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Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study
Physica Medica xxx (2014) 1e7
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Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study Mahsa Noori- Asl a, *, Alireza Sadremomtaz a, Ahmad Bitarafan-Rajabi b a b
Department of Physics, Faculty of Sciences, University of Guilan, Rasht, Iran Department of Nuclear Medicine, Rajaei Cardiovascular, Medical and Research Center, Iran University of Medical Sciences, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 October 2013 Received in revised form 9 May 2014 Accepted 28 May 2014 Available online xxx
Three practical methods for scatter correction of Tc-99m SPECT images are evaluated. Among these, two methods, three-energy window (TEW) methods using the trapezoidal and triangular approximations, have been described previously by investigators, and a new approximation is offered in this work. The SIMIND (SIMulation of Imaging Nuclear Detectors) Monte Carlo program is used to simulate a line source placed at on-axis and 5 cm off-axis locations, a cold-sphere/hot-background phantom, a hot-sphere/coldbackground phantom, and a more clinically realistic NCAT (Nonuniform Rational B-spline-based CArdiacTorso) phantom. For evaluation of these methods, the scatter line-spread functions and scatter fractions for the on- and off-axis line source, image contrast, signal-to-noise ratio and relative noise for the cold spheres, and recovery coefficient for the hot spheres of different diameters are compared. For the NCAT phantom, a line profile through a slice of the reconstructed image is considered before and after scatter correction, and also image contrast defined by this profile is used to compare the correction methods. The results of this study indicate that for the line source simulation the scatter fractions obtained from the proposed method are a better estimation of true scatter fractions. Also, for both the sphere simulation and NCAT simulation, the proposed method improves the image contrast as compared to the two other methods. © 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: SPECT Scatter correction Monte Carlo simulation
Introduction Use of the NaI(Tl) scintillation crystal as detector material in the gamma camera systems results in the inclusion of both scattered and primary photons within the photopeak energy windows used in single-photon emission computed tomography (SPECT) imaging [1]. Since Compton-scattered photons carry misleading information regarding location of their emission point, the detection of these photons in the photopeak window can degrade image contrast and lesion detection [2]. Thus, to improve both image quality and quantitative accuracy, scatter correction methods need to be used. A number of scatter correction methods have been developed by several groups of investigators. In the simplest technique, to take into account the contribution of the scattered photons, a smaller linear attenuation coefficient (typically 0.12 or 0.13 cm1 instead of 0.15 cm1 for 99mTc photons) is used for the attenuation correction [1,3]. Some other compensation techniques are based on the assumption that: (1) the measured projection data
* Corresponding author. Tel.: þ98 9113820691. E-mail address: [email protected] (M. Noori- Asl).
can be considered as sum of a scatter component and an unscattered component, and that the scatter component can be modeled as the convolution of (a) the measured projection data [1,4] or (b) the unscattered projection data [1,5] with an simple exponential function determined from the shape of line-spread function; (2) the spatial distribution of the scattered photons detected in the photopeak window is quantitatively equal to k times the spatial distribution of the scattered photons detected in a second window in the Compton-scattered region of the 99mTc energy spectrum [1,6,12]; (3) the photopeak window can be divided into two subwindows such that each subwindow includes approximately equal counts of the scattered photons [7,12]; (4) there is a regression relation between the ratio of counts within two subwindows splitting the photopeak window and the photopeak scatter fraction [2,8,9,12]; (5) the ratio of the scattered photons, and also the ratio of the unscattered photons detected in two subwindows splitting the photopeak window can be considered as constant values [10,12]; (6) the photopeak scatter spectrum can be estimated by a trapezoidal area [2,11,12]; or (7) a triangular area [12] using two narrow energy windows located on both sides of the photopeak window. Each correction method has its own limitations. However, because the two last correction methods do not need to calculate any
http://dx.doi.org/10.1016/j.ejmp.2014.05.008 1120-1797/© 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7
parameter calibration and therefore, can be applied directly on each pixel in a projection image, we focus on these two methods and offer a new correction approximation for better estimation of the area of the photopeak scatter spectrum. For evaluation of the proposed approximation, it is compared with both trapezoidal and triangular approximations using four different simulated activity distributions: a line source placed in locations on- and off-axis of the SPECT system; a cold-sphere/hot-background phantom; a hotsphere/cold-background phantom; and a 3D NCAT phantom for investigation of a more realistic clinical situation. In this study, the scatter correction is performed in projection space followed by FBP reconstruction rather than by modeling and correcting for scatter in the statistical reconstruction model [13,14], and objective criteria are used to evaluate each correction method.
ratio of the total counts acquired within the narrow energy window centered at each of these energies to the width of the narrow window. Therefore, the number of scattered photons in the photopeak window can be estimated as,
Spk ði; jÞ ¼
Cn1 ði; jÞ Cn2 ði; jÞ Wpk , þ wn1 wn2 2
(1)
where Cn1 and Cn2 are the total counts acquired in the lower and upper narrow windows, respectively, and (i,j) denotes the location (row and column number) of a given pixel in the projection matrix. The width of each of the narrow windows used for this correction approximation is equal to 2 keV. Triangular approximation
Materials and methods Two scatter correction methods that are commonly used to estimate the fraction of scatter counts in the photopeak window (Wpk ¼ 126e154 keV for Tc-99m) are the trapezoidal and triangular approximations. In both approximations, two narrow energy windows (wn1 and wn2) centered on lower- and upper-energy limits of the photopeak window are used for scatter correction. Trapezoidal approximation In this approximation [11], the trapezoidal area created by the total counts detected in the lower- and upper-energy limits of the photopeak window is used to approximate the scatter counts included in the photopeak window (see Fig. 1(a)). The counts at energies Elow ¼ 126 keV and Eup ¼ 154 keV are estimated by the
The triangular approximation [12] (see Fig. 1(b)) can be considered as a special case of the trapezoidal approximation. In this case, instead of the total counts, the scatter counts detected at energies Elow ¼ 126 keV and Eup ¼ 154 keV are used to estimate the photopeak scatter component. Also in this approximation, it is assumed that all of the photons detected at energy 154 keV are unscattered and that the photopeak is symmetric around 140 keV such that the number of unscattered photons at energies E1 ¼ 126 keV and E2 ¼ 154 keV is equal. Thus, using these assumptions, the number of scattered photons in the photopeak window can be estimated as,
Spk ði; jÞ ¼
Cn1 ði; jÞ Cn2 ði; jÞ Wpk , wn1 wn2 2
(2)
where wn1 and wn2 are equal to 6 keV and 8 keV, respectively.
Figure 1. Illustration of the energy windows used in (a) trapezoidal, (b) triangular and (c) proposed approximations overlaid on the 99mTc energy spectrum. (d) True scatter spectrum in the photopeak window along with the scatter area estimated by the three approximations. The scatter estimation of the proposed approximation (SPA) is approximately intermediate between the scatter overestimation using the trapezoidal approximation (Strap) and the scatter underestimation using the triangular approximation (Strian).
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7
Proposed approximation The hypotheses used for the new approximation are similar to those used for the triangular approximation as well as the assumption that a third narrow window (wn3) can also be considered within the photopeak window so that the number of scattered photons detected at the central energy of this narrow window is equal to the scatter counts estimated for the lowerenergy limit of the photopeak window (see Fig. 1(c)). Therefore, using this approximation, the photopeak scatter spectrum can be estimated using a trapezoidal area whose height is equal to that of the right triangle in the triangular approximation. Thus, the number of scattered photons in the photopeak window can be estimated as,
Spk ði; jÞ ¼
W1 þ Wpk Cn1 ði; jÞ Cn2 ði; jÞ , wn1 wn2 2
(3)
W1 is the difference between the central energy of the third narrow window and the lower-energy limit of the photopeak window. The width of the third narrow energy window is 6 keV, equal to the width of the lower narrow energy window, and is centered at energy 133 keV. Simulation and evaluation The SIMIND (SIMulation of Imaging Nuclear Detectors) Monte Carlo simulation program (version 4.9e) is used to produce the projection images from the different energy windows required for the three scatter correction methods of interest. The simulated SPECT system includes a cylindrical NaI(Tl) scintillation crystal with a radius of 25 cm and thickness of 0.95 cm, equipped with a lowenergy high-resolution (LEHR) collimator. The system energy resolution and intrinsic spatial resolution are 10% (full-width at halfmaximum (FWHM)) and 0.34 cm, respectively, at 140 keV. Using the SIMIND simulation program, it is possible to obtain the true scatter spectrum in the photopeak window and, therefore, compare the number of scattered photons estimated by the three approximations with the true number of photopeak scattered photons. The simulation is also able to separate the scattered from primary or total (scattered þ primary) photons and thus generate the projection images for each of them individually. For each approximation, scatter correction is performed in the projection space, that is, prior to reconstruction. The correction approximations, image reconstruction, and evaluation criteria are programmed in MATLAB (version 7.0.4). The uncorrected and corrected projections are reconstructed using the filtered back-projection (FBP) method with Hann filter. The images resulting from the primary photons are used as a reference for evaluation of the implementation of the scatter correction methods. Four source distributions simulated in this study are as follows. Line source simulation A 99mTc line source (radius 0.25 cm, length 16 cm) placed both on-axis and 5 cm off-axis of a water-filled cylindrical phantom (radius 10 cm, length 18 cm) is simulated. In this simulation, the projections (128 128 matrices with pixel size 0.3 cm) with 5,000,000 photons/projection are acquired using 128 views in a 360 rotation with a radius-of-rotation of 20 cm. For each correction approximation, the scatter fraction (scatter/primary) is calculated by two rectangular regions of interests (ROIs) in the projection image. ROI1 is a large region covering the entire area of the cylindrical phantom in the projection image and is the same for both on- and off-axis locations. ROI2 is a small region covering
3
only the area of the line source and is defined individually for each of the line source locations. Also, the difference between the “true” scatter line-spread function (SLSF) and the SLSFs estimated by the three approximations is calculated to evaluate the correction methods. Sphere simulation For qualitative and quantitative evaluation of the three scatter correction methods, both cold and hot spheres with diameters 3.2, 2.6, 2, 1.6, 1.3 and 1 cm placed in the water-filled cylindrical phantom are simulated. The imaging situation for this simulation is similar to that for the line source simulation. For cold-sphere/hot-background phantom, three parameters, image contrast (C), signal-to-noise ratio (SNR), and relative noise (RN) in the background, are used to evaluate the three correction methods [15]. The image contrast is defined as the ratio of the difference between the mean counts per pixel in the sphere's ROI ðNCS Þ and in the background's ROI ðNBG Þ to the mean counts per pixel in the background's ROI:
C¼
NCS NBG N BG
(4)
The SNR is defined as the same difference as defined for the image contrast divided by the standard deviation of the mean counts per pixel in the background's ROI:
SNR ¼
NCS NBG dBG
(5)
The RN is defined as the ratio of the standard deviation of the mean counts per pixel in the background's ROI (dBG) to the mean counts per pixel in the background's ROI:
RN ¼
dBG N BG
(6)
For hot-sphere/cold-background phantom, the recovery coefficient (RC) is defined as the percentage ratio of the mean counts per corrected
pixel in the sphere's ROI in the corrected image (NHS ) to the mean counts per pixel in the same sphere's ROI in the primary primary
image (N HS
):
corrected
RC ¼
N HS
primary
NHS
,100%
(7)
NCAT simulation For evaluation of a more realistic clinical situation, a 3D NCAT (Nonuniform Rational B-spline-based CArdiac-Torso) phantom [16,17] is simulated. This phantom provides a realistic model of human anatomy and also clinically realistic activity distributions. The activity distribution used for the different organs in this study is similar to that used by Segars et al. [17] that models the activity distribution of a typical patient study in the 99mTc SPECT imaging [18] (see Table 1). 32 projections (64 64 matrices with pixel size 0.4) with 7,142,737 photons per projection are acquired in a 180 rotation. To evaluate the scatter correction methods in this simulation, a line profile from the reconstructed image corrected by the three approximations is compared with the same profile from the uncorrected and primary images. The image contrast for the corrected and uncorrected images defined by the profiles is used to compare the three scatter correction methods.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7 Table 1 The 99mTc activity concentration used for the different organs in the NCAT phantom [17]. Organ
Activity concentration
Heart myocardium, liver, and kidneys Spleen Lungs Stomach, spine, rib, and body
75 60 4 2
Table 2 Scatter fractions estimated by the three approximations for the line source placed in on- and 5 cm off-axis along with “true” scatter fractions. For each estimated scatter fraction, the percentage deviation from the true scatter fraction is also given into the parenthesis. ROI
TEW1
TEW2
PA
On-axis, large On-axis, small Off-axis, large Off-axis, small
0.62 0.24 0.53 0.36
0.41 0.08 0.33 0.19
0.54 0.10 0.43 0.24
(17%) (60%) (29%) (38%)
(23%) (47%) (19%) (27%)
True (2%) (33%) (5%) (8%)
0.53 0.15 0.41 0.26
Results Line source simulation The difference between the true reconstructed SLSF and reconstructed SLSFs estimated by the three approximations is shown in Fig. 2. It can be seen that near the source location, the scatter estimated by the trapezoidal approximation is much greater than the true scatter. This overestimation is even greater when the line source is at an off-axis location. With increasing distance away from the source location, a small underestimation appears. For the triangular approximation, there is a positive peak showing the scatter underestimation close to the source location. For the offaxis line source, a partial overestimation can be seen with the increase of the distance from the source location and near the edge of the phantom. For the proposed approximation, there is a situation similar to the triangular approximation with a smaller scatter underestimation near the source location for both the on- and off-axis source locations. The scatter fractions calculated by the large and small ROIs for the on- and off-axis locations are given in Table 2. For both ROIs, the scatter fractions estimated by the trapezoidal approximation are much greater than the true scatter fractions while the triangular approximation underestimates the scatter fractions in both ROIs. The proposed approximation gives the best estimation for the scatter fractions, although it considerably underestimates the scatter fraction for the small ROI and the on-axis line-source position. In this case, the estimated scatter fractions for the large ROI in both the on-axis and off-axis locations is slightly greater than the true scatter fractions, while the estimated values for the small ROI in the off-axis and essentially on-axis location is lower than the true values. Sphere simulation Figure 1(d) shows the true scatter spectrum within the photopeak window along with the trapezoidal, triangular and proposed approximations. The results of the simulation indicate that the true
number of scattered photons included in the photopeak window, corresponding to the area under the photopeak scatter spectrum, is 387,000. Using Eq. (1), the number of scattered photons estimated using the trapezoidal approximation is equal to 545,300, representing an overestimation of about 41%. For the triangular approximation, the number of scattered photons detected at 154 keV is about 406, ~4.5% of the total counts acquired in this energy. On the other hand, from the assumptions of this approximation, the estimated number of scattered photons at 126 keV (Cn1/ wn1-Cn2/wn2) is about 24,254 with a relative difference of ~5.5% from the true scatter counts detected at this energy (Sn1/wn1). Therefore, using Eq. (2), the number of photopeak scattered photons estimated by the triangular approximation is 339,558, representing an underestimation of about 12%. For the proposed approximation, the true number of the scattered photons at energy 133 keV is 24,000 with a relative difference of ~1% from the scatter counts estimated for energy 126 keV. Therefore, using Eq. (3), the estimated number of photopeak scattered photons using the proposed approximation will be 424,447, representing an overestimation of about 9.7%. The image contrast of the six cold spheres calculated for the three approximations is given in Table 3. The trapezoidal approximation improves the image contrast of the cold sphere 1, 2, 3, 4, 5 and 6 about 19.3%, 15.4%, 13.9%, 3%, 11.5% and 1.6%, respectively. This approximation results in a somewhat irregular correction in that the corrected contrast for sphere 5 (diameter 1.3 cm) is actually greater than that for the next-larger sphere, sphere 4 (diameter 1.6 cm). For the triangular approximation, the improvement in the image contrast of these six cold spheres is about 22.6%, 16.9%, 13.8%, 8.2%, 8.5% and 4.7%, respectively, representing a higher level of improvement than the trapezoidal approximation for all of the cold spheres. On the other hand, for the proposed approximation, the image contrast of the cold sphere 1, 2, 3, 4, 5 and 6 is improved about 31.1%, 23.3%, 18.9%, 11.3%, 11.7% and 6.4%, respectively, that is, the proposed approximation results in more improvement in the image contrasts compared to the two other approximations. The relative noise in the background for the uncorrected image and the
Figure 2. Profiles representing the difference between the true reconstructed SLSF and SLSFs estimated by the three approximations; trapezoidal approximation (labeled as TEW1), triangular approximation (labeled as TEW2) and proposed approximation (labeled as PA), for a line source placed in (a) on-axis and (b) 5 cm off-axis. (The vertical axis is normalized to unit intensity.)
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7 Table 3 Comparison of the image contrasts resulting from three scatter correction methods for six cold spheres. Cold sphere (diameter)
No Trapezoidal correction approximation
Triangular approximation
Proposed approximation
1 2 3 4 5 6
0.624 0.540 0.358 0.154 0.104 0.055
0.850 0.709 0.496 0.236 0.189 0.102
0.935 0.773 0.547 0.267 0.221 0.119
(3.2 cm) (2.6 cm) (2 cm) (1.6 cm) (1.3 cm) (1 cm)
0.817 0.694 0.497 0.184 0.219 0.071
Table 4 Comparison of the signal-to-noise ratios resulting from the three approximations for six cold spheres. Cold sphere (diameter)
No Trapezoidal correction approximation
Triangular approximation
Proposed approximation
1 2 3 4 5 6
23.8 20.6 13.7 5.87 3.96 2.10
21.5 18.0 12.6 5.98 4.79 2.57
20.2 16.7 11.8 5.79 4.79 2.58
(3.2 cm) (2.6 cm) (2 cm) (1.6 cm) (1.3 cm) (1 cm)
11.7 9.93 7.10 2.62 3.13 1.01
5
Table 4 shows the signal-to-noise ratios calculated for the six cold spheres. The SNRs for the trapezoidal approximation are uniformly lower than those for the uncorrected image. For the triangular approximation, the SNRs for the three largest spheres are lower than those for the uncorrected image, but for the three smallest spheres are somewhat higher than those for the uncorrected image. For the proposed approximation, the SNRs for the three largest spheres are uniformly lower than those for the triangular approximation, but for the three smallest spheres are approximately equal to those for the triangular approximation. The hot-sphere recovery coefficients (RCs) calculated relative to the primary image for the three scatter correction approximations are given in Table 5. For the trapezoidal approximation, the RCs for all of the cold spheres are in a range of 10% lower than 100%, while for the triangular and proposed approximations, the RCs are in the range of about 7% and 5% higher than 100%, respectively. A slice from the reconstructed image of the cold spheres and hot spheres with and without the scatter corrections along with the primary image is indicated in Fig. 3.
NCAT simulation Table 5 Hot-sphere recovery coefficients with and without scatter corrections. Cold sphere (diameter)
Trapezoidal approximation
Triangular approximation
Proposed approximation
1 2 3 4 5 6
92.5 92 91.3 91 90.7 90.5
106.2 105.6 105 104.6 104.4 104
104.8 104.4 104 103.8 103.6 103
(3.2 cm) (2.6 cm) (2 cm) (1.6 cm) (1.3 cm) (1 cm)
Figure 4 shows a slice from the reconstructed image of the NCAT phantom with a line profile through this slice with no corrections, with primary photons only, and with each of the three scatter corrections applied. From this profile, image contrast (C) is defined as the ratio of the difference between the mean of two first peaks and the valley (V) between them to the mean of the two peaks:
C¼
images corrected by the trapezoidal, triangular and proposed approximations is about 0.026, 0.066, 0.04 and 0.046, respectively. The trapezoidal approximation thus results in the largest increase in noise among the three correction methods.
Meantwopeaks V Meantwopeaks
(8)
Based on this definition, the contrast of the uncorrected image is 0.835. The contrasts calculated for the images corrected by the trapezoidal, triangular and proposed approximations are equal to 0.941, 0.936 and 0.967, representing a relative increase of 12.7%, 12.1% and 15.8%, respectively.
Figure 3. The first row shows a slice from the reconstructed image of the cold-sphere/hot-background phantom before correction and corrected using the trapezoidal, triangular and proposed approximations along with primary image. The second row shows corresponding images for the hot-sphere/cold-background phantom.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7
Figure 4. A slice from reconstructed image of the NCAT phantom with no corrections, with primary photons only, and with each of the three scatter corrections applied. For comparison, a line profile from the denoted row is also shown.
Conclusion In this phantom-simulation study, three practical scatter correction methods have been evaluated using the SIMIND Monte Carlo program. Three-energy window methods using the
trapezoidal and triangular approximations have been compared with a new approximation with assumptions similar to those of the triangular approximation. For the proposed method applied to Tc99m (140 keV), an additional narrow energy window is centered at energy 133 keV with a width equal to that of the lower narrow
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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energy window centered at energy 126 keV. The proposed scattercorrection method yielded slightly improved scatter fractions, coldsphere image contrasts, and hot-sphere recovery coefficients (RCs) calculated relative to the primary image than those with the trapezoidal and triangular corrections but with a slightly greater noise content. References [1] Jaszczak RJ, Greer KL, Floyd CE, Coleman RE. Scatter compensation techniques for SPECT. IEEE Trans Nucl Sci 1985;32:786. [2] Ljungberg M, King MA, Hademenos J, Strand SE. Comparison of four scatter correction methods using Monte Carlo simulated source distribution. J Nucl Med 1994;35:143e51. [3] Jaszczak RJ, Coleman RE, Whitehead FR. Physical factors affecting quantitative measurements using camera based single photon emission computed tomography (SPECT). IEEE Trans Nucl Sci 1981;28:69e80. [4] Axelsson B, Msaki P, Israelsson A. Subtraction of compton-scattered photons in single photon emission computerized tomography. J Nucl Med 1984;25: 490e4. [5] Floyd CE, Jaszczak RJ, Greer KL, Coleman RE. Deconvolution of compton scatter in SPECT. J Nucl Med 1985;26:403e8. [6] Jaszczak RJ, Greer KL, Floyd CE, Harris CC, Colema RE. Improved SPECT quantification using compensation for scattered photons. J Nucl Med 1984;25: 893e900. [7] Logan KW, McFarland WD. Single photon scatter compensation by photopeak energy distribution analysis. IEEE Trans Med Imaging 1992;11:161e4.
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[8] King MA, Hademenos GJ, Glick SJ. A dual-photopeak window method for scatter correction. J Nucl Med 1992;33:605e12. [9] de Vries DJ, King MA. Window selection for dual photopeak window scatter correction in Tc-99m imaging. IEEE Trans Nucl Sci 1994;14:2771e8. € tter MG, Serfontein DE, [10] Pretoris PH, van Rensburg AJ, van Aswegen A, Lo Herbst CP. The cannel ratio method of scatter correction for radionuclide image quantification. J Nucl Med 1993;34:330e5. [11] Ogawa K, Harata Y, Ichihara T, Kubo A, Hashimoto S. A practical method for position dependent compton-scatter correction in single photon emission CT. IEEE Trans Med Imaging 1991;110:408e12. [12] Buvat I, Rogriguez-Villafuerte M, Todd-Pokropek A, Benali H, Paola RD. Comparative assessment of nine scatter correction methods based on the spectral analysis using Monte Carlo simulations. J Nucl Med 1995;38(8): 1476e88. [13] Beekman FJ, Kamphuis C, Frey EC. Scatter correction methods in 3D iterative SPECT reconstruction: a simulation study. Phys Med Biol 1997;42:1619e31. [14] Bowsher JE, Floyd Jr CE. Treatment of compton scattering in maximumlikelihood, expectation-maximization reconstructions of SPECT images. J Nucl Med 1991;32:1285e91. €hler E, Sundstro € m T, Axelsson J, Larsson A. Detecting small liver tumors [15] Ma with In-111-pentetreotide SPECT-A collimator study based on Monte Carlo simulations. IEEE Trans Nucl Sci 2012;59(1):47e53. [16] Segars WP, Lalush DS, Tsui BMW. A realistic spline-based dynamic heart phantom. IEEE Trans Nucl Sci 1999;46:503e6. [17] Segars WP, Tsui BMW. Study of the efficiency of respiratory gating in myocardial SPECT using the new 4D NCAT phantom. IEEE Trans Nucl Sci 2002;49:675e9. [18] Jaszczak R, Gilland D. An experimental phantom based on quantitative SPECT analysis of patient MIBI biodistribution. J Nucl Med 1996;33:451e7.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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Technical notes
Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study Mahsa Noori- Asl a, *, Alireza Sadremomtaz a, Ahmad Bitarafan-Rajabi b a b
Department of Physics, Faculty of Sciences, University of Guilan, Rasht, Iran Department of Nuclear Medicine, Rajaei Cardiovascular, Medical and Research Center, Iran University of Medical Sciences, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 October 2013 Received in revised form 9 May 2014 Accepted 28 May 2014 Available online xxx
Three practical methods for scatter correction of Tc-99m SPECT images are evaluated. Among these, two methods, three-energy window (TEW) methods using the trapezoidal and triangular approximations, have been described previously by investigators, and a new approximation is offered in this work. The SIMIND (SIMulation of Imaging Nuclear Detectors) Monte Carlo program is used to simulate a line source placed at on-axis and 5 cm off-axis locations, a cold-sphere/hot-background phantom, a hot-sphere/coldbackground phantom, and a more clinically realistic NCAT (Nonuniform Rational B-spline-based CArdiacTorso) phantom. For evaluation of these methods, the scatter line-spread functions and scatter fractions for the on- and off-axis line source, image contrast, signal-to-noise ratio and relative noise for the cold spheres, and recovery coefficient for the hot spheres of different diameters are compared. For the NCAT phantom, a line profile through a slice of the reconstructed image is considered before and after scatter correction, and also image contrast defined by this profile is used to compare the correction methods. The results of this study indicate that for the line source simulation the scatter fractions obtained from the proposed method are a better estimation of true scatter fractions. Also, for both the sphere simulation and NCAT simulation, the proposed method improves the image contrast as compared to the two other methods. © 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: SPECT Scatter correction Monte Carlo simulation
Introduction Use of the NaI(Tl) scintillation crystal as detector material in the gamma camera systems results in the inclusion of both scattered and primary photons within the photopeak energy windows used in single-photon emission computed tomography (SPECT) imaging [1]. Since Compton-scattered photons carry misleading information regarding location of their emission point, the detection of these photons in the photopeak window can degrade image contrast and lesion detection [2]. Thus, to improve both image quality and quantitative accuracy, scatter correction methods need to be used. A number of scatter correction methods have been developed by several groups of investigators. In the simplest technique, to take into account the contribution of the scattered photons, a smaller linear attenuation coefficient (typically 0.12 or 0.13 cm1 instead of 0.15 cm1 for 99mTc photons) is used for the attenuation correction [1,3]. Some other compensation techniques are based on the assumption that: (1) the measured projection data
* Corresponding author. Tel.: þ98 9113820691. E-mail address: [email protected] (M. Noori- Asl).
can be considered as sum of a scatter component and an unscattered component, and that the scatter component can be modeled as the convolution of (a) the measured projection data [1,4] or (b) the unscattered projection data [1,5] with an simple exponential function determined from the shape of line-spread function; (2) the spatial distribution of the scattered photons detected in the photopeak window is quantitatively equal to k times the spatial distribution of the scattered photons detected in a second window in the Compton-scattered region of the 99mTc energy spectrum [1,6,12]; (3) the photopeak window can be divided into two subwindows such that each subwindow includes approximately equal counts of the scattered photons [7,12]; (4) there is a regression relation between the ratio of counts within two subwindows splitting the photopeak window and the photopeak scatter fraction [2,8,9,12]; (5) the ratio of the scattered photons, and also the ratio of the unscattered photons detected in two subwindows splitting the photopeak window can be considered as constant values [10,12]; (6) the photopeak scatter spectrum can be estimated by a trapezoidal area [2,11,12]; or (7) a triangular area [12] using two narrow energy windows located on both sides of the photopeak window. Each correction method has its own limitations. However, because the two last correction methods do not need to calculate any
http://dx.doi.org/10.1016/j.ejmp.2014.05.008 1120-1797/© 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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parameter calibration and therefore, can be applied directly on each pixel in a projection image, we focus on these two methods and offer a new correction approximation for better estimation of the area of the photopeak scatter spectrum. For evaluation of the proposed approximation, it is compared with both trapezoidal and triangular approximations using four different simulated activity distributions: a line source placed in locations on- and off-axis of the SPECT system; a cold-sphere/hot-background phantom; a hotsphere/cold-background phantom; and a 3D NCAT phantom for investigation of a more realistic clinical situation. In this study, the scatter correction is performed in projection space followed by FBP reconstruction rather than by modeling and correcting for scatter in the statistical reconstruction model [13,14], and objective criteria are used to evaluate each correction method.
ratio of the total counts acquired within the narrow energy window centered at each of these energies to the width of the narrow window. Therefore, the number of scattered photons in the photopeak window can be estimated as,
Spk ði; jÞ ¼
Cn1 ði; jÞ Cn2 ði; jÞ Wpk , þ wn1 wn2 2
(1)
where Cn1 and Cn2 are the total counts acquired in the lower and upper narrow windows, respectively, and (i,j) denotes the location (row and column number) of a given pixel in the projection matrix. The width of each of the narrow windows used for this correction approximation is equal to 2 keV. Triangular approximation
Materials and methods Two scatter correction methods that are commonly used to estimate the fraction of scatter counts in the photopeak window (Wpk ¼ 126e154 keV for Tc-99m) are the trapezoidal and triangular approximations. In both approximations, two narrow energy windows (wn1 and wn2) centered on lower- and upper-energy limits of the photopeak window are used for scatter correction. Trapezoidal approximation In this approximation [11], the trapezoidal area created by the total counts detected in the lower- and upper-energy limits of the photopeak window is used to approximate the scatter counts included in the photopeak window (see Fig. 1(a)). The counts at energies Elow ¼ 126 keV and Eup ¼ 154 keV are estimated by the
The triangular approximation [12] (see Fig. 1(b)) can be considered as a special case of the trapezoidal approximation. In this case, instead of the total counts, the scatter counts detected at energies Elow ¼ 126 keV and Eup ¼ 154 keV are used to estimate the photopeak scatter component. Also in this approximation, it is assumed that all of the photons detected at energy 154 keV are unscattered and that the photopeak is symmetric around 140 keV such that the number of unscattered photons at energies E1 ¼ 126 keV and E2 ¼ 154 keV is equal. Thus, using these assumptions, the number of scattered photons in the photopeak window can be estimated as,
Spk ði; jÞ ¼
Cn1 ði; jÞ Cn2 ði; jÞ Wpk , wn1 wn2 2
(2)
where wn1 and wn2 are equal to 6 keV and 8 keV, respectively.
Figure 1. Illustration of the energy windows used in (a) trapezoidal, (b) triangular and (c) proposed approximations overlaid on the 99mTc energy spectrum. (d) True scatter spectrum in the photopeak window along with the scatter area estimated by the three approximations. The scatter estimation of the proposed approximation (SPA) is approximately intermediate between the scatter overestimation using the trapezoidal approximation (Strap) and the scatter underestimation using the triangular approximation (Strian).
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7
Proposed approximation The hypotheses used for the new approximation are similar to those used for the triangular approximation as well as the assumption that a third narrow window (wn3) can also be considered within the photopeak window so that the number of scattered photons detected at the central energy of this narrow window is equal to the scatter counts estimated for the lowerenergy limit of the photopeak window (see Fig. 1(c)). Therefore, using this approximation, the photopeak scatter spectrum can be estimated using a trapezoidal area whose height is equal to that of the right triangle in the triangular approximation. Thus, the number of scattered photons in the photopeak window can be estimated as,
Spk ði; jÞ ¼
W1 þ Wpk Cn1 ði; jÞ Cn2 ði; jÞ , wn1 wn2 2
(3)
W1 is the difference between the central energy of the third narrow window and the lower-energy limit of the photopeak window. The width of the third narrow energy window is 6 keV, equal to the width of the lower narrow energy window, and is centered at energy 133 keV. Simulation and evaluation The SIMIND (SIMulation of Imaging Nuclear Detectors) Monte Carlo simulation program (version 4.9e) is used to produce the projection images from the different energy windows required for the three scatter correction methods of interest. The simulated SPECT system includes a cylindrical NaI(Tl) scintillation crystal with a radius of 25 cm and thickness of 0.95 cm, equipped with a lowenergy high-resolution (LEHR) collimator. The system energy resolution and intrinsic spatial resolution are 10% (full-width at halfmaximum (FWHM)) and 0.34 cm, respectively, at 140 keV. Using the SIMIND simulation program, it is possible to obtain the true scatter spectrum in the photopeak window and, therefore, compare the number of scattered photons estimated by the three approximations with the true number of photopeak scattered photons. The simulation is also able to separate the scattered from primary or total (scattered þ primary) photons and thus generate the projection images for each of them individually. For each approximation, scatter correction is performed in the projection space, that is, prior to reconstruction. The correction approximations, image reconstruction, and evaluation criteria are programmed in MATLAB (version 7.0.4). The uncorrected and corrected projections are reconstructed using the filtered back-projection (FBP) method with Hann filter. The images resulting from the primary photons are used as a reference for evaluation of the implementation of the scatter correction methods. Four source distributions simulated in this study are as follows. Line source simulation A 99mTc line source (radius 0.25 cm, length 16 cm) placed both on-axis and 5 cm off-axis of a water-filled cylindrical phantom (radius 10 cm, length 18 cm) is simulated. In this simulation, the projections (128 128 matrices with pixel size 0.3 cm) with 5,000,000 photons/projection are acquired using 128 views in a 360 rotation with a radius-of-rotation of 20 cm. For each correction approximation, the scatter fraction (scatter/primary) is calculated by two rectangular regions of interests (ROIs) in the projection image. ROI1 is a large region covering the entire area of the cylindrical phantom in the projection image and is the same for both on- and off-axis locations. ROI2 is a small region covering
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only the area of the line source and is defined individually for each of the line source locations. Also, the difference between the “true” scatter line-spread function (SLSF) and the SLSFs estimated by the three approximations is calculated to evaluate the correction methods. Sphere simulation For qualitative and quantitative evaluation of the three scatter correction methods, both cold and hot spheres with diameters 3.2, 2.6, 2, 1.6, 1.3 and 1 cm placed in the water-filled cylindrical phantom are simulated. The imaging situation for this simulation is similar to that for the line source simulation. For cold-sphere/hot-background phantom, three parameters, image contrast (C), signal-to-noise ratio (SNR), and relative noise (RN) in the background, are used to evaluate the three correction methods [15]. The image contrast is defined as the ratio of the difference between the mean counts per pixel in the sphere's ROI ðNCS Þ and in the background's ROI ðNBG Þ to the mean counts per pixel in the background's ROI:
C¼
NCS NBG N BG
(4)
The SNR is defined as the same difference as defined for the image contrast divided by the standard deviation of the mean counts per pixel in the background's ROI:
SNR ¼
NCS NBG dBG
(5)
The RN is defined as the ratio of the standard deviation of the mean counts per pixel in the background's ROI (dBG) to the mean counts per pixel in the background's ROI:
RN ¼
dBG N BG
(6)
For hot-sphere/cold-background phantom, the recovery coefficient (RC) is defined as the percentage ratio of the mean counts per corrected
pixel in the sphere's ROI in the corrected image (NHS ) to the mean counts per pixel in the same sphere's ROI in the primary primary
image (N HS
):
corrected
RC ¼
N HS
primary
NHS
,100%
(7)
NCAT simulation For evaluation of a more realistic clinical situation, a 3D NCAT (Nonuniform Rational B-spline-based CArdiac-Torso) phantom [16,17] is simulated. This phantom provides a realistic model of human anatomy and also clinically realistic activity distributions. The activity distribution used for the different organs in this study is similar to that used by Segars et al. [17] that models the activity distribution of a typical patient study in the 99mTc SPECT imaging [18] (see Table 1). 32 projections (64 64 matrices with pixel size 0.4) with 7,142,737 photons per projection are acquired in a 180 rotation. To evaluate the scatter correction methods in this simulation, a line profile from the reconstructed image corrected by the three approximations is compared with the same profile from the uncorrected and primary images. The image contrast for the corrected and uncorrected images defined by the profiles is used to compare the three scatter correction methods.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7 Table 1 The 99mTc activity concentration used for the different organs in the NCAT phantom [17]. Organ
Activity concentration
Heart myocardium, liver, and kidneys Spleen Lungs Stomach, spine, rib, and body
75 60 4 2
Table 2 Scatter fractions estimated by the three approximations for the line source placed in on- and 5 cm off-axis along with “true” scatter fractions. For each estimated scatter fraction, the percentage deviation from the true scatter fraction is also given into the parenthesis. ROI
TEW1
TEW2
PA
On-axis, large On-axis, small Off-axis, large Off-axis, small
0.62 0.24 0.53 0.36
0.41 0.08 0.33 0.19
0.54 0.10 0.43 0.24
(17%) (60%) (29%) (38%)
(23%) (47%) (19%) (27%)
True (2%) (33%) (5%) (8%)
0.53 0.15 0.41 0.26
Results Line source simulation The difference between the true reconstructed SLSF and reconstructed SLSFs estimated by the three approximations is shown in Fig. 2. It can be seen that near the source location, the scatter estimated by the trapezoidal approximation is much greater than the true scatter. This overestimation is even greater when the line source is at an off-axis location. With increasing distance away from the source location, a small underestimation appears. For the triangular approximation, there is a positive peak showing the scatter underestimation close to the source location. For the offaxis line source, a partial overestimation can be seen with the increase of the distance from the source location and near the edge of the phantom. For the proposed approximation, there is a situation similar to the triangular approximation with a smaller scatter underestimation near the source location for both the on- and off-axis source locations. The scatter fractions calculated by the large and small ROIs for the on- and off-axis locations are given in Table 2. For both ROIs, the scatter fractions estimated by the trapezoidal approximation are much greater than the true scatter fractions while the triangular approximation underestimates the scatter fractions in both ROIs. The proposed approximation gives the best estimation for the scatter fractions, although it considerably underestimates the scatter fraction for the small ROI and the on-axis line-source position. In this case, the estimated scatter fractions for the large ROI in both the on-axis and off-axis locations is slightly greater than the true scatter fractions, while the estimated values for the small ROI in the off-axis and essentially on-axis location is lower than the true values. Sphere simulation Figure 1(d) shows the true scatter spectrum within the photopeak window along with the trapezoidal, triangular and proposed approximations. The results of the simulation indicate that the true
number of scattered photons included in the photopeak window, corresponding to the area under the photopeak scatter spectrum, is 387,000. Using Eq. (1), the number of scattered photons estimated using the trapezoidal approximation is equal to 545,300, representing an overestimation of about 41%. For the triangular approximation, the number of scattered photons detected at 154 keV is about 406, ~4.5% of the total counts acquired in this energy. On the other hand, from the assumptions of this approximation, the estimated number of scattered photons at 126 keV (Cn1/ wn1-Cn2/wn2) is about 24,254 with a relative difference of ~5.5% from the true scatter counts detected at this energy (Sn1/wn1). Therefore, using Eq. (2), the number of photopeak scattered photons estimated by the triangular approximation is 339,558, representing an underestimation of about 12%. For the proposed approximation, the true number of the scattered photons at energy 133 keV is 24,000 with a relative difference of ~1% from the scatter counts estimated for energy 126 keV. Therefore, using Eq. (3), the estimated number of photopeak scattered photons using the proposed approximation will be 424,447, representing an overestimation of about 9.7%. The image contrast of the six cold spheres calculated for the three approximations is given in Table 3. The trapezoidal approximation improves the image contrast of the cold sphere 1, 2, 3, 4, 5 and 6 about 19.3%, 15.4%, 13.9%, 3%, 11.5% and 1.6%, respectively. This approximation results in a somewhat irregular correction in that the corrected contrast for sphere 5 (diameter 1.3 cm) is actually greater than that for the next-larger sphere, sphere 4 (diameter 1.6 cm). For the triangular approximation, the improvement in the image contrast of these six cold spheres is about 22.6%, 16.9%, 13.8%, 8.2%, 8.5% and 4.7%, respectively, representing a higher level of improvement than the trapezoidal approximation for all of the cold spheres. On the other hand, for the proposed approximation, the image contrast of the cold sphere 1, 2, 3, 4, 5 and 6 is improved about 31.1%, 23.3%, 18.9%, 11.3%, 11.7% and 6.4%, respectively, that is, the proposed approximation results in more improvement in the image contrasts compared to the two other approximations. The relative noise in the background for the uncorrected image and the
Figure 2. Profiles representing the difference between the true reconstructed SLSF and SLSFs estimated by the three approximations; trapezoidal approximation (labeled as TEW1), triangular approximation (labeled as TEW2) and proposed approximation (labeled as PA), for a line source placed in (a) on-axis and (b) 5 cm off-axis. (The vertical axis is normalized to unit intensity.)
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7 Table 3 Comparison of the image contrasts resulting from three scatter correction methods for six cold spheres. Cold sphere (diameter)
No Trapezoidal correction approximation
Triangular approximation
Proposed approximation
1 2 3 4 5 6
0.624 0.540 0.358 0.154 0.104 0.055
0.850 0.709 0.496 0.236 0.189 0.102
0.935 0.773 0.547 0.267 0.221 0.119
(3.2 cm) (2.6 cm) (2 cm) (1.6 cm) (1.3 cm) (1 cm)
0.817 0.694 0.497 0.184 0.219 0.071
Table 4 Comparison of the signal-to-noise ratios resulting from the three approximations for six cold spheres. Cold sphere (diameter)
No Trapezoidal correction approximation
Triangular approximation
Proposed approximation
1 2 3 4 5 6
23.8 20.6 13.7 5.87 3.96 2.10
21.5 18.0 12.6 5.98 4.79 2.57
20.2 16.7 11.8 5.79 4.79 2.58
(3.2 cm) (2.6 cm) (2 cm) (1.6 cm) (1.3 cm) (1 cm)
11.7 9.93 7.10 2.62 3.13 1.01
5
Table 4 shows the signal-to-noise ratios calculated for the six cold spheres. The SNRs for the trapezoidal approximation are uniformly lower than those for the uncorrected image. For the triangular approximation, the SNRs for the three largest spheres are lower than those for the uncorrected image, but for the three smallest spheres are somewhat higher than those for the uncorrected image. For the proposed approximation, the SNRs for the three largest spheres are uniformly lower than those for the triangular approximation, but for the three smallest spheres are approximately equal to those for the triangular approximation. The hot-sphere recovery coefficients (RCs) calculated relative to the primary image for the three scatter correction approximations are given in Table 5. For the trapezoidal approximation, the RCs for all of the cold spheres are in a range of 10% lower than 100%, while for the triangular and proposed approximations, the RCs are in the range of about 7% and 5% higher than 100%, respectively. A slice from the reconstructed image of the cold spheres and hot spheres with and without the scatter corrections along with the primary image is indicated in Fig. 3.
NCAT simulation Table 5 Hot-sphere recovery coefficients with and without scatter corrections. Cold sphere (diameter)
Trapezoidal approximation
Triangular approximation
Proposed approximation
1 2 3 4 5 6
92.5 92 91.3 91 90.7 90.5
106.2 105.6 105 104.6 104.4 104
104.8 104.4 104 103.8 103.6 103
(3.2 cm) (2.6 cm) (2 cm) (1.6 cm) (1.3 cm) (1 cm)
Figure 4 shows a slice from the reconstructed image of the NCAT phantom with a line profile through this slice with no corrections, with primary photons only, and with each of the three scatter corrections applied. From this profile, image contrast (C) is defined as the ratio of the difference between the mean of two first peaks and the valley (V) between them to the mean of the two peaks:
C¼
images corrected by the trapezoidal, triangular and proposed approximations is about 0.026, 0.066, 0.04 and 0.046, respectively. The trapezoidal approximation thus results in the largest increase in noise among the three correction methods.
Meantwopeaks V Meantwopeaks
(8)
Based on this definition, the contrast of the uncorrected image is 0.835. The contrasts calculated for the images corrected by the trapezoidal, triangular and proposed approximations are equal to 0.941, 0.936 and 0.967, representing a relative increase of 12.7%, 12.1% and 15.8%, respectively.
Figure 3. The first row shows a slice from the reconstructed image of the cold-sphere/hot-background phantom before correction and corrected using the trapezoidal, triangular and proposed approximations along with primary image. The second row shows corresponding images for the hot-sphere/cold-background phantom.
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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M. Noori- Asl et al. / Physica Medica xxx (2014) 1e7
Figure 4. A slice from reconstructed image of the NCAT phantom with no corrections, with primary photons only, and with each of the three scatter corrections applied. For comparison, a line profile from the denoted row is also shown.
Conclusion In this phantom-simulation study, three practical scatter correction methods have been evaluated using the SIMIND Monte Carlo program. Three-energy window methods using the
trapezoidal and triangular approximations have been compared with a new approximation with assumptions similar to those of the triangular approximation. For the proposed method applied to Tc99m (140 keV), an additional narrow energy window is centered at energy 133 keV with a width equal to that of the lower narrow
Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008
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energy window centered at energy 126 keV. The proposed scattercorrection method yielded slightly improved scatter fractions, coldsphere image contrasts, and hot-sphere recovery coefficients (RCs) calculated relative to the primary image than those with the trapezoidal and triangular corrections but with a slightly greater noise content. References [1] Jaszczak RJ, Greer KL, Floyd CE, Coleman RE. Scatter compensation techniques for SPECT. IEEE Trans Nucl Sci 1985;32:786. [2] Ljungberg M, King MA, Hademenos J, Strand SE. Comparison of four scatter correction methods using Monte Carlo simulated source distribution. J Nucl Med 1994;35:143e51. [3] Jaszczak RJ, Coleman RE, Whitehead FR. Physical factors affecting quantitative measurements using camera based single photon emission computed tomography (SPECT). IEEE Trans Nucl Sci 1981;28:69e80. [4] Axelsson B, Msaki P, Israelsson A. Subtraction of compton-scattered photons in single photon emission computerized tomography. J Nucl Med 1984;25: 490e4. [5] Floyd CE, Jaszczak RJ, Greer KL, Coleman RE. Deconvolution of compton scatter in SPECT. J Nucl Med 1985;26:403e8. [6] Jaszczak RJ, Greer KL, Floyd CE, Harris CC, Colema RE. Improved SPECT quantification using compensation for scattered photons. J Nucl Med 1984;25: 893e900. [7] Logan KW, McFarland WD. Single photon scatter compensation by photopeak energy distribution analysis. IEEE Trans Med Imaging 1992;11:161e4.
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Please cite this article in press as: Noori- Asl M, et al., Evaluation of three scatter correction methods based on estimation of photopeak scatter spectrum in SPECT imaging: A simulation study, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.05.008