Pergamon Computerized Medical Imaging and Graphics, Vol. 2 I, No. 5, pp. 283-29 I, 1997

0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain

089161 II/97 $17.00 + .OO

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SCATTER REJECTION IN MODULAR GAMMA CAMERAS FOR USE IN DYNAMIC 3D SPECT BRAIN IMAGING SYSTEM

J. C. Chen Division of Radiologic Science and Technology, National Yang-Ming University, Taipei, Taiwan

(Received 12 March 1997; revised 26 August 1997)

Abstract-AU gamma cameras used in nuclear medicine have finite energy resolution, tbereby making discrimination of scattered radiation from pbotopeak events extremely ditBcult. Different scatter-correction methods have been developed to prevent scattered radiation from degrading tbe image quality of a gamma-ray image. Rejecting scatter events on an event-by-event basis in data acquisition as much as possible is a preferable option. However, the fact that all scattered events cannot be rejected witbout sacticiag prbnary pboton sensitivity might require applying scatter correction after acquisition; nevertheless, tbe scattered photons should not be aIlowed to enter into tbe image. Most conventional approaches reject scatter events by using energy windows (EWs). MIlster el al. introduced tbe Iikelilrood window (LW) as an alternative. We also employed this metbod in a modular gamma scintillation camera that has a 2x2 array of photomultipliers (PMTs) coupled to a NaI(T’I) crystal. In tbis work, another scatter rejection scheme, the &ye&n window (BW), is developed. In contrast to the LW and the EW, the BW takes into account tbe simulated or actual scatter spectrum in making a decision to accept or reject ‘a particular photon. This work compares the effectiveness of scatter rejection by BW, LW, and EW through receiver operating charucteristic (ROC) studies. Results Indicate that tbe BW method is the preferable choice. 0 1997 Elsevier Science Ltd.

Key Worrls: Scatter rejection, Gamma cameras, SPECT, Brain imaging

INTRODUCTION

One of the aims of nuclear medicine is quantitation of activity in specific regions of interest with respect to the background in the patient. Up until now, quantitative single photon emission computed tomo- graphy (SPECT) is still not possible due to non- uniform attenuation and scatter in the patient. Attenuation is harmful to quantitative SPECT because the detected signals do not reflect the absolute activity along the line of flight of a gamma ray. On the other hand, a scattered photon could have originated anywhere in the patient and still scattered into the line of sight of the detector element; a hot spot in one area will contribute scattered counts to distant regions in the reconstruc- tion of SPECT images. Thus scattered events affect the contrast and resolution over the whole image. So some kind of scatter rejection and correction methods are needed to improve image quality. We now explain briefly our own attempt at scatter rejection in below. For a review of current scatter- correction techniques in SPECT, the curious reader is encouraged to consult White (1).

Any gamma camera for use in nuclear medicine utilizes some method of energy discrimination. In a conventional Anger camera, a linear energy estimate is formed by adding the photomultiplier signals,

perhaps with some correction for position-dependent light-collection efficiency. The event is accepted if this energy estimate lies within some preset energy window. In the modular cameras being used at the University of Arizona (2), the conventional type of energy estimation is not feasible since the variations in light-collection efficiency are large. Therefore, our previous works have used a different approach based on a likelihood window (LW) rather than an energy window (EW). In this method, a maximum-likelihood (ML) estimate of the position of the event is computed while assuming that the photon has not been scattered. Next, the likelihood of the PMT signals for this position is computed and the event is rejected if it falls below a preset threshold.

In this work, a new kind of EW that is applicable to the modular cameras is devised to make compar- isons. The ML principle is not used merely for position estimation, but is extended to include energy estimation. In this proposed method, a nonlinear ML energy estimate is obtained that can be tested against a window just as in conventional Anger cameras.

Neither the EW nor the LW uses the energy spectrum of the scattered photons in making a decision to accept or reject a particular photon. This study has developed a Bayesian method of scatter rejection, referred to here as a Bayesian window (BW), that uses this information. Directly

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comparing this method with the EW and the LW is probability density function p(A,B,C,D 1 H,,) is calcu- the primary objective of this study. lated as:

To compare the three methods of scatter rejec- tion, three lookup tables (LUTs) are generated for a single modular camera. Each LUT is addressed by the PMT signals, and the information stored at each location is the ML position estimate for those signals. This is accompanied by a flag which determines whether the event should be accepted or rejected according to one of the three principles. Each method includes a threshold value setting the tradeoff between primary rejection and scatter acceptance. In all cases, curves of primary and scatter acceptance are generated as a function of this threshold value. These curves are also known as receiver operating characteristic (ROC) curves. Moreover, the resulting curves are compared for the three methods. Different forms of the scatter spectrum are also used, including one derived from Monte Carlo simulations.

P(44C,Dl~o) = 7”;” P(~B>C,DIX,Y,EO) (1)

where EO is the primary-photon energy. Next, an event is rejected if p(A,B,C,D I Ho) < TLw.

Energy window In a conventional Anger camera, the total light

detected by the PMT arrays is proportional to the summation of the voltage signals Vi and is indepen- dent of position. Therefore, the sum of the outputs of all PMTs is used as an estimate of the energy signal to determine the photopeak events. This energy signal can be estimated by

&=k+., u I’ i=l

(2)

METHODS

Likelihood window The output signals from the four PMTs of a

modular camera are denoted as (A,B,C,D). The likelihood p(A,B,C,D I x,y,&) is calculated, where EO is the true primary energy, for all x and y positions based on a Poisson probability model that assumes that the signals from each PMT are statistically independent. Next, x-y space is searched for to identify the maximum value of p(A,B,C,D 1 x,y, EO). The (x,y) that maximizes p(A,B,C,D I x,y,E,,) is the ML estimate (a$) corresponding to that parti- cular (A&C,@ combination. Next a procedure called “likelihood windowing” (3) is used to verify whether the event is primary or scattered. In doing so, we compute p(A,B,C,D I Q,&) (maximum like- lihood) and compare it to a preset threshold TLw (where LW represents likelihood window). If p(A,B, C,D I2,9,&) > T,,, this (A,B,C,D) signal is assumed to result from a primary or photopeak event; in addition, the ML estimate (&, EML) is valid and stored in the LUT address. If p(A,B,C,D I B,y,EO) < TLW, the event that produces (A,B,C,D) is not a photopeak event and is rejected by placing a tag in the LUT address to indicate a scatter event. There- fore, when that location is addressed, the image memory recognizes the tag and does not accumulate the count. This technique is called the LW because the likelihood function p(A,B,C,D I Q,EO) rather than the total energy signal is used for event discrimination. Briefly, a null hypothesis Ho is obtained: photon is unscattered. In addition, the

where k’ is a constant which converts the units from voltage to keV. The energy estimate fi is a linear function of voltage signals and ( fi ) a E#f(x, y). The difference between the energy signal and the mean energy signal EO is compared to a preset energy window BE. An event in which the energy signal difference is less than AE is accepted as a photopeak eyent. On the other hand, the event is rejected if 1 E- EO I> AE, where EO is the primary energy and AE is the EW width.

In the modular cameras, the sum of the PMT signals is a function of position, thereby making usual EW inapplicable. Therefore, in this work, a similar energy window is developed that is applic- able to the modular cameras. As in the LW method, p(A, B,C,D j x,y,E) is first calculated for a given signal (A, B,C,D). Next x-y-E space is searched for to identify the ML estimate (2, 9, 8) that maximizes p(A,B,C, D Ix, y, E). Since this extended energy estimation approach is computer intensive, the energy range is limited from 110 keV to 140 keV in 1 keV steps. Thus, nonlinear ML position and energy estimates are obtained, and the position estimate (~2, 9) and energy estimate l? are stored in separate LUT memories. Next, energy windowing can be used to test whether the event is primary or scattered by comparing the energy estimate with a preset lower energy threshold Eth which is the lower energy limit of the EW, and an upper energy threshold E, which is the upper energy limit of the EW. If fi is within the EW, the event is valid and the count is accumulated in image memory. If & < Et,, or 8> E,, the event is rejected by not accumulating the count in image memory.

Scatter rejection in modular gamma cameras l J. C. CHEN 285

The EW width could be 20% of the photopeak energy Ee (e.g. 140 keV for ‘%Tc), centered at the peak; this kind of EW is called a 20% symmetric EW. On the other hand, the EW width could be 10% of the photopeak energy with E, slightly greater than Ee; this kind of EW is called a 10% asymmetric EW (the EW is not centered at the photopeak energy).

Application of Bayesian decision theory to scatter rejection

Only a null hypothesis about y-photon energy is obtained so far: each event is due to an unscattered photon (E= &,). A method is now proposed, capable of utilizing two hypotheses: each event is due to either a primary photon or a scattered photon. None of the two windowing methods uses the actual spectrum of the scattered photons in reaching a decision to either accept or reject a single photon. We have now developed a Bayesian method of scatter rejection that uses this important information. The method is referred to here as a Bayesian window ‘JW (4).

This section applies Bayesian decision theory to scatter rejection which is a binary-decision problem. In contrast to ML methods, Bayesian decision theory explicitly considers the statistics of two hypotheses. The first hypothesis, He, corresponds to primary photons. The second hypothesis, Hi, corresponds to scattered photons. Because only two alternative hypotheses exist, this test is also called a binary hypothesis test. Under each hypothesis we then have

HO : g results from unscattered photons,

HI : g results from scattered photons (3)

where the data g in this case are signals (A,B,C,D) from four PMTs. The He is frequently called the null hypothesis because it represents the hypothesis under which the photon is not scattered.

In a Bayesian test, the first step calculates the optimal test statistic, which is the likelihood ratio (LR) A(g) defined as

qg> ~ Pk I Ho) Pk I HI) (4

for a binary Bayesian decision problem from the given data vector g. The likelihood ratio is the optimal test statistic because LR minimizes the Bayes risk. The second step compares A to a threshold 1 to select a hypothesis or reach a decision. Notably, A(g) requires only that the conditional probability density functions, p(g I HO) and p(g I HI), are known. Next,

accurate expressions for probability densities must be found. A likelihood ratio test (LRT) can be found, i.e.

Ho

where 1 is the test threshold. To apply this test, p(g I HO) is computed by

p(g I Ho) = ~7 pk I X,Y, Eo) (6)

where Ee is the energy of primary photon. For the alternative hypothesis, we have

PkIHl) =yy 1 s

E”-d~p(gIx,y,Elp(El~c) (7) 0

where SC refers to scatter events. Restated, an ML estimate of x and y can be 4nade under the assumption that the photon is unscattered. We then evaluate p(g 1 x,y,Eo) at x=xML and y=fMr. A similar procedure is performed for equation (7). Therefore, not only can the likelihood ratio A(g) be determined, but optimal Bayesian decisions can be made according to the likelihood ratio test as defined in equation (5). The test threshold is normally selected on the basis of different decision criteria without knowing the prior probabilities of the hypotheses, P(Ho) and P(H,), which in this case correspond to the probabilities of primary and scatter events. However, if the priors are known, a different threshold, say P(Hl)/P(H,), can be chosen for the test. The threshold value generally depends also on costs.

Bayesian window A comparison is next made with the other two

methods of scatter rejection: LW and EW. A BW LUT is generated for a single modular camera using the method discussed in the previous section. Similar to LW and EW, BW LUT is addressed by the PMT signals. Also, the information stored at each location in the LUT is the ML position estimate for those signals, as well as a flag determining whether the event should be accepted or rejected according to the Bayesian decision criterion. This method, as in the other two, includes a threshold value setting the tradeoff between primary rejection and scatter acceptance. All three LUT calculations involve classification (discriminate type-of-event) and estima- tion (in which the position estimates and/or energy estimates are determined). In the BW method,

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classification is achieved through the likelihood ratio test, while the other two methods use likelihood windowing and energy windowing, respectively. Various forms of the scatter spectrum are used in BW, including one derived from Monte Carlo simulations described below.

Exactly how the BW estimate is calculated for a particular (A,B,C,D), i.e. for one address in the LUT is described as follows. First, the likelihood function p(A,B,C,D I x,y,Eo) is calculated, where E0 is the primary photon energy (140 keV). Next, x-y space is searched to obtain the maximum of p(A,B,C,D I x,y, E,,), which yields p(g I He) (see equation (6)). Second, the likelihood function p(A,B,C,D ) x,y,E) is calcu- lated (where E is the scattered-photon energy that ranges from 0 to 139 kev), which is equal to the multiplication of &4 I x,y,E)p(B I x,y,E)p(C I x,y,E)p (D / x,y,E) since A, B, C and D are independent random variables. The function is then multiplied by various forms of the scatter spectrum p(E) SC). So far, a uniform scatter spectrum (see Fig. 1) and a Monte Carlo-simulated first-order Compton scatter spectrum (simulated by Tim White) have been used. First order implies that the spectrum includes only those photons that have scattered in the object once. Figure 2 shows this simulated spectrum. This spectrum is generated for a point source in the centre of the scattering medium (water in a sphere) that has a diameter of 10 cm. In the BW LUT calculation, we sum (instead of integrate) the product in equation (7) from 110 keV to 139 keV. Then x-y space is searched to obtain the maximum of the sum, which yields p(g / Hi) (see equation (7)). Finally, a Bayesian decision criterion is applied to determine whether the event corresponds to a photopeak event. This procedure is referred to here as “Bayesian windowing”. For instance, if we choose the threshold value A = P(Sc)/P(Pr) = 1, an event will be rejected if p(g I Hi) >p(g I He). Otherwise, the event is accepted as a primary event and the corresponding ML position estimate is stored in the LUT.

WE) A l/2

l/60. -1

Fig. I. An artificial energy spectrum.

Fig. 2. Monte Carlo-simulated first-order Compton-scat- tered energy spectrum (simulated by Tim White).

RESULTS

ROC analysis Using a curve (5) is one approach of comparing

test performances. The curve is a plot of the probability of detection, or the true positive fraction (TPF), vs the probability of false alarm, or the false positive fraction (FPF), as a function of decision threshold. The threshold I can be varied from zero to infinity to generate a curve. This curve is called an ROC curve since: (a) it describes the inherent detection characteristics of the test; and since (b) the receiver of the test information can operate at any point on the curve by using an appropriate decision threshold. In our case, TPF is the probability of accepting an unscattered photon, while FPF is the probability of accepting a scattered photon.

Simulation results To compare the three scatter rejection methods,

simulations are performed to produce scattered photons with a known energy. Two point arrays are simulated. Each image has an array of 64 collimated sources imaged in air. One point array corresponds to primary photons that have an energy of 140 keV. For simplicity, the second simulated point array has an artificial spectrum where the scattered photons are all at an energy of 112 keV, i.e. 20% lower than the energy of primary photons. In this case, the spectrum of the scattered photons used for testing scatter-rejection performance of LUT is a delta function while the scatter spectrum used to create the LUT is either uniformly distributed (Fig.

Scatter rejection in modular gamma cameras l J. C. CHEN 287

1) or more realistic (Fig. 2). Each array consists of sixty four locations on an 8 x 8 grid. At each location, we simulated Poisson-distributed photons moving in the direction normal to the camera face with a mean number of y-ray photons equal to 1000.

Two images were generated by using these simulated data and a LUT. For each image, total counts in an image can be calculated and then divided by the number of total events to determine the probability of accepting 140 keV photons, P(Pr I140), and the probability of accepting 112 keV photons, P(Pr 1 112) or FPF as if they were 140 keV photons. Here Pr means accepted as primary photons. These probabilities represent the percentages of photons that pass through the LUT window. From these two numbers, one point on an ROC curve is obtained. For each method, a set of LUTs are generated merely by varying the threshold values. Next an ROC curve is generated. By repeating the other methods, different ROC curves corresponding to different windowing methods are generated.

In all cases we generated ROC curves (TPF versus FPF) with each point on the curves corre- sponding to a threshold value. The resulting ROC curves were compared for the three methods. Two forms of the scatter spectrum were used to create BW LUTs, including one derived from Monte Carlo simulations.

As an example of the data obtained, Fig. 3 shows the ROC curves as a function of the threshold value

.

for the EW, the LW and the two BWs. The two BW LUTs differ in the assumed p(E( SC) used in calculating p(g I Hi). The curve labelled BWl corre- sponds to the flat scatter spectrum (p(E I SC) =con- stant (Fig. 1)); BW2 uses p(E I SC) as determined by the Monte Carlo simulation (Fig. 2). The graph shows, for this case, the LW window is the worst method in terms of scatter rejection except at high primary acceptance probability. The two BWs have similar performances; however, the one using the uniform scatter spectrum is slightly better because the area under the ROC curve (AUC) is larger. Simulation results indicate that EW and BW (with uniform scatter spectrum) are the preferable choices. Since these two ROC curves cross each other, selecting the better one cannot be determined by AUC. When the threshold is set to discriminate more strongly against the 112 keV photons, the BW yields a higher probability of accepting the primary 140 keV photon. However, EW is better if more low-energy photons can be accepted.

The following figures show some images of simulated primary and scatter point arrays using three LUTs corresponding to three windowing methods with different thresholds. Note that the thresholds are chosen such that the TPFs are about the same with different FPFs. Since all the three images generated from simulated primary source are very similar, we only show the one created by the BW LUT. In Fig. 4, upper left is an image of a primary point array using the BW LUT with a threshold of

> 0 -y 80.00

T

- 60.00

0 20.00 d

- EW - LW -6ul ----a42

0.00 1,,,,,,,,,,,~,,,,,,,,..,...,,,..,.,,,,,.~.,,,,,,, 0.00 20.00 40.00 60.00 80.00 100.00

P. of accep. 112 tev ph.

Fig. 3. ROC curves corresponding to LW, EW, and BW method, respectively.

288 Computerized Medical Imaging and Graphics September--October/l997, Volume 21, Number 5

Pr-BW SC-BW

fig 4

SC-EW SC-LW Fig. 4. Images of simulated point array generated using LW, EW, and BW LUT, respectively, all with less strict threshold; upper two are images of primary and scattered photons through BW LUT; lower left is an image of

scattered photons through EW LUT; lower right is an image of scattered photons through LW LUT.

the test equal to 1. Upper right is an image of a scatter point array using the same BW LUT. Lower left is an image of the same scatter point array using the EW LUT with lower energy-window threshold equal to 122 keV or a window width of 18 keV (140- 122 keV). Lower right is the same data using the ML LUT with likelihood window threshold equal to 0.01. The brightness of each pixel in each image corre- sponds to the number of counts recorded in it. We can see in all three scatter-event images that most counts are rejected by the respective LUT window, except at the edges. This shows scattered photons tend to build up near the edges and are harder to reject in the edge area than in the central area of the scintillation crystal of the modular camera. This

scatter packing effect at the edges of modular cameras was seen by Conrad ef al. (6). Figure 5 shows similar images as in Fig. 4 except using more strict thresholds in the respective LUTs. Upper left is an image of the primary point array using the BW LUT with a threshold of the test equal to 3. Upper right is an image of the scatter point array using the same BW LUT. Lower left is an image of the same scatter point array using the EW LUT with energy threshold equal to 140 keV (only photons with 140 keV are accepted). Lower right is the same data using the ML LUT with likelihood threshold equal to 0.05. Obviously the scatter fraction in each scatter-event image is less than the corresponding one in Fig. 4 because each LUT now uses higher

Scatter rejection in modular gamma cameras l J. C. CHBN

Pr-BW SC-BW

289

SC-EW SC-LW Fig. 5. Images of simulated point array generated using LW, EW, and BW LUT, respectively, all with more strict threshold; upper two are images of primary and scattered photons through BW LUT, lower left is an image of

scattered photons through EW LUT; lower right is an image of scattered photons through LW LUT.

threshold but at the expense of primary sensitivity. Again, even at very strict threshold of each LUT, we can still see a very small fraction of scattered photons at the edges. Among these three methods, the LW performs less efficiently for scatter rejection than the EW or the BW.

DISCUSSION

In the above evaluation of the Bayesian window method, the energy spectrum used as a prior in the LUT creation was different from the one used to test the resulting LUT. The BW ROC was next compared to the EW ROC under the circumstance in which the same spectrum was used for the BW LUT generation

and scatter spectrum to test the LUT. The actual 57Co was used as the source of our scattered photons. Also 57Co was used to collect a point-array histogram of roughly 900,000 total counts. More- over, a BW LUT was created using the spectrum shown in Fig. 6 as a prior. Notably, most of the y- photons emitted by “Co have an energy of 122 keV except that a small fraction of y-photons have an energy of 136 keV. Actual 99mTc was used to emit primary photons. Here, 99mT~ was used to collect a point-array histogram of about 1.4 million total counts. With the two histogram data collected from the two sources and LUTs (BW and EW), two ROC curves were generated by varying the respective thresholds in each method as described previously.

290 Computerized Medical Imaging and Graphics September-October/l997, Volume 21, Number 5

P(E) 04

Fig. 6. An idealized energy spectrum of 57Co (122 and 136 keV) and ggmT~.

Figure 7 displays those curves. Those curves reveal that, in this case, BW performs better than EW because its curve lies above the EW one (the AUC is larger).

In practice, if we desire to operate at lower scatter acceptance probability (FPF) on an ROC curve we can choose a strict threshold value to reject more of the scatter at the expense of primary acceptance probability (TPF). This is fine with simulation data and phantom studies because we can increase computer or exposure time to get enough counts.

Our concern in this work has been the effects of Compton-scattered photons on SPECT imaging with finite detector energy resolution. A scattered photon can cause an indeterminacy on the location of the emission of the gamma ray, hence degrades image spatial resolution. Since we are interested in building a high-resolution brain SPECT imager, image

Fig. 7. ROC curves

resolution is of primary significance. Thus a better scatter rejection method is needed to improve image resolution. Results reveal that, among the three windowing forms that we have compared, BW technique is a preferable alternative for scatter rejection in modular gamma cameras.

SUMMARY

In this work, we developed three LUTs for scatter rejection based on three different windowing methods (LW, EW, and SW), respectively. The methods were also compared by ROC analysis. Also, the probability of accepting an unscattered photon versus the probability of accepting a scat- tered photon was plotted as a function of threshold value for EW, LW, and BW. The object was a simulated point array. The graph indicated that LW is generally the worst method. BW with a flat spectrum (p(E I Sc)=constant) is superior at low scatter acceptance probability; however, EW is better when the threshold value is set to be moderate. However, the BW ROC curve would lie above the EW one if the same spectrum was used as a prior for creating the BW LUT and as the scatter spectrum for testing the scatter rejection of the LUTs.

Acknowledgement-I wish to express my gratitude to Prof. Harrison H. Barrett. This work would not have been possible without his intellectual support. Timothy A. White is also appreciated for supplying the simulated scatter spectrum used in the Bayesian windowing method.

- BW -EW

corresponding to EW and BW method, respectively, using real radioisotopes. displays those curves (7).

Scatter rejection in modular gamma cameras l J. C. CHEN 291

REFERENCES 1. White, T.W. SPECT reconstruction directly from photomul-

tiplier tube signals. PhD dissertation. University of Arizona, Tucson, Arizona, USA; 1994.

2. Milster, T.D. Design and construction of a modular gamma camera. PhD dissertation. University of Arizona, Tucson, Arizona, USA; 1987.

3. Milster, T.D.; Aarsvold, J.N.; Barrett, H.H. et al. A full-field modular gamma camera. J. Nucl. Med. 31:632-639; 1990.

rejection, and characterization and initial clinical application. PhD dissertation. University of Arizona, Tucson, Arizona, USA; 1995.

About the AI&IOF--JYH-CHENG CHEN received the BS degree in physics from National Central University, Taiwan, R.O.C., in 1983, and the MS degree in physics and PhD degree in optical sciences from the University of Arizona in 1988 and 1995, respectively. In 1995, he joined the Opto-Electronics and System Laboratories, Industrial Technology Research Institute, Taiwan, R.O.C. as a research associate working on semiconductor laser packaging. In 1996, he became a member of the faculty of Division of Radiological Science and Technology, Department of Medical Technology, National Yang-Ming University, Taiwan, R.O.C., where he is now teaching and pursuing his research interests in areas of radiological imaging and nuclear medicine instrumenta- tion. Dr. Chen is a member of Optical Engineering Society, R.O.C., and Chinese Society of Medical Physics, Taipei.

4. Chen, J.C. Likehood window, energy window, and Bayesian window for scatter rejection in gamma cameras. IEEE Nucl. Sci. Symp. 3:1414-1416; 1993.

5. Metz, C.E. Basic principles of ROC analysis. Seminar in Nucl. Med. 8:283-298; 1978.

6. Conrad, B.; Klingenbeck-Regn, K. Scatter sensitivity of modular gamma-cameras. Siemen’s technical report; 1991.

7. Chen, J.C. Modular gamma cameras: improvements in scatter