pet clin 2 (2007) 219 234 scatter compensation techniques ... · many nuclear medicine physicians...

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Scatter Compensation Techniquesin PETHabib Zaidi, PhD, PD*, Marie-Louise Montandon, PhD

In PET scatter detection usually refers to Comp-ton scattering in which one or both annihilationphotons undergo an interaction with matter (eg,the patient), changing direction and losing energy.The scattering angle is closely related to the energytransferred to the electron, so that the energy lossapproaches zero when the change in direction ap-proaches zero. Because of its small contribution tothe total cross section for PET energies, coherentscattering is often overlooked [1]. The detected scat-tered photons falling within the energy acquisitionwindow (eg, 350–650 kilo electron volts [keV]) arethose for which one wishes compensation. Usually,annihilation photons can scatter in the patient andin material outside the patient (eg, the bed support-ing the patient, the detector material, the electronicsbehind the detector. or anywhere within the gan-try). This article focuses on scattering within the pa-tient, because the magnitude of other scatterings

probably is small enough to justify ignoring them.One should keep in mind that multiple scatter de-tection might occur in two or more places in thesame object. When developing and implementinga scatter-compensation method, one should beaware of which types of scatter are expected andare being corrected.

The rationale behind scatter compensation gen-erally is to enhance the contrast of reconstructedPET images, to improve the accuracy of activityquantification, or both. The final goal may guidethe choice of the technique. Whereas it is well ac-knowledged that Compton scatter degrades imagequality by substantially reducing the contrast,many nuclear medicine physicians and cliniciansare puzzled by the clinical relevance of this im-age-degrading factor that is inherent to the mo-dality. Among the frequently asked questionsare the degree to which scatter detection affects

P O S I T R O NE M I S S I O N

T O M O G R A P H Y

PET Clin 2 (2007) 219–234

This work was supported by the Swiss National Science Foundation under grant SNSF 3100A0-116547.Division of Nuclear Medicine, Geneva University Hospital, CH-1211 Geneva, Switzerland* Corresponding author.E-mail address: [email protected] (H. Zaidi).

- What is Compton scatter?- Practical and clinical consequences

of scatter detection- Modeling the scatter component in

uniform and non-uniform media- Scatter component in small-animal

positron emission tomographyimaging

- Scatter-correction strategies in positronemission tomography

Hardware approaches using coarse septaor beam stoppers

Multiple-energy-window (spectral)approaches

Approaches based on convolutionor deconvolution

Approaches based on direct calculationof scatter distribution

Iterative reconstruction-basedscatter-correction approaches

Comparison of methods- Scatter correction in transmission imaging- Summary- References

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1556-8598/07/$ – see front matter ª 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.cpet.2007.10.003pet.theclinics.com


image interpretation and clinical diagnosis,whether it affects diagnostic accuracy, and whatis the real added value of scatter compensationin clinical PET imaging. Although these issuesare difficult to elucidate, physicists are deeplyconvinced that scatter correction is a vital compo-nent in producing high-resolution, artifact-freequantitative images [2]. It is, however, theirduty to debate the important issues related to de-sign aspects of PET technology (eg, the need forscintillation crystals with improved energy resolu-tion for better scatter discrimination) and opti-mal data acquisition and processing protocols,with the aim of improving image quality and ob-taining accurate quantitative measures throughefficient scatter removal [3,4].

Thorough reviews of scatter modeling and cor-rection strategies in nuclear medicine imagingwere published in 1994 [5] and 2004 [2]. Thisarticle addresses this issue from a different per-spective: it focuses on scatter modeling and cor-rection in fully three-dimensional (3D) PETimaging with special emphasis on most recentdevelopments in the field in general and themost promising approaches in particular. Becauseof the widespread interest in both preclinical anddual-modality PET/CT imaging instrumentation,the problem of scatter detection in small-animal PET and transmission imaging is discussedalso.

What is Compton scatter?

In Compton scattering, the photon interacts withan atomic electron and is scattered through an an-gle q relative to its incoming direction, carryingless energy than it had originally (Fig. 1A). Onlya fraction of the initial photon energy is transferredto the electron. After Compton (or incoherent) scat-tering, the scattered photon energy Es is given by thefollowing equation:

Es 5E

11 Emoc2ð1� cosqÞ

where E is the energy of the incident photon, m0 isthe rest mass energy of the electron, and c is thespeed of light. This equation is derived on the as-sumption that an elastic collision occurs betweenthe photon and the electron, and that the electronis initially free and at rest. It is obvious from thisequation that the maximum energy transfer takesplace when the photon is back-scattered 180� rela-tive to its incoming direction and that the relativeenergy transfer from the photon to the electron in-creases for increasing photon energies. This equa-tion is plotted in Fig. 1B for 511 keV photons andillustrates that rather large angular deviationsoccur for a relatively small energy loss. There arecorrections to that equation that take into accountthe fact that the electron actually is moving and isbound to an atom. The result is that the photons

Fig. 1. (A) Compton scatter detection in PET. In Compton scattering a photon undergoes an interaction withinthe patient’s body whereby it changes direction and looses energy. In single-photon emission CT neither scat-tered nor unscattered LoRs can be formed outside the body. In PET, scattered LoRs can be formed outside thebody, but unscattered LoRs cannot. (B) The residual energy of a 511-keV incoming photon after Compton scat-tering through a given angle.

Zaidi & Montandon220


that are scattered through a given angle actuallyhave a distribution of energies sharply peakedabout the value calculated by the simple formula[6]. Although this effect, which is called ‘‘Dopplerbroadening,’’ has some importance for Comptoncameras [7], its impact in PET is limited becausethe energy distribution is peaked so sharply.

Two additional issues are worth mentioning inthe context of PET imaging. The first is that theloss of energy can lead to the removal of a Comp-ton-scattered photon by the lower-level discrimina-tion threshold set for data acquisition. Eventsfalling outside the energy window are no longerof importance for scatter correction. The second isthat the change of direction is the fundamental rea-son the problem needs correction, because a wrongline of response (LoR) will be assigned to this event.As a result, the recorded coincidence event istracked back incorrectly during reconstruction, ifit is assumed to be from an emission site.

Detected Compton-scattered photons may scat-ter only once or multiple times (two or more scat-ters) in the patient, the PET scanner’s gantry, ortable that supports the patient. In addition, the in-coming photon may originate from outside the fieldof view (FoV) of the scanner (out-of-FoV scatter).Earlier implementations of scatter-correction algo-rithms ignored both these possibilities, thus open-ing the opportunity to address them separately asadditional effects that led to bias in the corrected es-timate. ‘‘Bias’’ is a statistical term defined as a devia-tion (either up or down) in the estimated countdensity of the reconstructed image as comparedwith the true count density. These issues, however,have been considered in the more recently devel-oped and more advanced correction procedures.

Practical and clinical consequencesof scatter detection

In the earliest literature on the deleterious effect ofscatter detection, the major consequence of scatterwas judged to be a loss of contrast in reconstructedPET images. In addition to a decrease in the imagecontrast, events also may appear in regions of theimage where there is no activity (eg, outside the pa-tient). In the most straightforward depiction, a truezero count density in a reconstructed image occursas a positive value. This effect was demonstrated inthe 1970s by imaging a line source in air and thenin a water-filled bucket (see Fig. 3.22 in [8]) andby imaging nonradioactive spheres in a radioactivebackground [9]. The corruption commonly wasportrayed as a pedestal on which the true imagesat. Later, imaging scientists realized the complexityof artifacts resulting from Compton scatter detec-tion that affect visual interpretation in at least parts

of the image and impinge on the accuracy of quan-titative analysis of PET data. Consequently, Comp-ton scatter was recognized as a non-negligiblephysical degrading factor, because in most situa-tions an accurate quantitative image with the bestpossible contrast possible is desirable. The extentto which scatter can be shown to interfere withthe purpose for which the image is to be used(eg, clinical diagnosis or outcome of studies) isa complicated issue and should be addressedthrough further research [10].

In radionuclide imaging, Compton scatter is thecompanion of photon attenuation, in that a substan-tial portion of the photons that are attenuateddirectly drop into the class of potential scatter-corrupting photons [2]. For PETenergies, the interac-tion cross section of photoelectric absorption forbiologic tissues is relatively small compared withCompton scattering, which is the dominant interac-tion process. For the potentiality to become a reality,the scattered photon must be detected and also mustfall within the energy acceptance window that gener-ally is set according to the energy resolution of thescintillation detectors used. An important differenceexists between Compton scatter in single-photonemission CTand PET. In the former, scattered and un-scattered LoRs cannot be formed outside the bodyand carry information that can be useful for determi-nation of the body outline or of the non-uniform at-tenuation map [11–13]. In PET, however, scatteredLoRs sometimes are formed outside the body and/or outside the imaging FoV, as discussed earlier.

In activity quantification, attenuation and scatterhave opposite effects on the activity estimate. Therationale is that attenuation tends to decrease thenumber of detected counts, thus reducing the activ-ity estimate, whereas Compton scatter tends toincrease the number of detected counts, thusoverestimating the activity. Both result in a loss ofcontrast and amplify quantitative errors or bias.The trend in nuclear medicine has been to correctfor Compton scatter and for attenuation indepen-dently and in that order. This trend is driven bythe desire to separate the complex compensationproblem of two interrelated processes into two sim-pler components. In some sense, this situation isanalogous to conventional two-dimensional (2D)reconstruction versus fully 3D reconstruction,which considers oblique LoRs. Taking advantageof the 3D acquisition mode increases the sensitivityby approximately a factor of five compared with the2D acquisition mode. This advantage, however, isachieved at the expense of an increased system sen-sitivity to random and scattered coincidences andthe greater complexity and computational burdenof the 3D reconstruction algorithm. Novel methodsof handling scatter and attenuation simultaneously

Scatter Compensation Techniques in PET 221


have many advantages over conventional correctionmethods. The most ambitious approaches aimingto achieve combined corrections, originally referredto as ‘‘inverse Monte Carlo’’ simulations [14], en-deavor to reconstruct Compton-scattered photonsinto their voxel of origin. These approaches, whichare discussed in a later section, seem to be too am-bitious to be feasible in a clinical setting [15–19].More realistic approaches include both attenuationand scatter in the forward projection operator of aniterative reconstruction algorithm (eg, maximum-likelihood expectation maximization, ML-EM), inwhich only unscattered photons are ‘‘put back’’[20–23].

The magnitude of the included scatter in PET de-pends heavily on the acquisition mode, the place-ment and width of the energy acceptance window,the body section being imaged (eg, brain, thorax,abdomen, or pelvis), and patient size. The modedepends on whether the FoV for a given detector

is restricted in the axial direction (along the patientaxis) by the placement of lead or tungsten septa (2Dmode) or is left considerably more open (3Dmode). For standard energy window settings, thescatter fraction—defined as the ratio between thenumber of scattered photons and the total numberof photons (scattered and unscattered) detected—represents 10% to 20% of the total counts acquiredin the 2D mode, whereas in the 3D mode it in-creases to 30% to 35% of the data collected in brainscanning and can reach 50% to 60% of the data col-lected in whole-body scanning (Fig. 2) [2,24]. It hasbeen demonstrated that in the 3D acquisitionmode, the variation of the scatter fraction as a func-tion of the phantom size is not linear, reachinga maximum of 66% for a point source located inthe center of a cylindrical phantom (diameter50 cm, height 20 cm) [25]. The scatter fraction forthe same point source in air is higher in the 2Dmode (6%) than in the 3D mode (2%) because of

Fig. 2. Scattered photons arise from the whole attenuating medium, including the imaging table and the variouscomponents of a PET tomograph. The scatter fraction in PET in the 3D mode ranges from 30% to 35% of thedata acquired in brain scanning to more than 50% of the data acquired in whole-body scanning, dependingon the scanner geometry, the energy window setting, the region to be explored, and patient size. In additionto a decrease in the image contrast, events also may appear in regions of the image where there is no activity(eg, outside the patient).



the contribution of scatter in the septa in the 2Dmode. Another concern in 3D PET, in contrast to2D PET, is the scatter contribution from activityoutside the FoV and the contribution of multiplescatter.

The scientific literature lacks thorough studies fo-cusing on the clinical impact of different scatter-correction strategies versus no correction in 3DPET imaging. It is well established that scatter cor-rection improves the contrast compared with nocorrection but does so at the expense of decreasedsignal-to-noise ratio when subtraction-basedscatter-correction techniques are used [26]. Scattercompensation improves the contrast between thedifferent brain tissues and removes backgroundcounts in the abdomen and lungs, allowing betterrecovery of tracer-avid or low-count regions andstructures [2]. The value of scatter compensationis well established within the PET community,both for optimal qualitative assessment of recon-structed images and for quantification of parame-ters governing physiologic and biologic processes.

There are still, however, some applications inwhich the benefit of scatter correction remainscontroversial. These applications include 15O-[H2O]–based brain-activation protocols that are charac-terized by low-count studies in which scattersubtraction enhances noise, thus jeopardizingthe power of statistical analysis. The goal of thesestudies is to identify functional differences betweensubjects scanned under different conditions (ie,baseline and following an activation task). Whetherthe scatter component in the two conditions can beconsidered as a constant for intersubject compari-sons still needs to be demonstrated. This constancyis needed to substantiate the hypothesis that theoutcome of statistical analysis (reflecting subtlechanges in radiotracer distribution) does notchange significantly before and after scattercorrection.

In tracer kinetic modeling studies, differencesranging from 10% to 30% in the parameter estimatesderived from patient studies are often found to besignificant [27]. The magnitude of the scatter correc-tion may cause some parameter values to increase byseveral fold, with an associated increase in noise. Theuse of subtraction-based scatter correction mightjeopardize the ability to detect slight biologic effectsif the decrease in signal-to-noise ratio cannot becircumvented. Very few studies have addressed theissue of the effect of scatter compensation on param-eter estimates derived from kinetic models that fo-cused mainly on 3D brain PET studies [27,28].Further studies using different PET tracers in variousclinical situations are necessary to characterize fullythe effect of scatter correction on the estimation oftracer kinetic parameters.

Modeling the scatter component in uniformand non-uniform media

The transport of annihilation photons is describedby the integro-differential Boltzmann equation,which is the governing equation for a givenmonoenergetic, isotropic source of photons anda scattering medium. The differential part de-scribes the generation, propagation, and attenua-tion of photons. The integral part describes thescattering of photons as an integral over directionand energy. The Boltzmann equation describes theevolution of the spatial and angular distributionof photons with respect to time resulting fromthe generation, propagation, attenuation, andscattering of photons within the medium. Thisequation is difficult to solve because of the scatterintegral and the size of the problem when discre-tized. Many techniques deal with the scatter inte-gral by considering successive orders of scatteringdiscretely.

The probability of Compton scattering is given bythe Klein-Nishina equation, which gives the differ-ential scattering cross section ds=dU as a functionof scattering angle q [29]:

ds

dU5

r2e

2ð1 1 cos2qÞ

�1

1 1 að1� cosqÞ

�2

�1 1

a2 ð1� cosqÞ2

½1 1 að1� cosqÞ� ð1 1 cos2qÞ

�

where a 5 E=moc2 and re the classical radius of the

electron. This equation was used extensively tobuild appropriate scatter models to correct for thiseffect in PET. Because all unscattered events inPET have 511 keV before scattering, a 5 1 for thefirst scatter. Therefore, the differential Comptonscattering cross section relative to that for unscat-tered annihilation photons is

ds

dU5

r2e

2

�1

ð2� cosqÞ2��

1 1 cos2q 1ð1� cosqÞ2

ð2� cosqÞ

�

This equation gives the differential scatteringprobability. The integral of this from 0� to any anglegives the integral cross section. The integral gives in-formation about what fraction of scattered photonswill be scattered into a cone with a given half-angle.The theoretic angular and energy distributions ofCompton-scattered photons are plotted as a func-tion of the scattering angle and energy in Fig. 3Aand B, respectively, for an initial energy of 511keV. The figure shows that small-angle scattering ismore likely than large-angle scattering and thatthe most probable scattering angle is around 35�.The corresponding energy of the Compton-scat-tered photon is about 433 keV, which is within



the acquisition energy window used on most cur-rent, state-of-the-art PET scanners.

The process of modeling the scatter componentin PET consists of creating a representation of thescatter counts (magnitude and spatial distribution)in a projection or sinogram that corresponds toa particular tracer activity distribution and attenua-tion map in the object [2]. The ideal research toolfor scatter modeling through accurate photon trans-port is the Monte Carlo method [1]. The complexityand computing requirements of Monte Carlo simu-lations led to the development of analytic modelsbased on the integration of the Klein–Nishina equa-tion or simplifying approximations to improvecomputational speed, particularly in media ofnon-uniform density. Analytic scatter modeling inuniformly attenuating objects is more straightfor-ward and usually has been performed by scanningpoint or line sources placed at various locations ina water-filled cylinder as a first step toward model-ing scatter from multiple and distributed sourceswithin non-uniform scattering media using anat-omy-dependent models. Point- or line-spread scat-ter-response functions are generated, and thescatter fraction is assessed by fitting the scatter tailsof the response function to an appropriate mathe-matical expression (eg, Gaussian, mono- or dual-exponential kernels). This approach was performedextensively by Barney and colleagues [30] duringthe early days of fully 3D PET imaging to developand validate an analytic scatter model that can beused for scatter correction. Likewise, Adam and col-leagues [25] used Monte Carlo simulations to ex-tend the assessment of the spatial characteristics ofscatter to contributions from outside the FoV using

various phantoms. The spatial distribution of mul-tiple scatter is quite different from the simple scattercomponent, preventing the use of simple rescalingof the latter to take into account the effect of the for-mer for scatter-correction purposes. Fig. 4 showsMonte Carlo–simulated scatter distribution func-tions for a line source located at the center of theFoV and displaced 5 cm radially off center obtainedusing the Eidolon simulation package [31]. The pro-jections for the line source at the center are symmet-rical and were summed over all projection angles.The projections are not symmetric when the sourceis moved off center. For this reason, a profile of a sin-gle angular view was used. It can be seen that theprojections of a line source placed in a uniform, wa-ter-filled cylinder are dominated in the wings by theobject scatter and in the peak by the unscatteredphotons. This discussion remains valid when theline source is shifted out of the symmetry center.The amplitude of the short side of the projectioncompared with that of the symmetric case is in-creased, because the path of the photons throughthe phantom is shorter. The amplitude of the longside is decreased, because the pathway throughthe attenuating medium is longer.

Because of the limitations of Gaussian models,a new approach that allows the modeling of non-Gaussian object-dependent scatter was developedby Chen and colleagues [32]. Images of simpleand more complex phantoms were used to derivethe 24 parameters of the model, which consists ofeight simple functions. The parameters for variousobjects were derived from those of a referenceobject consisting of a cylinder 21.5 cm in diameter,using empiric rules.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100 120 140 160 180

Angle of photon scattering

0

0.001

0.002

0.003

0.004

0.005

0.006

0 100 200 300 400 500 600 700

Energy of scattered photons (keV)

A B

Fig. 3. The theoretic (A) angular and (B) energy distributions of Compton single-scattered photons having aninitial energy of 511 keV, according to the Klein-Nishina expression.



The effect of lower energy discrimination onsingle- and multiple-scatter distributions was alsoassessed through Monte Carlo calculations for 3DPET using both a 45.6-cm (full object) anda 15.2-cm (short object) section of the VoxelMananthropomorphic model [33]. Consistent with theobservations made by Adam and colleagues [25],the multiple-scatter component was well estimatedwith a Gaussian convolution of the single-scatterevents (for the full object), but significant errorsmay occur if the attenuation and activity outsidethe FoV are not included in the estimation of thesingle-scatter component. Using the same anthro-pomorphic model with the lungs and heart in theFoV and the abdomen outside the FoV, the scatterfraction was 57% and 36%, when using a low en-ergy discrimination of 300 keV and 425 keV, respec-tively. Of the total scatter, 7.4% was found to comefrom outside-FoV matter and 24% from outside-FoV activity when using a low energy discrimina-tion of 300 keV whereas they were only 5.3% and17% when using a low energy discrimination of425 keV. Moreover, the spatial distributions of scat-ter from external matter and external activity werefound to be different [34]. More recently, a moresophisticated and promising approach that offersdistinct features for modeling multiple-orderCompton scatter, which uses the absolute probabil-ities relating the image space to the projection spacein 3D whole-body PET, was proposed [35]. Suchmodeling is valuable for large, attenuating mediain which scatter is a prevailing component of themeasured data and in which multiple scatter maydominate the scatter component (depending onenergy discrimination and object size).

Another category of methods uses analyticmodels or Monte Carlo simulations to computethe transition matrix, which represents the map-ping from the activity distribution onto the projec-tions. Monte Carlo simulation can handle complexactivity distributions and non-uniform media read-ily [14,16,18,19]. Unfortunately, hundreds of giga-bytes up to several terabytes of memory are requiredto store the complete nonsparse transition matrixwhen the fully 3D Monte Carlo matrix approachis used, and without approximations it can take sev-eral weeks to generate the full matrix on standardcomputing platforms. In addition, the proceduremust be repeated for each patient. One of the ad-vantages of such an approach is that the scattermodel can be incorporated readily in direct 3Dlist-mode iterative reconstruction algorithms [36].This advantage has spurred further research aimingat reducing memory constraints through the devel-opment of appropriate, parallelizable compressionschemes to enable storing the matrices of the fullMonte Carlo scatter system [37].

Scatter component in small-animal positronemission tomography imaging

With the introduction of commercial preclinicalPET systems, small-animal imaging is becomingreadily accessible and increasingly popular. Becausein most cases the choice of a particular system is dic-tated by technical specifications, special attentionmust be paid to the methodologies followedwhen characterizing system performance. Becausedifferent methods can be used to assess the scatterfraction, differences may be methodologic rather

A B

101

102

103

104

105

-15 -10 -5 0 5 10 15

distance (cm)

101

102

103

104

105

-15 -10 -5 0 5 10 15

distance (cm)

Fig. 4. The scatter-response functions simulated using Monte Carlo calculations when the line source is located atthe center of the FOV (A) and displaced 5 cm radially (B). The projections for the line source at the center aresymmetric and were summed over all projection angles.



than reflecting any relevant difference in the per-formance of the scanner. Standardization of the as-sessment of performance characteristics is thushighly desired [38].

Little has been published on modeling the scattercomponent in small-animal PET scanners, becausein imaging rodents the scatter fraction is relativelysmall (compared with clinical imaging). The originof scatter for small-animal imaging has not beenwell characterized but has been proposed to stemmainly from the gantry and environment ratherthan from the animal itself [39]. The scatter compo-nent for a prototype PET scanner based on avalanchephotodiode readout of two layers of lutetium oxyor-thosilicate crystals with depth of interaction infor-mation (called the ‘‘Munich-Avalanche-Diode-PET’’[MADPET]) was assessed using Monte Carlo calcula-tions [40]. In the most advanced version of this pro-totype (MADPET-II), the scatter fraction in a mouse-like cylindrical phantom (6 cm in diameter, 7 cm inheight) containing a spherical source (5 mm in di-ameter) placed at its center was 16.2% when the cyl-inder was cold and increased to 37.7% when thecylinder was radioactive for a lower energy discrimi-nator of 100 keV and no restrictions in the accep-tance angle [41]. Monte Carlo simulations showedthat small-animal PET scanners also are sensitive torandom and scattered coincidences from radioactiv-ity outside the FoV [42].

Important contributions to the field were madeby Bentourkia and colleagues [43] who used multi-spectral data acquisition on the Sherbrooke small-animal avalanche photodiode PET scanner to fitthe spatial distribution of individual scatter compo-nents of the object, collimator, and detector usingsimple mono-exponential functions. The scatterfraction of this scanner for rat imaging was esti-mated as 33.8% with a dominant contribution bythe single-scatter component (27%) as assessed byMonte Carlo calculations [44]. The position-depen-dent scatter parameters of each scatter componentthen are used to design nonstationary scatter-cor-rection kernels for each point in the projection.These kernels are used in a convolution-subtractionmethod that consecutively removes object, collima-tor, and detector scatter from projections [45]. Thistechnique served as the basis for the implementa-tion of a spatially variant convolution-subtractionscatter-correction approach using dual-exponentialscatter kernels on the Hamamatsu SHR-7700 ani-mal PET scanner [46].

Exhaustive experimental measurements also werecarried out to characterize the magnitude and ori-gin of scattered radiation for the microPET IIsmall-animal PET scanner [39]. It has been shownthat for mouse scanning, the scatter from the gantryand room environment as measured with a line

source placed in air dominates over object scatter.The environmental scatter fraction increases rapidlyas the lower energy discriminator decreases and canexceed 30% for an open energy window of 150 to750 keV. The scatter fraction originating from themouse phantom is very low (3%–4%) and doesnot change considerably when the lower energy dis-criminator is increased. The object-scatter fractionfor the rat phantom varies between 10% and 35%for different energy windows and increases as thelower energy discriminator decreases.

Likewise, the measured scatter fractions for themouse (rat) National Electrical Manufacturers Asso-ciation count rate phantom in the microPET-R4and the microPET—FOCUS-F120 were 14%(29%) and 12.3% (26.3%), respectively, whena low energy discrimination of 250 keV was used[47]. If the discriminator is increased to 350 keV,the scatter fraction drops to 8.3% (19.6%) and8.2% (17.6%), respectively. Scatter correction thusis more important for rat scanning, whereas a largeenergy window (ie, 250–750 keV) would be moreappropriate to increase system sensitivity whenscanning small objects (eg, mouse brain).

Similar approaches were undertaken for positronemission mammography units, in which high spa-tial and contrast resolution and sensitivity are re-quired for early detection of breast tumors, henceavoiding biopsy intervention. In this context, a scat-ter-correction method for a regularized list-modeML-EM reconstruction algorithm was proposed[48]. The object-scatter component is modeled asadditive Poisson random variant in the forwardmodel of the reconstruction algorithm. The meanscatter sinogram, which needs to be estimatedonly once for each positron emission mammo-graphic configuration, is estimated using lengthyMonte Carlo simulations.

Scatter-correction strategies in positronemission tomography

During the last 2 decades various techniques havebeen proposed for reducing scatter-corrupting pho-tons and the resulting degradation of image con-trast and loss of quantitative accuracy in PET. Themajor disparity among the correction algorithmsis the way in which the scatter component in theenergy acquisition window is assessed. The mostreliable method to estimate the real amount andspatial distribution of scatter in the image is accu-rate modeling of scatter formation to resolve theobserved energy spectrum into its unscattered andscattered components. Scatter-compensation tech-niques can be optimized by examining how accu-rately a scatter-compensation algorithm estimatesthe amount and spatial distribution of scatter under



conditions where it can be measured accurately orotherwise independently determined.

A number of PET scatter-compensation algo-rithms have been proposed in the literature. Follow-ing the review by Zaidi and Koral [2], they fall intofive broad categories: (1) hardware approaches us-ing coarse septa or beam stoppers; (2) multiple-energy-window (spectral-analytic) approaches; (3)convolution/deconvolution-based approaches; (4)approaches based on direct estimation of scatterdistribution; and (5) approaches based on statisti-cal reconstruction.

The review by Zaidi and Koral [2] and chapters inother books [49–51] offer a thorough review of PETscatter-correction methods as of 2004. Readers inter-ested in these techniques are referred to these refer-ences. This article focuses on the most recenttechniques, suggested during the last few years,that were not covered in these reviews.

Hardware approaches using coarse septaor beam stoppers

In addition to empiric methods, in which the mostobvious approach consists of shifting the detectionwindow towards the high energies to reduce scatterevents in the energy acquisition window, manyhardware-based approaches have been proposed.Among these approaches is the use of coarse septa,which results in higher sensitivity than obtainedwith the conventional 2D acquisition mode usinginterslice septa but a lower scatter fraction than inthe 3D acquisition mode without septa [52]. Thescatter component is determined from acquireddata for those LoRs that are intercepted by thecoarse septa. The technique seems to deal relativelywell with scatter from radioactivity outside the FoV.

A related method uses a beam-stopper devicemade of lead, which is placed around the patientto attenuate primary beams, thus making it possibleto estimate the scatter component directly in the PETsinogram domain from those LoRs blocked by stop-pers [53]. By assuming that the spatial distributionof scatter varies slowly, the scatter component canbe recovered using the cubic-spline interpolationfrom the local measurements or through combina-tion using the dual-energy-window technique [54].The authors claim that the technique clearly outper-forms the dual-energy window technique for scattersubtraction and allows effective removal of multiplescatter and scattering from outside the FoV.

Multiple-energy-window (spectral)approaches

The development of the 3D acquisition mode andthe improvements in detector energy resolution inPET have allowed the implementation of scatter cor-rection based on the analysis of energy spectra [55].

Interest in energy-based scatter-correction tech-niques has been revived with the introduction oflist-mode data storage in commercial PET scanners,which stores the energy information for the photonpair. The basic assumption of multiple-energy-win-dow methods is that, given a sufficient number ofwindows below and above the photopeak window,one can estimate either the complete energy spec-trum of the scattered counts or at least the integralof that spectrum from the lower energy discrimina-tor of the photopeak window to the upper energydiscriminator of that window. These techniques usu-ally put in additional information to get potentiallymore accurate results, with the objective of subtract-ing the scattered counts, pixel by pixel.

During recent years, a few such techniques havebeen proposed. The method suggested by Chenand colleagues [56] uses energy-dependent weights;the values of its two energies indicate the probabil-ity an event being a ‘‘true’’ event. These weights areobtained from a precomputed representative true-fraction table obtained by averaging Monte Carlocalculation estimates for a variety of activity andattenuation distributions representative of clinicalsituations. One of the advantages of the method isthat it requires minimal computations and isattractive for practical use.

A more comprehensive energy-based scatter-correction approach was suggested more recentlyby Popescu and colleagues [57]. The techniqueexploits the noticeable dissimilarity between theenergy spectra of the unscattered and the scatteredphotons and uses the complete energy informationfrom the list-mode data to assess the distribution ofthe scattered events in the data space. In addition,energy-dependent weights that individualize thecorrection terms (scatter and randoms) for each coin-cidence event, depending on its position and energyinformation, are incorporated in an iterative ML-EMreconstruction algorithm. The method relies on a 2Ddetector energy-response model corresponding tofour possible combinations of the state of detectedevents: (1) both photons unscattered; (2) the firstphoton scattered and the second not scattered; (3)the second photon scattered and the first photonnot scattered; and (4) both photons scattered. Thestatistical model also allows the variation of scatterfraction with the energies of coincident photons foreach position in the projection space to be estimated.The use of a model with four energy components isthe key difference between this technique and previ-ously proposed energy-based approaches.

Approaches based on convolutionor deconvolution

The convolution- or deconvolution-based ap-proaches used in PET estimate the distribution of



scatter from the coincidence data collected in thestandard energy acquisition window. These ap-proaches are older and, especially in their simplestforms, are used less frequently than newer, morepromising methods; therefore a minimum amountof space is given to them here. As discussed earlier,a spatially variant convolution-subtraction scattercorrection was developed for a Hamamatsu SHR-7700 animal PET scanner designed for studies ofconscious monkeys [46]. The technique builds onthe approach adopted by Bentourkia and Lecomte[45], but a dual-exponential scatter kernel that takesinto account the Compton scatter both inside theobject and in the gantry and detectors was adoptedinstead of using separate mono-exponential ker-nels. The innovation is that this technique wasused for scatter correction of both PET emissionand transmission data, allowing a more accurate es-timate of attenuation coefficients in the transmis-sion data. Correction of both data sets improvedimage contrast and quantitative accuracy, thus re-ducing the residual error to approximately 2% inwater.

Approaches based on direct calculationof scatter distribution

Approaches based on the direct calculation of scat-ter distribution assume that the distribution of scat-tered events can be estimated accurately from theinformation contained in either the emission dataalone or in the combined emission and the trans-mission data. Although the approach has metwith a high level of enthusiasm, the role and clini-cal feasibility of direct Monte Carlo–based scattercorrection in PET still needs to be demonstrated[19,58–60]. To this end, combining the advantagesof general-purpose Monte Carlo codes developedfor high-energy physics applications to allowmore accurate modeling of complex PET detectorgeometries and those of dedicated PET simulatorsfor modeling voxel-based anthropomorphic com-putational models of the human anatomy mightbe beneficial [61].

Analytic model-based scatter-correction algo-rithms generally use both the PET emission andtransmission scans and a mathematical model ofthe scanner incorporating the physics of Comptonscattering in a forward calculation of the numberof events for which one photon has undergonea Compton interaction. Techniques using this classof algorithms remain the most popular and themost widely used in clinical settings, because theywere successfully implemented on software sup-plied by virtually all vendors [62–64]. Fig. 5 showsthe working principle of a model-based simulationscatter-correction technique proposed originallyby Watson [62]. The magnitude and spatial

distribution of Compton scatter is determined us-ing preliminary PET emission and transmission im-ages and the Klein-Nishina formulation(analytically or using Monte Carlo calculations).The calculation usually is simplified by assumingphotons scatter only once; then multiple scatter ismodeled using the single-scatter component. Agrid of scatter points is applied to calculate scatterprojections, which are subtracted from measuredprojections before reconstruction. The techniqueusually is performed iteratively. Various implemen-tations of the single-scatter simulation techniquehave been reported in the literature [21,62–66].The approach was improved further to scale the es-timated scatter sinogram more appropriately to themeasured data, allowing more reliable compensa-tion of scatter from outside the FoV, and to addresssome issues specific to combined PET/CT scanners(eg, the problem of CT image truncation) [67].

Interest in scatter correction for PET scannersusing time-of-flight (ToF) information [68] was re-vived with the renewed interest in this oldtechnology, which now can be exploited to its fullpotential because of the availability of faster scintil-lation crystals. The rational is that scatter-compen-sation techniques developed for conventional PETmay not be adequate for ToF-PET, particularly thosemodel-based techniques that simulate scatter con-tributions. The correction algorithm must takeinto account the time offsets of detected scatteredphoton pairs, because the variation of scatter contri-bution may depend on time offset in a different waythan do unscattered coincidences. To this end, thesingle-scatter simulation technique was extendedto support the reconstruction of list-mode PETdata with ToF information to consider the case inwhich Compton scatter is discriminated accordingto its differential ToF [69] and to predict the varia-tion of scatter as a function of ToF [70]. The ap-proach by Werner and colleagues [70] wasdesigned for incorporation into list-mode ToF re-construction. The algorithm computes high-resolu-tion scatter time distributions at 585-picosecondtiming resolution (because important structure isvisible in the time distributions at this timing reso-lution) and uses an alternative tail-fit–based scalingtechnique. Preliminary results seem to suggest thata ToF-dependent scatter-correction technique isessential to achieve the fast convergence expectedfrom ToF reconstruction while preserving or im-proving quantitative accuracy. Watson [69] charac-terized discrepancies between ToF-dependent andnon–ToF-dependent scatter components and re-ported good agreement between calculated andmeasured ToF-dependent scatter using phantomand clinical studies. The computational burden ofthis technique, however, is significantly higher (by



a factor of five) than the initial non-ToF implemen-tation of the algorithm.

Iterative reconstruction-basedscatter-correction approaches

The scatter component can be either precomputed(using one of the techniques described previously)and used during iterative reconstruction or can begenerated as well as used during iterative recon-struction [71]. In the former approach the estimatedscatter component is included with a forward pro-jection in the statistical model instead of being ex-plicitly subtracted from the measured projectiondata. That is, the goal of a given iteration becomesfinding the object that, when it is forward projectedand the scatter estimate is added, best fits the mea-sured projection data, with ‘‘fit’’ quantified by thelog-likelihood of the Poisson statistical model. Inthat model, the variance equals the mean, and themean includes both the unscattered and scatteredcontributions [2].

The normal approach for implementation ofa scatter model is to incorporate the scatter estima-tion directly in the transition matrix (aij) of theML-EM algorithm, in which case it becomes

considerably larger than when only attenuationand geometric factors are included. One class ofcorrection methods uses Monte Carlo simulationsto compute the complete transition matrix that rep-resents the mapping from the activity distributiononto the projections [14–19], including scatterevents. Compression schemes are being developedto alleviate memory constraints and to make nu-meric implementation on current state-of-the-artcomputing platforms feasible [37]. In most cases,the scatter estimate is added or subtracted as a con-stant term or is recalculated in the projector at eachiteration and is not considered in the back-projector:

f newj 5

f oldjP

l

alj

Xi

aij

piPk

aikfoldk 1 s

where pi is the discrete set of projection pixel values,f newj and f old

j refer to the current and previous esti-mates of the reconstructed object respectively, andðsÞ is the scatter estimated on all projections.

Comparison of methods

The assessment and validation of scatter-correctionalgorithms is inherently difficult and sometimes is

Fig. 5. Principle of model-based scatter-correction techniques. The magnitude and spatial distribution of Comp-ton scatter is determined using preliminary PET emission and transmission images and the Klein-Nishina equa-tion (analytically or using Monte Carlo calculations). Calculations usually are simplified by assuming photonsscatter only once and then modeling multiple scatters using the single-scatter component. A grid of scatterpoints is applied to calculate scatter projections, which are subtracted from measured projections before recon-struction. The technique usually is performed iteratively.



unconvincing. There is a clear need for guidelines toevaluate correction techniques and other image-processing issues in PET. Most of the algorithmsdeveloped so far have been evaluated using eithersimulated or experimentally measured phantomstudies, in addition to subjective visual interpre-tation of clinical studies followed by rankingperformed by experienced physicians. This assess-ment has been extended to objective assessmentof image quality using receiver operating character-istics analysis based on human or numeric ob-servers [72], evaluation of the impact on theestimation of tracer kinetic parameters [27,28],and voxel-based statistical analysis in brain PETstudies [73]. In the last instance, the impact ofmodel-based scatter correction on the spatial distri-bution of 18F-labeled fluorodeoxyglucose (18F-[FDG]) in reconstructed brain PET images ofhealthy subjects was assessed using statistical para-metric mapping analysis. It has been shown thatsignificant differences in 18F-[FDG] distributionarise when images are reconstructed with and with-out explicit scatter correction for some cerebralareas. Fig. 6 illustrates areas with significantchanges in brain metabolism obtained by compar-ing distributions with and without explicit scattercorrection, normalized using the same 18F-[FDG]template. The knowledge gained might help readersaccustomed to interpreting non–scatter-corrected

images achieve adequate interpretation of 18F-[FDG] 3D brain PET images after scatter correctionis applied.

In a clinical environment, the evaluation of scat-ter correction is hampered further by the multiplic-ity of medical purposes for which the correctionsmay be studied. There is no single figure of meritthat summarizes algorithm performance, becauseperformance ultimately depends on the diagnostictask being performed. Well-established figures ofmerit known to have a large influence on manytypes of task performance are generally used to as-sess image quality. Generally it is difficult to estab-lish the superiority of one method over another.The impact of scatter correction on estimates oftracer kinetic parameters has been assessed ina few studies using brain FDG-PET data [27,28].Further investigation using different tracers for var-ious applications are necessary to characterize fullythe effect of scatter correction on the estimation oftracer kinetic parameters.

A limited number of studies reported the com-parative evaluation of different scatter-correctionstrategies in PET [28,59,60,74,75]. Most of thecomparative evaluation studies concluded thatvirtually all correction methods improved the im-age contrast considerably compared with no correc-tion but did so at the expense of a decrease insignal-to-noise ratio when using subtraction-based

Fig. 6. Statistical parametric maps resulting from the comparison of images reconstructed using model-basedscatter correction and those corrected for attenuation using an effective linear attenuation coefficient withoutexplicit scatter correction normalized using the same 18F-[FDG] template showing (A) areas of significantregional decreases and (B) areas of significant regional increases in brain metabolism. (From Montandon M-L,Slosman DO, Zaidi H. Assessment of the impact of model-based scatter correction on 18F-[FDG] 3D brain PETin healthy subjects using statistical parametric mapping. Neuroimage 2003;20:1855; with permission.)



scatter-correction techniques. More importantly,some reports seem to suggest that the differencesin the estimated scatter distributions did not havea significant impact on the final quantitative results.Thus, it can be argued that the important thing atpresent is to use some form of correction; futurestudies probably will ascertain the best methodfor a particular application.

Scatter correction in transmission imaging

An issue that deserves special attention but has notbeen addressed sufficiently in the literature is thenecessity for accurate modeling and correction ofscatter in radionuclide transmission scanning,where the determined attenuation map generallyis used for both attenuation and scatter-correctionpurposes, especially when using simultaneousemission/transmission scanning on standalonePET systems [76]. Some studies have reported theuse of model-based approaches for scatter estima-tion in transmission imaging [77,78]. With the in-troduction and successful clinical implementationof dual-modality PET/CT systems, comparable ap-proaches for scatter correction in x-ray CT imagingshould be targeted for further research to allowthe derivation of an appropriately scaled patient-specific attenuation map for correcting the PETemission data. This effect is more pronounced inthe next generation of CT scanners with flat-panel,detector-based cone-beam configurations, whichare much less immune to scatter than fan-beamCT scanners. In the past, in the context of usingCT for quantitative measurements, different groupshave addressed this problem by using experimentalstudies, mathematical modeling, and Monte Carlosimulations for both fan- [79–82] and cone-beam[83–88] (including flat- panel [89–95]) geometries.Pure Monte Carlo simulations and hybrid calcula-tions (combining deterministic calculations andMonte Carlo simulations) will play a pivotal rolein assisting these developments [96–98], becausethey also will help in the characterization of scatterresulting from the presence of additional materialin future simultaneous PET/MR systems (eg, usingfield-cycled MRI technology [99]).

Summary

It is gratifying to see the progress that scattercompensation has made in the last decade, fromsimple but practical energy-based approaches,through model-based strategies, and, more recently,iterative reconstruction-based approaches to scattercorrection. Recent advances have been enormous,especially in improved accuracy, precision, andcomputational speed, in conjunction with

decreased calibration data. The need for scatter cor-rection in PET is well accepted in research environ-ments, where there is a greater emphasis onaccurate quantitative measurements. Implementa-tion of validated techniques in commercial soft-ware packages supplied by vendors would beuseful to attract the interest of the clinical commu-nity. This greater interest, in turn, would lead to in-creased refinement of scatter-correction techniques.It is expected that, with the availability of greatercomputing power and more sophisticated toolsthrough open-source software, more complex andambitious computer-intensive scatter-modelingand -correction algorithms will become clinicallyfeasible.

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pet clin 2 (2007) 219 234 scatter compensation techniques ... · many nuclear medicine physicians...

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