Michael King, Ph.D., and Troy Farncombe, Ph.D. Department of Radiology, Division of Nuclear Medicine, University of Massachusetts Medical. School, 55 Lake ...
AN OVERVIEW OF ATTENUATION AND SCATTER CORRECTION OF PLANAR AND SPECT DATA FOR DOSIMETRY STUDIES Michael King, Ph.D., and Troy Farncombe, Ph.D. Department of Radiology, Division of Nuclear Medicine, University of Massachusetts Medical School, 55 Lake Ave North, Worcester, MA 01655
ABSTRACT A number of factors impact the accuracy of activity quantitation in planar and single photon emission computed tomographic (SPECT) imaging. Two important such factors are attenuation and scattering in the medium containing the activity. The first removes photons which otherwise would have been included in the images, and the second adds events to the images from photons which would not have otherwise been imaged. A number of methods have been developed to compensate for these biases to activity quantitation. This review will briefly introduce planar quantitation which is commonly used for dosimeter purposes, and then present a slightly more detailed overview of SPECT quantitation which is arguably more accurate. It will conclude by cautioning users of commercial reconstruction software to validate it for quantitation before using it for dosimetric purposes.
INTRODUCTION In order to calculate the absorbed dose for a target organ as a result of the administration of a radiopharmaceutical, one must have an estimate of the activity in the source organs as a function of time.1 One way of performing absolute quantitation of activity is via imaging the photons emitted by the radiopharmaceutical. Generally, the number of counts per second (cps) detected by an imaging system is not equal to the activity in becquerel (number of disintegrations per second).1, 2 If we denote A as the tissue activity in becquerel (Bq) then it is equal to A (Bq) = R (cps) / [D (c/photon) x n (photon/disintegration)]
eq. 1
where R is the observed counting rate for a given energy photon, D is the detection efficiency for that energy photon in counts detected per photon emitted, and n is the fractional emission rate for the given energy photon is photons emitted per disintegration. The product of D and n is usually called the sensitivity of the detection system. Among the factors that impact the sensitivity are:1-6 1) the absorption and scattering of photons, 2) collimator efficiency, 3) detector detection efficiency and window fraction, 4) counting rate losses, 5) volume-of-interest (VOI) definition and the partial volume effect, 6) counts detected within the VOI which originated from outside of it, 7) kinetics of the radiopharmaceutical during the period of imaging, 8) reconstruction parameters and implementation in the case of SPECT, and 9) noise. In this review we will focus on compensating for the absorption and scattering of photons.
ATTENUATION AND SCATTER
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Attenuation is the loss of counts which would otherwise have been included in the images by the photons interacting in the medium via the Photoelectric Effect, Compton Scattering, Coherent Scattering, Pair Production, or Photo-disintegration.2 If I0 is the intensity of a beam of photons (photons per cm2 per second) incident on some medium of thickness x, then the intensity of the beam after passing through the medium (I(x)) divided by I0 or transmitted fraction (TF) is TF(x) = exp(µx)
eq. 2
where µ is the linear attenuation coefficient of the medium. The linear attenuation coefficient is the fractional probability of being attenuated for a very thin layer of medium. It depends on the physical density and atomic number of the medium, and the energy of the photons. If the photons were to pass through multiple materials, then the line integral would replace the product µx in equation 2. This loss of counts through attenuation must be accounted for if accurate quantitation of activity is to be achieved. Equation 2 holds only for a mono-energetic beam of photons, and the case of goodgeometry counting. In good-geometry counting all scattered photons are removed from the beam so that they are not counted. Thus under good-geometry conditions any interaction of a photon in the medium leads to its loss. In imaging, photons that would not otherwise have been detected can be scattered so that they can now pass through the collimator and increase the number of counts compared to that predicted by eq. 2. Equation 2 is modified to account for such broadbeam conditions by including a buildup factor (B) in front of the exponential giving TF(x) = B exp(µx) .
eq. 3
The buildup factor is equal to the total number of counts detected (primary and scattered) divided by the number of primary counts detected. In the absence of scatter it becomes 1.0 yielding eq. 2. Otherwise B is greater than 1.0, and indicates the extent to which scatter has changed the TF or sensitivity from that of good-geometry imaging.
ATTENUATION AND SCATTER COMPENSATION IN PLANAR QUANTITATION OF ACTIVITY There are primarily two approaches used to correct for attenuation and scatter in planar imaging. The first is to use a combination of conjugate views to reduce the variability in the sensitivity as a function of location from one side to the other in patients.1,5,7-9 The second method is to determine the effective source depth and apply appropriate corrections based on this depth.1,10 As it is the most commonly used, we will briefly review the use of conjugate views and then discuss the limitations of planar quantitation. If we acquire an anterior image of a patient as illustrated in Figure 1, then the TF of photons from a point source will decrease exponentially with depth from the anterior side of the patient as shown in Figure 2. If we acquire a posterior image of a patient, then the TF will increase exponentially with depth from the anterior side of the patient as seen in Figure 2. The goal of combining conjugate views is to reduce the dependence of the TF on the location of the
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source with depth into the patient. One way of combining the conjugate views which accomplishes this for a single point source is to calculate the geometric mean of the TF’s
0 .5
T r a n s m itte d F r a c tio n
Anterior View - IA xA xP
µ
TFA
0 .4
TFP
0 .3
TFGMS 0 .2
TFGM 0 .1
Posterior View - IP
0 .0 0
5
10
15
20
25
30
D e p th in C m
Figure 1. Illustration of conjugate-view counting.
Figure 2. Plot of transmitted fraction for anterior view, posterior view, geometric mean, and geometric mean with scatter included.
from the opposing views. If TFA is the TF for the anterior view, and TFP is the TF for the posterior view, then using the symbols from Figure 1 these can be calculated as TFA(x) = exp(-µxA)
and
TFP(x) = exp(-µxP)
.
eq. 4
The TF of the geometric mean (TFGM) of these can be calculated as TFGM(x) = [exp(-µxA) exp(-µxP)]-1/2 = exp(-µxT/2)
eq. 5
where xT is the total thickness and is equal to the sum of xA and xP. Thus the TFGM depends on the total thickness and on the attenuation coefficient µ, but not on the depth of the point source within the patient. The TFGM is shown as a flat line in Figure 2. One does need to calculate the TFGM as a function of patient thickness in order to determine the sensitivity for imaging the point source at that location within the patient. This is usually done by calculating the effective patient thickness using transmission imaging, but can also be obtained from CT studies of the patient. It should be remembered that what one is calculating is the line integral at each point through the attenuator and not the actual thickness. It should also be remembered that if this is done by transmission imaging then one will be imaging under broad-beam conditions (eq 3), even if the transmission source is collimated. There are some problems with use of the geometric mean however.1.7,9 One problem is that we have neglected to consider scatter in the analysis thus far. If we calculate TFGM with the inclusion of the buildup (using eq 3 as opposed to eq 2). With scatter included TFGMS becomes
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TFGM(x) = [BA exp(-µxA) BP exp(-µxP)]-1/2 = [BA BP]-1/2 exp(-µxT/2) .
eq. 6
With the inclusion of the buildup factors which depend on depth, the TFGMS is larger and no longer independent of depth. This is illustrated in Figure 2, where the buildup factors were calculated for a Tc-99m point source along the minor axis of a 30 by 30 cm cylindrical tub using the SIMIND Monte Carlo package.11 Ways of correcting for the inclusion of scatter include the calculation of sensitivity with the inclusion of scatter12, using the buildup factor method,1,13 and correcting the projection data for the contribution of scatter prior to calculating the geometric mean using, for example, the triple-energy-window (TEW) method.1,14 TEW and other scatter compensation methods for projection data will be discussed under scatter compensation of SPECT imaging later in this review. Another problem is that the geometric mean is not linear. That is, the TFGM obtain from imaging multiple point sources, is not the same as that of the TFGM obtained from averaging the TFGM’s from the same point sources imaged separately. For example, the TFGM for any of the Tc-99m point sources in Figure 2 (disregarding scatter) is 0.105. Whereas, it is 0.112 for the simultaneous imaging of points at 5 and 10 cm deep. Corrections for finite source thickness, for a source embedded in background activity, and overlapping source regions have been derived.1,15 Planar quantitation methods have been widely employed, and can provide an accuracy of up to 10% for non-overlapping structures in the absence of significant background activity. Planar methods can also be used with whole body scanning, and usually take less patient imaging time than with SPECT imaging. They also are less technically demanding to acquire and process than SPECT. SPECT imaging has the advantage of being able to provide a volume to go along with the activity, thus allowing the calculation of the activity concentration. SPECT also diminishes the problems of under and over-lying activity, and when used with patient specific attenuation maps and iterative reconstruction, methods can be more accurate than planar imaging. In the remainder of this overview we will focus on some of the developments in SPECT imaging which address the problems of attenuation and scatter.
CORRECTION FOR ATTENUATION IN SPECT IMAGING In order to correct for attenuation one needs to know the attenuation coefficient distribution or attenuation map for the individual patient being reconstructed. Primarily to address the attenuation artifacts in cardiac imaging, a number of strategies for estimating attenuation maps have been proposed16, some of which are currently available commercially. The idea behind transmission imaging with a gamma camera is simple. All one needs to do is image the photons from a source located on the side of the patient opposite the camera. One then compares this to the counts obtained when the patient is not in place. The attenuation map is then reconstructed using either filtered-backprojection (FBP) or an iterative reconstruction algorithm.17 The problems, of course, are in the details such as what is the source of photons, how is the patient anatomy sampled, how are the emission and transmission photons separated, and what are the counting rate limitations of the detector(s). Figure 3 summarizes the transmission imaging geometry for three methods of transmission imaging using the camera head(s) as the detector(s).
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The multiple line-source array illustrated in Figure 3A, uses a set of collimated line sources aligned parallel to the axis of rotation of the camera18. The spacing and activity of the line sources is tailored to provide a greater flux near the center of the FOV, where the attenuation from the patient is greater. As the line sources decay, two new line sources are inserted into the center of the array. The rest of the lines are moved outward one position, and the weakest pair removed. The transmission profiles result from the overlapping irradiation of the individual lines. A major advantage of this configuration is that no scanning motion of the sources is required as such motion can be problematic mechanically and electronically. A major disadvantage of this system is the separation of the cross-talk between the emission and transmission photons. Alternatively, a scanning-line source can be used to image the patient by sweeping across the field-of-view (FOV) from one side to the other as illustrated in Figure 3B.19 The camera head opposed to the line source is electronically windowed to store only the events detected in a narrow region opposed to the line source in the transmission image. The transmission counts are concentrated in this moving spatial window thereby increasing their relative contribution compared to the emission events. Similarly using the portion of the FOV outside the transmission electronic window for emission imaging results in a significant reduction in the amount of cross-talk between transmission and emission imaging. The scanning-line source does have the disadvantage of requiring synchronized mechanical motion of the source with the electronic windowing employed to accept the transmission photons. The result can be an irradiation of the opposed head that changes with gantry angle, or erratically with time. Also, communication and synchronization between the camera and moving the line source can be problematic.
A
Camera Head
Camera Head
Camera Head
Patient
Patient
Patient
C
B
Figure 3. Three geometries for transmission imaging using the camera head as the radiation detector. A. Multi line-source array. B. Scanning line source. C. Collimator septal penetration by high-energy photons from scanning point source.
Asymmetric fan-beam collimators can be used to provide attenuation maps by imaging line sources, or moving point sources, located at their focus.20,21 As illustrated in Figure 3C, such systems will partially truncate the cross-section of the patient unless data is acquired for a 360-
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degree rotation. One problem with use of this design is that the fan-beam collimator is also used for emission imaging. This difficulty can be overcome, by using photons from a medium-energy scanning-point source to create an asymmetric fan-beam transmission projection through a parallel-hole collimator by penetrating the septa of the collimator.22 With this strategy, transmission imaging is performed sequentially after emission imaging to avoid transmission photons from contaminating the emission data. This lengthens the period of time which the patient must remain motionless on the imaging table. Another problem with this method of transmission imaging is that it really is only useful for imaging with low-energy parallel-hole collimators. For imaging medium to high energy photon emitters, an asymmetric fan-beam collimator would need to be employed.21 Alternatives to transmission imaging using the camera head for the estimation of attenuation maps do exist. The emission data does contain information regarding photon attenuation, and efforts have been made at extracting information on the attenuation coefficients directly from the emission data.23 Another approach is to align CT slices with a SPECT study so that can be used to perform attenuation compensation.24 An even better approach is to couple a CT system with a SPECT system.25 This not only provides high quality attenuation maps for use in attenuation correction, but provides one with high-resolution CT images of anatomy registered with the SPECT slices for use in defining VOI. Once one has estimated the attenuation map, the next step is to employ it in reconstruction to compensate for the diminishing probability that photons make it out of the patient’s body as the depth of emission increases. There are a number of attenuation correction algorithms.26 One widely used iterative algorithm is maximum-likelihood expectationmaximization (MLEM)27. The advantages of MLEM which have lead to its popularity include: 1) it has a good theoretical base; 2) it converges; 3) it readily lends itself to the incorporation of the physics of imaging such as attenuation and the inclusion of scattered photons; and 4) it compensates for non-uniform attenuation with a high degree of accuracy. MLEM is however very slow. Block-iterative versions of MLEM such as ordered-subset expectation maximization (OSEM)28 can significantly reduce computation time to the point of reconstructing images in clinically acceptable periods of time. The MLEM method works as illustrated in Figure 4. First, as represented by the arrows
Current Voxel Estimates
2. Divide Pixel Estimate into Acquired Pixel Value.
Update Matrix
3. Backproject Ratios for All Projection Angles.
1. Project All Voxels for All Projection Angles.
Figure 4. Schematic drawing of MLEM reconstruction.
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on the left side of Figure 4 and in the denominator on the right side of eq. 7, projections are made from the initial (current) estimate of the voxel counts. The initial estimate is typically a uniform count in each voxel such as the total projection count divided by the product of number of projections times the number of voxels. It is in the process of projecting (mathematically emulating imaging) that one includes the physics of imaging. For example, as represented in Figure 4 one can create the four projections shown by summing the row and column counts in the directions indicated. Projecting along rows or columns is computationally inexpensive. Arbitrary projection angles can be placed in this orientation by appropriately rotating the estimated emission voxel slices and attenuation maps.29 Given an aligned attenuation map for an estimate of an emission slice, one could include attenuation by starting with the voxel on the side opposite the projection being created and multiplying its value by the TF for passing through one-half the voxel distance of an attenuator of the given attenuation coefficient. The value of one-half the pixel dimension is usually used as an approximation for the self-attenuation of the activity in the voxel. One would then move to the next voxel along the direction of projection and add its value after correction for self attenuation to the current projection sum attenuated by passing through the entire thickness of the voxel. One would then continue this process until having passed through all voxels along the path of projection. The result would be the discrete approximation to the calculation of the line integral through the emission estimate with each voxel location corrected for attenuation. The second step is to divide the estimated projection
Voxel old Pixels Pr ojectionDa ta ( pixels ) i Voxel new = ) ∑ Backproj ( Pixels voxels i old ) ∑ Backproj 1.0 ∑ Pr oj (Voxel i
eq. 7
value into the value actually acquired as shown by the division on the right side of eq. 7. The ratio of the two indicates if the voxels along the given path of projection are too large (ratio below one), just right (ratio of one), or too small (ratio larger than one). These ratios are then backprojected as shown on the right in Figure 4, and indicated in eq. 7, to create an update matrix. This update matrix is then multiplied by the current voxel estimates and normalized by dividing by the backprojection of 1.0’s, in order to obtain the updated estimates. OSEM speeds this process by forming and applying the update matrix from subsets of the projection set which are selected in an ordered fashion. The result is a reduction in the number of iterations by a factor approximately equal to the number of subsets employed.30 An example of the impact of attenuation correction using OSEM on reconstructed slices is given in Figure 5. This figure shows FBP and OSEM reconstructed slices, as well as the attenuation maps used in reconstruction, for Tc-99m acquisitions of activity in the Data Spectrum Anthropomorphic Phantom. The lung activity had a concentration one half that of the soft tissues, and the 2-cm diameter spherical tumor had a concentration eight times that of the soft tissues. Note the “hot” outer rim of the phantom, and relative warmth of the lungs in the FBP reconstructed slices on the left as compared to the better uniformity of the region outside the lungs, and better lung to outer region contrast in the OSEM reconstructed slices on the right. These changes are typical of those which occur with attenuation compensation.
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A
B
C
Figure 5. Four slices from Tc-99m filled Data Spectrum Anthropomorphic Phantom. A. FBP reconstruction with no attenuation compensation. B. Attenuation maps reconstructed from projections of a scanning line source. C. OSEM reconstructions with attenuation compensation.
CORRECTION FOR SCATTER IN SPECT IMAGING The best way to reduce the effects of scatter would be to improve the energy resolution of the imaging systems by using an alternative to the NaI(Tl) scintillator so that few scattered photons are acquired in the photopeak window. However given that most SPECT imaging occurs with NaI(Tl) based systems, a number of scatter compensation algorithms have been proposed for these systems. Generally, the methods of scatter compensation can be divided into two different categories. The first category, which we will call scatter estimation, consists of those methods that estimate the scatter contributions to the projections based on the acquired emission data. The data used may be information from the energy spectrum or a combination of the photopeak data and an approximation of scatter point spread functions (PSF’s). The scatter PSF gives the spatial distribution of the relative probabilities of detecting scattered photons at each location in the projection for a given location in the source distribution. The scatter estimate can be used before, during, or after reconstruction. The second category consists of those methods that model the scatter PSF’s during the reconstruction process. The second approach will be called reconstruction-based scatter compensation (RBSC) herein. Energy-distribution-based methods seek to estimate the amount of scatter in a photopeakenergy-window pixel by using the variation of counts acquired, in the same pixel, in one or more energy windows. The pixel-based nature of this method allows for the generation of a scatter estimate for each pixel in the photopeak-window data. One example of an energy based scatter compensation method is the triple-energy-window (TEW) method14 previously mentioned. In this method scatter is estimated as the area under the trapezoid formed by the heights of the counts per keV in each of the two narrow windows on either side of the photopeak, and a base with the width of the photopeak window as illustrated in Figure 6 for one of the photopeaks of Ga-67. Also shown on the right of Figure 6 is the actual scatter distribution in a Monte Carlo simulated11 projection from a Ga-67 source distribution, the TEW estimate of this distribution
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from “noise free” projections, the TEW estimate from noisy projections, and the low-pass filtered TEW estimate. Note that the TEW estimate from “noise free” projection data looks very similar to the true scatter projection. However, in the presence of noise, heavy low-pass filtering is needed to reduce the noise level, and this filtering distorts the scatter estimate.
Figure 6. On the left is shown a Ga-67 energy spectrum with TEW windows and scatter estimate indicated for its 185 keV photon. On the right side is shown the actual Monte Carlo simulated scatter distribution in a posterior projection of a Ga-67 source distribution, the TEW estimate from “noise free” projections, the TEW estimate for noisy projections, and the low-pass filtered TEW estimate from the noisy projection data. Another subclass of scatter-estimation methods is the spatial-distribution-based methods. These methods seek to estimate the scatter contamination of the projections on the basis of the acquired photopeak window data, which serves as an estimate of the source distribution, and a model of the blurring of the source into the scatter distribution. The latter is typically an approximation to the scatter PSF. An example of a spatial-distribution method for scatter compensation in SPECT is the convolution-subtraction method31, which models the scatter response as decreasing exponentially from its center maximum value. The center value and slope of the exponential are obtained from measurements made with a finite length line source. In RBSC a unique scatter PSF is estimated for each location in the patient using a patientspecific attenuation map and the underlying principles of scattering interactions. This scatter PSF is then included in the transition matrix and used in iterative reconstruction. The transition matrix represents the fraction of photons of a given energy emitted from a voxel in the patient, which are detected in a given pixel in the projection images. With RBSC methods compensation is achieved, in effect, by mapping scattered photons back to their point of origin instead of trying to determine a separate estimate of the scatter contribution to the projections.32 All of the photons are used in RBSC, and it has been argued that there should be less noise increase than with the other category of compensations.32,33 The first RBSC method for SPECT was the inverse Monte Carlo method.34 This algorithm provided compensation for scatter, attenuation, and system resolution by calculation the transition matrix for the given patient using a Monte Carlo simulation. Since obtaining a “noise-free” estimate of the 3D transition matrix with Monte Carlo methods is extremely time consuming, a number of approximate methods have been investigated which provide excellent compensation in computationally acceptable reconstruction times.32,33
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Recently, methods of vastly speeding-up Monte Carlo simulation have been developed such that for Tc-99m, fully 3D reconstruction can be obtained in approximately 30 minutes on a personal computer.35
SUMMARY Correction for attenuation and scatter are required for the accurate estimation of activities. Both planar and SPECT imaging can be used to estimate the activities of radiopharmaceuticals. Planar methods have been the most widely employed for this purpose. With the accurate modeling of imaging in iterative reconstruction, SPECT methods will prove to be more accurate. If SPECT reconstructions are used for quantitation care should be taken to verify the accuracy of the reconstruction implementation. For example, one should employ zero padding when calculating the FFT’s of the projections and the band-limited version of the Ramp filter in FBP.36 One should also be aware of how negative values are handled in the reconstruction software they use.37 ACKNOWLEDGMENTS This work was supported by the National Cancer Institute under grant number CA-42165. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the National Cancer Institute. REFERENCES 1. Siegel JA, Thomas SR, Stubbs JB, Stabin MG, Hays MT, Koral KF, Robertson JS, Howell RW, Wessels BW, Fisher DR, Weber DA, Brill AB. MIRD pamphlet No. 16: Techniques for quantitative radiopharmaceutical biodistribution data acquisition and analysis for use in human radiation dose estimates. J Nucl Med 40: 37S (1999). 2. Sorenson JA, Phelps ME. Physics in Nuclear Medicine. 2nd Edition, Grune & Stratton, Orlando, 1987. 3. Jaszczak RJ, Coleman RE, Whitehead FR. Physical factors affecting quantitative measurements using camera-based single photon computed tomography (SPECT). IEEE Trans Nucl Sci 28: 69 (1981). 4. Zanzonico PB, Bigler RE, Sgouros G, Strauss A. Quantitative SPECT in Radiation Dosimetry. Sem Nucl Med 19: 47 (1989). 5. Leichner PK, Koral KF, Jaszczak RJ, Green AJ, Chen GTY, Roeske JC. An overview of imaging techniques and physical aspects of treatment planning in radioimmunotherapy. Med Phys 20: 569 (1993). 6. Rosenthal MS, Cullom J, Hawkins W, Moore SC, Tsui BMW, Yester M. Quantitative SPECT imaging: A review and recommendations by the focus committee of the Society of Nuclear Medicine Computer and Instrumentation Council. J Nucl Med 36: 1489 (1995). 7. Arimizu N, Morris AC. Quantitative measurement of radioactivity in internal organs by area scanning. J Nucl Med 10: 265 (1969). 8. Graham LS, Neil R. In vivo quantitation of radioactivity using the Anger camera. Radiol 112: 441 (1974).
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28. Hudson HM, Larkin RS. Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans Med Imag 13: 609 (1994). 29. Wallis JW, Miller TR. An optimal rotator for iterative reconstruction. IEEE Trans Med Imag 16: 118 (1997). 30. Meikle SR, Hutton BF, Bailey DL, Hooper PK, Fulham MJ. Accelerated EM reconstruction in total-body PET: potential for improving tumour detectability. Phys Med Biol 39: 1689 (1994). 31. Axelsson B, Msaki P, Israelsson. Subtraction of Compton-scattered photons in single-photon emission computed tomography. JNM 25: 490 (1984). 32. Kadrmas DJ, Frey EC, Tsui BMW: Application of reconstruction-based scatter compensation to thallium-201 SPECT: implementations for reduced reconstruction image noise. IEEE Trans Med Imag 17: 325 (1998). 33. Beekman FJ, Kamphuis C, Frey EC. Scatter compensation methods in 3D iterative SPECT reconstruction: A simulation study. Phys Med Biol 42: 1619 (1997). 34. Floyd CE, Jaszczak RJ, Coleman RE. Inverse Monte Carlo: a unified reconstruction algorithm. IEEE Trans Nucl Sci 32: 799 (1985). 35. Beekman FJ, de Jong HWAM, van Geloven S. Efficient fully 3D Monte Carlo based statistical SPECT reconstruction. IEEE Trans Med Imag, submitted (2002). 36. Kak AC, Slaney M. Principles of Computerized Tomographic Imaging. IEEE Press. New York. 1987. pp. 69-75. 37. Chang W, Henkin RE, Buddemeyer E. The sources of overestimation in the quantification by SPECT of uptakes in a myocardial phantom. JNM 25: 788 (1984).
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