, and thus the results converged in 4 iterations in the correction process. Fig. 8 shows the final aluminum- and water-thickness maps and images after the scatter correction.

AHN et al.: SCATTER CORRECTION USING THICKNESS ITERATION 137 Fig. 8. Separated images of (left) aluminum and (right) water after scatter correction. The resultant separated images show much clear steps in the images and better results in thickness estimation on the maps. III. RESULTS AND DISCUSSION Longitudinal and transversal profiles of the results are plotted in Fig. 9 and the relative-thickness errors are listed in Table I. In each graph, the real values and the results without scatter correction are plotted as dashed lines and open dots. The results with the scatter correction are much closer to the real values than those without any scatter correction. Without scatter correction, the average relative-thickness errors are 32% for aluminum and 41% for water, and the maxima are 44% and 75% in the longitudinal direction. The scatter correction reduces these errors to 3.4% for aluminum and 2.8% for water on average, and 11% and 9% as a maximum. In the zero-thickness regions, which are located right immediately next to the first steps (0.1 cm-step in the aluminum object and 1 cm-step in the water object), the errors are greater than the average because the scatter point spread functions have quite different shapes at the edges of the objects. It should be noted that these effects are especially emphasized in this study because of the steps in the phantom. In the transversal direction, the average relative-thickness errors decrease from 14% without correction to 6.1% with correction for 3 mm of aluminum, and 44% to 1.9% for 3 cm of water. The errors are greater for the thin region and the maxima reach 21% and 27% for 1 mm of Al and for 1 cm of water after correction. Detailed error comparisons are listed in Table I. The thickness is slightly more overestimated in the left-hand side region because the other material, which is stacked as presented in Fig. 1, is thicker in that region. IV. CONCLUSION A new scatter correction method in dual-energy radiography was suggested. We performed scatter correction by iterative thickness estimation using unique SPSFs. Our method uses information from a dual-energy algorithm to correct the images. This is the most distinct aspect of the proposed method in comparison with other conventional correction methods, which are applied in the same manner in conventional radiography and dual-energy radiography. In order to verify the effectiveness of this method, we conducted a MCNP simulation. The scatter information for each combination of thickness of an aluminum-water phantom was generated. Based on the uncorrected signals, the thickness of each material could be calculated by a conventional dual-energy algorithm. The scatter information of corresponding thickness from the database is then used to correct the original signals. For the aluminum-water object, the suggested iterative correction reduced the rms error in the thickness estimation. The method described in this paper does not use additional blocks and therefore does not need additional exposure.

138 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 1, FEBRUARY 2006 TABLE I RELATIVE ERRORS WITH AND WITHOUT SCATTER CORRECTION One drawback of the proposed approach arises from a characteristic of the SPSF. SPSFs with several different orders of object materials or with a different air gap thickness may have different shapes and magnitudes. In contrast with a CT, dual-energy radiography does not specify the arrangement of the material, i.e., which material is located on the top and which is on the bottom. Also, SPSFs are not symmetric near the object edge. This may constitute a handicap for the application of perfect correction in a blind object situation. Inclusion of these effects can help to decrease errors in regions of abrupt material thickness variations. It is noted that these effects were not taken into account in the present study, because preliminary simulation results indicated that the differences are insignificant for the range of interest in this study. Nevertheless, the correction method improved the dual-energy imaging considerably, even though it is not perfect. Most applications are not in a blind situation. For example, abnormal dense tissue is always located inside soft tissue in mammography. This scatter correction method can be applied to two-material dual-energy radiography such as mammography, contrast imaging, and industrial inspections. Expansion of the correction algorithm to other materials will be the next step in developing the proposed scatter correction method. Fig. 9. (a), (b) Longitudinal and (c), (d) transversal profiles of central and iso-thickness lines in the aluminum and the water images. The average relative thickness errors are 3.4% for aluminum and 2.8% for water in the longitudinal, and 6.1 7.0% for 1 3 mm of aluminum and 1.9 12% for 1 3 cm of water in the transversal direction. REFERENCES [1] L. A. Lehmann et al., Generalized image combinations in dual KVP digital radiography, Med. Phys., vol. 8, no. 5, pp. 659 667, 1981. [2] C. E. Floyd et al., Scatter compensation for digital chest radiography using maximum likelihood expectation maximization, Invest. Radiol., vol. 28, no. 5, pp. 427 433, 1993. [3] C.-G. Shaw et al., Quantitative digital subtraction angiography: Two scanning techniques for correction of scattered radiation and veiling glare, Radiology, vol. 157, pp. 247 253, 1985. [4] F. C. Wagner et al., Dual-energy X-ray projection imaging: Two sampling schemes for the correction of scattered radiation, Med. Phys., vol. 15, no. 5, pp. 732 748, 1988. [5] D. G. Kruger et al., A regional convolution kernel algorithm for scatter correction in dual-energy images: Comparison to single-kernel algorithms, Med. Phys., vol. 21, no. 2, pp. 175 184, 1994. [6] D. A. Hinshaw and J. T. Dobbins III, Plate scatter correction for improved performance in dual-energy imaging, Med. Phys., vol. 23, no. 6, pp. 871 876, 1996. [7] MCNPX 2.4.0, Oak Ridge Nat. Lab., Oak Ridge, TN, 2002. [8] K. Cranley, B. J. Gilmore, G. W. A. Fogarty, and L. Desponds, Catalogue of Diagnostic X-Ray Spectra and Other Data, 1997. Inst. Phys. Eng. Med. Rep. no. 78. [9] M. Honda et al., A technique of scatter-glare correction using a digital filtration, Med. Phys., vol. 20, no. 1, pp. 59 69, 1993. [10] D. E. G. Trotter et al., Thickness-dependent scatter correction algorithm for digital mammography, in Proc. SPIE, 2002, pp. 469 478.