Comparison of Three Different Techniques for Dual-EnergySubtraction Imaging in Digital Radiography:

A Signal-to-Noise Analysis

Chris C. Shaw and David Gur

Dual-energy subtraction imaging techniques allow thetissue and bone structures in the patient to be visual­ized and studied in two separate images, thus remov­ing the obscurity associated with overlapping of thetwo structures. In addition, they allow the subtractionimage signals to be used for quantifying the tissue andbone thicknesses. Thus, capability for dual-energysubtraction imaging is often incorporated with newdigital radiography systems. There are three differentapproaches to dual-energy image subtraction imagingtechniques. Among them, the dual-kilovolt (peak)[kV(p)] and sandwich detector techniques have beentwo widely used approaches. A third approach is thesingle-kV(p) dual-filter technique, which allows someflexible control of the spectra while avoiding thetechnical complexity of kV(p) value switching in slit­scan imaging. In this report, the noise propertiesassociated with these three techniques are studiedand compared by computing the noise variances in thesubtraction image signals as a function of the kV(p)values and filter thicknesses. It was found that thedual-kVp technique results in the least noisy subtrac­tion images, whereas the dual-filter technique resultsin slightly less noisy subtraction images than thesandwich detector technique. Following optimizationof the kV(p) value and filter thicknesses, the dual-filterand sandwich detector techniques result in a noiselevel of approximately three and four times higherthan that resulted from the dual-kV(p) technique,respectively.Copyright © 1992 by W.B. Saunders Company

KEY WORDS: medical imaging, digital radiography,dual-energy subtraction imaging.

ADVANCES IN DIGITAL radiography tech­niques in the past decade have opened the

door to the implementation of various imageacquisiton, processing, storage, and display ca-

From the Department of Diagnostic Radiology, UniversityofPittsburgh, Pittsburgh, PA.

Supported by research grants no. HL39299 from the Na­tional Heart, Lung and Blood Institute and no. CA5 I248fromthe National Cancer Institute.

Address reprint requests to Chris C. Shaw, PhD, A -44IScaife Hall, Radiological Imaging Division, University ofPittsburgh, Pittsburgh, PA 15261.

Reprinted with permission from SPIE Vol 1651: MedicalImaging VI: Instrumentation, 1992.

Copyright © 1992 by The Society ofPhoto-Optical Instrumen­tation Engineers

0-8194-0803-4/92/$4.00

262

pabilities that have been difficult if not impossi­ble with the conventional screen-film tech­niques. One such capability is the dual-energysubtraction imaging technique. With this tech­nique, low- and high-energy x-ray spectra areused to acquire two images, which are synthe­sized into a tissue-specific image and a bone­specific image. In the tissue-specific image, thebone structures are canceled out. Similarly, in abone-specific image, the tissue structures arecanceled out. This background cancellation hasbeen shown to improve the clarity of the anatom­ical details in general and to aid certain diagnos­tic tasks, the most notable example being thedetection of lung nodules overlapping with ribsin chest imaging.l-' Various techniques for imple­menting the dual-energy subtraction imagingcapability have been investigated.

TECHNIQUES FOR DUAL-ENERGY

SUBTRACTION IMAGING

Dual-Kilvalt (Peak) Technique

With the dual-kilovolt (peak) [kV(p)] tech­nique, the low- and high-energy spectra aregenerated at two different kV(p) levels requir­ing two separate exposures for low- and high­energy image acquisition. This can be achievedby performing the entire image-acquisition pro­cedure at two different kV(p) levels. The dual­kV(p) approach can be used with either broad­area' or slit-scan" imaging techniques. However,when patient or anatomical motions are in­volved, the time between the two images willresult in significant motion artifacts. With slit­scan imaging using a linear detector array, it ispossible to rapidly switch the kV(p) level duringacquisition of each image line to minimize themotion artifacts. Because of its complexity, ithas only been successfully implemented with alow-resolution spot-scan system and has beenused mainly for bone mineral measurement.Despite technical complexity and potential diffi­culty, the rapid kV(p) value change seems to bea viable approach to implementing the dual­kV(p) technique for dual-energy subtraction

Journal ofDigital Imaging, Vo15, No 4 (November), 1992: pp 262-270

COMPARISON OF DUAL-ENERGY IMAGING TECHNIQUES

imaging without motion artifacts. High-speedfilter change has also been used with a spot-scansystem to further improve the separation be­tween the low- and high-energy spectra; how­ever, it appears to be an extremely difficult taskto implement with a slit-scan imaging system.

Single kV(p) Dual-Filter Technique

The dual-kV(p) tehcnique can be signifi­cantly simplified by using double-slit collimationto generate two x-ray fan beams that are inde­pendently filtered for low- and high-energyimage acquisition. Two linear detector arraysare required for simultaneous low- and high­energy image acquisition during the scan. Alogical choice for filter materials would betungsten and copper for the low- and high­energy beams. Copper filtration shifts the x-rayspectrum toward the kV(p). Tungsten, on theother hand, attenuates the overall beam inten­sity while shifting the x-ray spectrum towards itsK-edge energy at 69.5 keY. The use of these twofilters results in the low- and high-energy spec­tra required for dual-energy subtraction imag­ing. Although the spectral separation achievedwith this method is not as good as with thedual-kV(p) technique, the resulting simplifica­tion in implementation may be worthwhile insome applications.

Sandwich Detector Technique

The sandwich detector technique uses twodetectors separated by a filter plate for simulta­neous low- and high-energy image acquisition.It has been successfully used in digital radiogra­phy techniques using either a linear detectorarray' or storage phoshors-" as the x-ray detec­tor. With this technique, the front detector andthe interdetector filter together filter the x-rayspectrum (already attenuated by the patient'stissue) and shift it toward the kV(p) level.Because the order of attenuation and filtrationis irrelevant as far as transmission is concerned,this is the equivalent of providing a higher­energy spectrum for image acquisition with theback detector. The most widely used filtermaterial for the sandwich detector technique iscopper. Although other materials have beentested, the difference in the resulting imagequality is minimal.

263

Selection of Techniques

The selection of a dual-energy subtractiontechnique for a digital radiography system isdetermined by several factors. Although thechoices are often limited by the shape, configu­ration, and operating characteristics of the de­tector used, there is often more than oneapproach that can be used to implement thedual-energy subtraction technique with a spe­cific imaging system. Therefore, it is worthwhileto compare the three techniques described forimage quality and other considerations.

The image quality of most imaging techniquescan be characterized by (1) signal response, (2)spatial-resolution properties, and (3) noise prop­erties or low-contrast performance. The signalresponses of a dual-energy subtraction imagingtechnique are the range and linearity of tissueand bone signals as the thickness measurement.The signal response is crucial to quantitativeimaging studies such as bone density measure­ment. In regular (qualitative) imaging studies,signal response is not as important and will notbe considered in this report. The spatial­resolution properties of dual-energy subtractionimages could be degraded in relation to the rawimages; however, the causes of such degrada­tion are not intrinsic to the dual-energy subtrac­tion imaging processing itself. They are mostlyrelated to the time lapse during image acquisi­tion, misregistration of the detectors, or patientmotion. Our main concern in this report is toshow how the noise properties of the threedifferent techniques compare with each other.Because the detectors used in a digital radiogra­phy system are often operated in the quantum­limited exposure range, we deal only with thex-ray quantum noise present in the raw imagedata and propagated to the subtraction imagesthrough the subtraction algorithms.

THEORY

To study the noise properties, the noisevariances in tissue and bone subtraction imageswere derived as a function of the noise ratios inlow- and high-energy x-ray measurements andparameters computed from the attenuation co­efficients averaged over the detected x-ray spec­tra. Similar derivations have been previouslydescribed and used to study effects of scatter in

264

dual-energy subtraction imaging." The followingderivation, taking a more general approach, isbased on the use of a broad-spectrum x-raybeam and nonlinear subtraction algorithm.

Dual-Energy Subtraction Algorithm

In dual-energy subtraction imaging, low- andhigh-energy x-ray image data are processed by aspecial subtraction algorithm to cancel out thebackground structures and generate the tissue­and bone-specific subtraction images. Duringprocessing, quantum noises are propagated fromthe original image data into the subtractionimages. Thus, noise level in the subtractionimages depends on three factors: noise ratio inthe raw image data, x-ray spectra, and thesubtraction algorithm used. Because polyener­getic x-rays are assumed to be used, as inpractical applications, a nonlinear subtractionalgorithm should be used to avoid beam­hardening effect and to ensure the accuracy ofthe tissue and bone signals as the thicknessmeasurements. Such algorithms have been de­veloped and reported elsewhere.t''-'! Althoughthese algorithms vary in their approaches andaccuracies, for the purpose of this report thetwo functions fa and fb can be determined andused to accurately convert the x-ray densities D,and D, into the tissue- and bone-thicknesssignals t, and tb in centimeters as follows:

(Equation 1)

and

SHAW AND GUR

and

Pl,h = JdER1,h<Pl,h(E)e->ea(E)la->eh(E)lhQ(E),

(Equation 4)

where R[ and Rh are the unattenuated low- andhigh-energy x-ray exposures in milliroentgens atthe detector plane, <p[(E) and <Ph(E) are theunattenuated photon flux per unit exposure perunit energy (photons/cmvrnlc/kev), and Q(E)is the detector response function and representsthe signal generated by each photon with anenergy near E (keV). J..La(E) and taare the linearattenuation coefficients (l/cm) and thickness in(centimeters) for soft tissue, and J..Lb(E) and tbare those for bone.

During the x-ray detection process, only partof the x-ray photon energy is converted intofluorescent light in an x-ray scintillator. Indigital imaging, this light is directly or indirectly(though an image intensifier and/or opticalcoupling) detected by a light-sensitive imager,eg, television target or charged-coupled device.The rest of the x-ray photon energy is dissipatedinto heat and does not conribute to imagesignals. In reality, the ratio of the x-ray photonenergy that contributes to the image signalsvaries slightly with the x-ray energy, E. How­ever, for good approximation, we can assumethat this ratio is constant for all diagnosticenergies (10 to 120 keY) and Q(E) is propor­tional to E. Thus, Equation 3 and 4 may berewritten as follows:

D1 = F,(ta, tb) = In[pNpl]

= In[J dER,<p,(E)

x E/JdER,<p,(E)e->ea(E)la->eh(E)lhE]

(Equation 7)

PI,h = JdER1,h<Pl,h(E)e->ea(E)la->eh(E)lhaE,

(Equation 6)

where a is a proportional constant. Thus, thex-ray densities D, and D, may be expressed as afunction of ta and tbas follows:

tb = fb(D" Dh), (Equation 2)

where, in analogy to the optical densities, thex-ray densities D[ and D; are defined to beIn(pNp,) and In(Pho/Ph), respectively, PI and Ploare the attenuated and unattenuated signalsfrom the low-energy spectrum, and Ph and Ph°are the attenuated and unattenuated signalsfrom the high-energy spectrum. We also assumethat scattered radiation and any optical scatterare properly controlled or corrected for so thatp,o, p., Pho, and Ph represent true primary mea­surements. Knowing the spectra of the incidentx-rays, p,o, PhO, p, and Ph can be expressed asfollows:

PI.ho = JdER"h<Pl,h(E)Q(E) (Equation 3)

and

PI,h°= JdERl,h<Pl,h(E)aE (Equation 5)

264

dual-energysubtractionimaging.9Thefollowing

derivation，taldngamoregeneralapproachヲis

basedontheuseofabroad-spectrumx-ray

beamandnonlinearsubtractionalgorithm.

Dual-EnergySubtractionAlgorithm

Indual-energysubtractionimaging，low-and

high-energyx-rayimagedataareprocessedbya

specialsubtractionalgorithmtocanceloutthe

backgroundstructuresandgeneratethetissue-

andbone-specificsubtractionimages.During

processing，quantumnoisesarepropagatedfromtheoriginalimagedataintothesubtraction

images.Thus，noiselevelinthesubtraction

imagesdependsonthreefactors:noiseratioin

therawimagedata，x-rayspectra，andthe

subtractionalgorithmused.Becausepolyener-

geticx-raysareassumedtobeused，asin

practicalapplications，anonlinearsubtraction

algorithmshouldbeusedtoavoidbeam-

hardeningeffectandtoensuretheaccuracyof

thetissueandbonesignalsasthethickness

measurements.Suchalgorithmshavebeende-velopedandreportedelsewhere.IO，11Although

thesealgorithmsvaryintheirapproachesand

accuracies，forthepurposeofthisreportthe

twofunctionsfaandfbcanbedeterminedand

usedtoaccuratelyconvertthex-raydensitiesDIandDhintothetissue-andbone-thickness

signalstaandtbincentimetersasfollows:

ta=fa(DbDh) (Equation1)

and

tb=fb(DbDh)， (Equation2)

where，inanalogytotheopticaldensities，thex-raydensitiesD[andDh aredefinedtobe

In(pNpI)andIn(Pho/Ph)，respectively，PIandploaretheattenuatedandunattenuatedsignals

fromthelow-energyspectrum，andPhandPh°aretheattenuatedandunattenuatedsignals

fromthehigh-energyspectrum.Wealsoassume

thatscatteredradiationandanyopticalscatter

areproperlycontrolledorcorrectedforsothat

plo，p"Pho，andPhrepresenttrueprimarymea-

surements.Knowingthespectraoftheincident

x-rays，plo，PhO，PIandPhcanbeexpressedas

follows:

PI.h°=JdERI，h<P1

SHAWANDGUR

and

PI，h=IdERI)凶岬h<P冷φ仇I.h岬(E)e一>ea(但臥E

(Equation4)

whereR[andRharetheu山i江nattenuat旬edlow-and

high-energyx-rayexposuresinmilliroentgensat

thedetectorplane，φ[(E)and<Ph(E)arethe

unattenuatedphotonfluxperunitexposureper

unitenergy(photons/cm2/mR/keV)，andQ(E)

isthedetectorresponsefunctionandrepresents

thesignalgeneratedbyeachphotonwithan

energynearE(keV).μ。(E)andtaarethelinear

attenuationcoefficients(1/cm)andthicknessin

(centimeters)forsofttissue，andμ(E)andtb

arethoseforbone.

Duringthex-raydetectionprocess，onlypart

ofthex-rayphotonenergyisconvertedinto

fluorescentlightinanx-rayscintillator.In

digitalimaging，thislightisdirectlyorindirectly

(thoughanimageintensifierand/oroptical

coupling)detectedbyalight-sensitiveimager，

eg，televisiontargetorcharged-coupleddevice.

Therestofthex-rayphotonenergyisdissipated

intoheatanddoesnotconributetoimage

signals.Inreality，theratioofthex-rayphoton

energythatcontributestotheimagesignals

variesslightlywiththex-rayenergy，E.How-

ever，forgoodapproximation，wecanassume

thatthisratioisconstantforalldiagnostic

energies(10to120keY)andQ(E)ispropor-

tionaltoE.Thus，Equation3and4maybe

rewrittenasfollows:

PI，h°=IdERI内

and

PI，h=IdERI，h<PI

(Equation6)

whereαiおsaproportionalconstant.Thus，thex-raydensitiesDIandDhmaybeexpressedasa

functionoftaandtbasfollows:

DI=FI(ta，tb)=In[pNpI]

=In[IdER似 E)

xE/IdER州 E)e->ea(叫(但臥E

(Equation7)

COMPARISONOFDUAL-ENERGYIMAGINGTECHNIQUES

and

Dh=Fh(ta，tb)=In[phO/ph]

=In[fdERhφh(E)

xEIfdERhφh(E)e山 (E)ta-州 E)tbE]

(Equation8)

Themajortasksofdual-energysubtraction

imagingaretodetermineC(D"Dh)andfb(D"Dh)astheinversefunctionsforFI(t出tb)andFh(ta，tb)andtousethemtoconvertthe

pixel-by-pixelmeasurementofDIandDhinto

thethicknessinformation，taandtb.Althoughit

isnotabsolutelynecessarytoconvertthex-ray

signalsPIandPIDintox-raydensitiesforsuch

conversion，suchpracticeofferstheadvantage

ofdealingwithadimensionlessquantity.This

advantagewillbecomeclearoncethenoise

varianceisderived.

NoiseVariance

Thelow-contrastperformanceofdual-energy

subtractionimagesisdictatedbythenoise

propagatedfromthex-raymeasurementsrepre-

sentedbyplo，PhD，PIandPh.Althoughsignals

throughaknownthicknessofsofttissuecanstill

beusedforcalibrationtolessenthedynamic

rangerequirement，suchactionmaybeunneces-sarybecauseofthesuperiordynamicrange

availablewithmostdetectorsusedindigital

radiography.Thus，wecanassumethatPlOand

PhDaremeasuredasopen-fieldairsignals(ie，

withoutanyattenuatingmaterialorpatientin

thex-raybeams)inthecalibrationprocedure.

Noiselevelsinthesemeasurementscanbe

minimizedtoaninsignificantlevelwithsuffi-

cientlyhighexposures(whilemaintainingthe

shapeofx-rayspectra).Thus，noiselevelsinplo

andPhDcanbeassumedtobezero.BecausePI

andPhareindependentlymeasured，thenoise

varianceintissue-andbone-imagesignals，σ1f

andσIb2，maybeexpressedastheweightedsum

ofthevariancesinmeasuringPIandPhラσPI2and

σPb2，asfollows:

σJ=(OfJaDl)2σ012+(afalaDh)2σDh2

(Equation9)

265

and

σIb2=(afblaDI)Zσ01

2+(afblaDh)2σDh2.

(Equation10)

NoticethatbecausePIandPhareuncorrelated

toeachother，thereisnocross-termineither

equation.BecauseDI=In[pNpd，σ01=(aDII

apl)σPI-σP/PIsimilarlyσ01=(aDIIapl)σPI-

σp/PI・Thus，thenoisefluctuationlevelsinthex-raydensities，DIandDh，arethenoiseratiosinthelow-andhigh-energyx-rayimagesignals

andEquations9and10canberewrittenas

follows:

σJzka12(σp/PI)Z+kah2(σPb/ph)Z

(Equation11)

and

σIJ=kbl2(σP/PI)Z+kbh2(σPh/ph)2ヲ

(Equation12)

wherekij isdefinedtobeafJaDj (i=a，b;j=I，h)，andσ日IPjarethenoiseratiosin

low-energyandhigh-energyx-raysignalsrespec-

tively.Obviously，kijvaluesarefunctionsofthex-raydensitiesor，alternatively，canbeevalu-

atedasafunctionoftheinputx-rayspectrum，tissueandbonethicknesses.However，becausethefunctionsfjarenotexplicitlyknown，anindirectmethodisusedtocomputethekjjvalue.Withthismethod，theaverageattenuationcoef-

ficientsμij'definedasaF/atj(i=a，b;j=I，h)，willfirstbeevaluatedandthenusedtocompute

thekijvalues.FromEquations7and8thevariationsofDI

andDh，dDIanddDh，maybeexpressedasalinearcombinationofdtaanddtbasfollows:

dDI=(aFIIata)dta+(aFIIatb)dtb

=μa，dta+μbldtb (Equation13)

and

dDh=(aFhlata)dta+(aFhlatb)dtb

=μahdta+μbhdtb' (Equation14)

ConverselyヲfromEquations1and2，dtaanddtbmaybeexpressedasalinearcombinationofdDI

266

and dD h as follows:

dt; = (afa/aDMDI + (af./ aDh)dDh

= ka,dDI + kahdDh (Equation 15)

and

du, = (afb / aD,)dD, + (afb/ aDh)dDh

= kbldD[ + kbhdDh. (Equation 16)

Thus, the coefficients f.lij and kij can be consid­ered as elements of two 2 x 2 matrices that areinverse to each other and kij can be evaluated asthe inverse matrix of f.lij as follows:

kal = f.lbh/ (f.lalf.lbh - f.lahf.lbl), (Equation 17)

kah = - f.lbd (f.lalf.lbh - f.lahf.lbl), (Equation 18)

kbl = - f.lah/ (f.lalf.lbh - f.lahf.lbl), (Equation 19)

and

(Equation 20)

However, using Equations 7 and 8, f.lij or aF/ ati

can be explicitly derived and expressed as fol­lows:

f.lij = [f f.li(E)dERj<\>j(E)e-fLa(E)la-fLb(E)lbE]/

[f dERjl\>j(E)e-fLa(E)la-fLb(E)lbE], (Equation 21)

where i = a, band j = I, h. Equation 21 showsthat f.lij has the meaning of the average attenua­tion coefficient for the material i (a or b)evaluated for the attenuated spectrum j (I or h).f.lij values can be numerically computed straight­forwardly from the input spectra <PI (E) and<Ph(E) and energy-dependent attenuation coeffi­cients f.la(E) and f.lb(E). Having evaluated the f.lijvalues, the kij values can be computed as theinverse matrix of f.lij according to Equations 17through 20.

The noise variances of image signals, (JP12and(JPh2, in Equations 11 and 12 can be evaluatedfrom the input spectra, <PI(E) and <Ph(E), andenergy-dependent attenuation coefficients, f.la(E)and f.lb(E), as follows:

(JPl,h2= f dER"h<Pl.h(E)e- fLa(E)la-fLb(E)lbQ(E)2

(Equation 22)

This has been the standard technique for com­puting the noise variance for a polychromaticx-ray spectrum. 15 Equations 11; 12, and 17through 22 provide the theoretical basis for the

SHAW AND GUR

numerical studies to be discussed in the follow­ing sections.

METHODS

Noise Variances in Xray Signals

Assuming that the subtraction signals areproperly generated to accurately represent theactual soft tissue and bone thicknesses, theimage contrast in the subtraction images shouldthen be the same no matter which technique isused. Thus, the low-contrast performance shouldbe determined only by the noise level in thesubtraction images. Because it is generally thesoft tissue that is of diagnostic interest in chestimaging, we have focussed our computations onthe tissue-specific image. To be able to useEquation 11 to estimate the noise variance inthe tissue image signal, (Jt/, we need to computethe coefficients, kaj values, and noise ratiosassociated with the x-ray signals, (Jp/PI and(JPb/Ph' Both require the use of the low- andhigh-energy x-ray photon flux spectra <PI(E) and<Ph(E). For numerical simulation, <PICE) and<Ph(E) were calculated in l-keV intervals fromthe published spectra" and attenuation coeffi­cients for the filters used.!'

For the dual-kV(p) technique, <PI(E) and<Ph(E) are two independent spectra specific tothe kV(p) values, target angle, and intrinsicfiltration used. For the dual-filter technique,they were generated from the same spectrum,<Pa(E), but filtered differently as follows:

<PI,h(E) = <po(E)e-fL1,h(E)IIh,

where f.l/(E) and t, are the attenuation coeffi­cients ahd thickness for the low-energy beamfilter (tungsten) and f.lh(E) and th are those forthe high-energy beam filter (copper). For thesandwich detector technique, <Ph(E) was gener­ated from <PI(E) as follows:

<Ph(E) = <po(E)e-fL1(E)lnt{E)lr,

where f.l/(E) and t, are the attenuation coeffi­cients and thickness for the front detector(BaFBr:Eu storage phosphor) and f.lf(E) and tfare those for the interdetector filter (copper).

The filtered photon spectra were normalizedto a total exposure of 10 mR using publisheddata. For simplicity, the soft tissue was assumedto consist of pure muscleonly. Attenuation coeffi-

266 SHAWANDGUR

and

anddDhasfollows:

dta=(afalaDMD¥+(af.1aDh)dDh

=ka，dDI+kahdDh (Equation15)

dtb=(afblaD，)dD，+(afblaDh)dDh

=kbldD[+kbhdDh. (Equation16)

Thus，thecoefficientsf.lijandkijcanbeconsid-

eredaselementsoftwo2x2matricesthatare

inversetoeachotherandkijcanbeevaluatedas

theinversematrixofμijasfollows:

kal=μbh/(μalμbhμ川 .Lbl)， (Equation17)

kah=一μbd(μalf.lbh一μahf.lbl)， (Equation18)

kbl=一μahl(μalf.lbh一μahf.lbl)， (Equation19)

and

However，usingEquations7and8，f.lijoraF/atjcanbeexplicitlyderivedandexpressedasfol-

lows:

μij=[ff.li(E)dER向(E)e-fLa(E)t巾 (E)tbE]1

[fdER沖《州1正(E)e一山fLa<州 附附州，(作(但州E

wherei=a丸，bandj=I，h.Equation21shows

thatμijhasthemeaningoftheaverageattenua-

tioncoefficientforthemateriali(aorb)

evaluatedfortheattenuatedspectrumj(Iorh).

μijvaluescanbenumericallycomputedstraight-forwardlyfromtheinputspectraφI(E)and

φh(E)andenergy-dependentattenuationcoeffi-

cientsμaCE)andμbeE).Havingevaluatedthef.Lij

values，thekjjvaluescanbecomputedasthe

inversematrixoff.lijaccordingtoEquations17

through20.

Thenoisevariancesofimagesignals，σP12andσPh2，inEquations11and12canbeevaluated

fromtheinputspectra，<¥>¥(E)andφh(E)，andenergy-dependentattenuationcoe伍cients，μaCE)andμbeE)，asfollows:

σP町lhJ2=jdER民凡R"hυ仙h仇1

(Equation22)

Thishasbeenthestandardtechniqueforcom-

putingthenoisevarianceforapolychromaticx-r悶ays叩pectr叩urn乱1お5 Equations1日1; 12，and 17through22providethetheoreticalbasisforthe

numericalstudiestobediscussedinthefollow-

lUgsectIOns.

METHODS

NoiseれlriancesinXraySignals

Assumingthatthesubtractionsignalsare

properlygeneratedtoaccuratelyrepresentthe

actualsofttissue且nd bonethicknesses，the

imagecontrastinthesubtractionimagesshould

thenbethesamenomatterwhichtechniqueis

used.Thus，thelow-contrastperformanceshouldbedeterminedonlybythenoiselevelinthe

subtractionimages.Becauseitisgenerallythe

softtissuethatisofdiagnosticinterestinchest

imaging，wehavefocussedourcomputationson

thetissue-specificimage.Tobeabletouse

Equation11toestimatethenoisevariancein

thetissueimagesignal，σtよweneedtocompute

thecoefficients，kajvalues，andnoiseratios

associatedwiththex-raysignals，σp/PIand

σPh/ph・Bothrequiretheuseofthelow-and

high-energyx-rayphotonfluxspectraφI(E)and

φh(E).Fornumericalsimulation，<¥>ICE)and

φh(E)werecalculatedinl-keVintervalsfrom

thepublishedspectra12andattenuationcoe血司

cientsforthefiltersused.13

Forthedual-kV(p)technique，φI(E)and

φh(E)aretwoindependentspectraspecificto

thekV(p)values，targetangle，andintrinsic

filtrationused.Forthedual-filtertechnique，

theyweregeneratedfromthesamespectrum，<¥>o(E)，butfiltereddifferentlyasfollows:

。l，h(E)=φ。(E)e凡嗣)hh，

whereμ，(E)andt，aretheattenuationcoeffi-

cientsahdthicknessforthelow-energybeam

filter(tungsten)andμh(E)andtharethosefor

thehigh-energybeamfilter(copper).Forthe

sandwichdetectortechnique，φh(E)wasgener-

atedfromφI(E)asfollows:。h(E)=φ。(E)eμl(E)IlME)If，

whereμ，(E)andt，aretheattenuationcoe伍.

cientsandthicknessforthefrontdetector

(BaFBr:Eustoragephosphor)andμ'feE)and今

arethosefortheinterdetectorfilter(copper).

Thefilteredphotonspectrawerenormalized

toatotalexposureof10mRusingpublished

data.Forsimplicity，thesofttissuewasassumed

toconsistofpuremuscleonly.Attenuationcoeffi-

(Equation20)kbh=μall(μalμbh一μahμbl)'

COMPARISON OF DUAL-ENERGY IMAGING TECHNIQUES

cients and compositions for muscle and bonewere taken from previously published data."The average attenuation coefficients were calcu­lated using Equation 21. The results were thenused to compute kij values in accordance withEquations 17 and 18. The variance of the x-raysignals was calculated by dividing the spectruminto 1-keV intervals, calculating the variance foreach interval first and then summing the resultsover the entire energy range.

For all techniques, the detectors were as­sumed to be a BaFBr:Eu storage phosphorscreen whose absorption coefficients are known.The storage phosphors are normally used as anarea detector in digital radiography. However,because of their ability to emit fluorescent lightduring the x-ray exposure, they can also be usedwith linear diode arrays for slit-scan imaging.

PatientExposure

Patient exposure is often used as a measurefor the risk to the patient in diagnostic imagingor measurement. Therefore, the noise varianceshould be computed for a fixed total patientexposure for optimization of comparison pur­poses. However, the image noise is directlyrelated to the exposure received by the detectorrather than the x-ray output or exposure re­ceived by the patient. Depending on the imag­ing geometry, various detector exposures mayresult from the same patient exposure. There­fore, for fair comparison, our comparisons weremade for a fixed total unattenuated detectorexposure (defined as the exposure to the detec­tor when no patient or any other attenuator ispresent in the x-ray beam). Given any imaginggeometry, the patient entrance exposure can becomputed from this exposure via the inversesquare law. For instance, assuming that thepatient entrance plane and detector are 12 and72 inches away from the x-ray source, a detectorexposure of 10 mR corresponds to approxi­mately 15 mR of patient entrance exposure.

Optimization

Before comparison, each of the three tech­niques was optimized to a limited extent. FromEquations 11 and 12, the noise levels in thesubtraction images were determined by thenoise ratios in low- and high-energy imagesignals and the coefficient kij values. The former

267

depends on (1) total unattenuated detectorexposure (fixed for comparison), (2) distribu­tion of the exposure between low- and high­energy image acquisition (exposure ratio), and(3) attenuation by the patient's body (tissue andbone thicknesses). The latter depends on (1)kV(p) levels of the x-ray sources, (2) filtration ofthe incident x-ray beams (filter types and thick­nesses), and (3) filtration by the front andinterdetector filter in the sandwich detectorapproach.

Although all aforementioned factors can beoptimized to minimize the noise level in thesubtraction images, the optimization is oftenlimited by practical considerations. For in­stance, adjustment of the exposure ratio isvirtually impossible with the sandwich detectortechnique and is technically difficult in imple­mentation with a slit-scan imaging system. An­other fact is that the technique can be optimizedfor either tissue or bone images but not both,and only for a specific combination of tissue andbone thicknesses. Thus, the value of optimiza­tion is somewhat limited if one is interested inboth tissue and bone images and/or in a widerange of tissue and bone thickness combina­tions.

In this study, we did not attempt to optimizeall parameters. For the dual-kV(p) technique,the low-kvfp) value was maintained at 70 whilethe high-kV(p) value and exposure ratios, de­fined as the ratio of the 10w-kV(p) exposure tothe total exposure, were varied and optimized.No additional beam filtration was considered.For the single-kV(p), dual-filter technique, boththe x-ray kV(p) value and filter (tungsten andcopper) thicknesses were varied and optimized.The prefiltration exposures of the low- andhigh-energy beams were assumed to be identi­cal to each other. For the sandwich detectortechnique, both the x-ray kV(p) value andinterdetector filter (copper) thickness were var­ied and optimized. No additional (prepatient)filtration was considered.

Tissue and Bone Thicknesses

The noise levels in the subtraction images arehighly dependent on the attenuating thick­nesses. Furthermore, the subtraction imagingtechnique can only be optimized for a specificcombination of tissue and bone thicknesses.

268 SHAW AND GUR

Therefore, we have chosen 10 cm tissue and 0.6em bone as the representative thickness combi­nation for our studies. This combination roughlycorresponds to the outer edges of the lung fieldwhere rib bone segments may overlap with anintermediate tissue thickness.

" O~--------------~

Cu

Cu W

Fig 2. Spectra of detected x-rays for the dual-filter tech­nique. The low- and high-energy x-rays were assumed to begenerated at 120 kV(p) and filtered by 0.14 mm of tungsten and1 mm of copper, respectively.

Dual-kV(p) Technique

In Figure 4, the noise level in the tissue imagesignal has been plotted as a function of theexposure ratio for the dual-kV(p) technique.The plots were made for several different kV(p)values of the high-energy x-ray spectrum. ThekV(p) value for the low-energy spectrum is keptfixed at 70. The plots show that the exposureratio should be kept around 50% to minimizethe noise. However, the dependence of thenoise on the exposure ratio is less sensitivewhen the kV(p) value's difference is large. Thenoise level decreases with the kV(p) value ofthe high-energy beam, ranging from approxi­mately 0.04 em for 80 kV(p) to 0.01 ern for 140kV(p).

"0'000060'0

' 0

RESULTS AND DISCUSSION

Spectra ofDetected X-rays

With the nonlinear dual-energy subtractiontechniques, it is unnecessary to completely sepa­rate the low- and high-energy spectra from eachother. None of the three techniques results incompletely separated spectra. Figure 1 shows atypical set of spectra generated for the dual­kV(p) technique. The low- and high-energyx-rays are assumed to be generated at 70 and120 kV(p) and attenuated by 10 ern of tissue and0.6 ern (1 g/crn") of bone. Figure 2 shows atypical set of spectra generated for the dual­filter technique. The x-rays are assumed to begenerated at 120 kV(p) and filtered by 0.1 mmof tungsten and 1 mm of copper to form the low­and high-energy beams. Both beams are alsoassumed to transmit through 10 ern tissue and0.6 cm bone before entering the detectors.Figure 3 shows the typical spectra for x-raysdetected by the low- (front) and high-energy(back) detectors in the sandwich detector tech­nique. The x-rays were assumed to be generatedat 120 kV(p) and attenuated by 10 em of tissueand 0.6 em of bone before entering the frontdetector. The interdetector filter is a 0.5-mm­thick copper plate.

40

"".0'0' 0

frDnt

'0

"se

"""",.i-

"On"& ~ "! = '0

.!~ ·. ·.i,•,4

" 0'00. 0

10 kVp

_____~l -20 'iWp

'04.

Fig 1. Spectra of detected x-ravs computed for the dual­kV(p) technique. The low- and high-energy x-rays were as­sumed to be generated at 70 kV(p) and 120 kV(p), respectively.

Fig 3. Spectra of detected x-rays computed for the sand­wich detector technique. The x-rays were assumed to begenerated at 120 kV(p) and filtered by 0.5 mm of copperbetween the front and back detectors.

COMPARISON OF DUAL-ENERGY IMAGING TECHNIQUES 269

Low energy exposure ratIo

When the kV(p) lies between 110 and 120kV(p), the noise level can be further reduced toabout 0.03 em with 4-mm copper filtration.

SandwichDetector Technique

Noise in the sandwich detector technique isdictated by the kV(p) value of the incidentx-rays and thickness of the copper filter used. InFigure 6, the noise level in the tissue imagesignal is plotted as a function of the copper filterthickness for several different kV(p) values. Theplots show that the optimal kV(p) value isgreater than 90 kV(p). A noise level of 0.04 cmcan be achieved by using a copper filter with athickness of 0.4 mm or greater.

90

80

D.,;!

100H8

j::::::::2~~~~~~~~~::::::2:l'40

c +---.----------,;---.--.-----,-----.----.-----10.1

Fig 4. Noise level in the tissue image versus the exposureratio (ratio of 10w-kV(p) exposure to the total exposure). The10w-kV(p) was kept fixed at 70 while the high-kV(p) was variedfrom 80 to 140.

Dual-filter Technique

Noise in the single-kV(p), dual-filter tech­nique is dictated by the kV(p) value of the x-raysource and thicknesses of the tungsten andcopper filters used. However, for each copperthickness used, there is an optimal tungstenthickness that would minimize the noise level inthe tissue image (for a specific combination oftissue and bone thicknesses). We have variedthe copper thickness from 0.1 to 1 ern andnumerically determined the corresponding opti­mal tungsten thickness. In Figure 5, the result­ing noise (minimized) is plotted as a function ofthe copper thickness for several different kV(p)values. The plots show that the optimal kV(p)value for the single kV(p) tungsten and copperfilter technique is between 110 and 120 kV(p).With 1-mm copper filtration, all kV(p) valuesresult in a noise level slightly below 0.04 em.

CONCLUSIONS

To compare the three techniques from thesame perspective, the noise level has beenplotted as a function of the kV(p) value for eachtechnique in Figure 7. The noise level wascomputed for a fixed patient exposure andminimized by selecting the optimal filter thick­nesses or exposure ratio. As expected, the dualkV(p) results in the lowest noise level. Thedual-filter and sandwich detector techniquesresult in approximately three and four timeshigher noise levels, respectively. It should benoted that to reduce these noise levels to that ofthe dual-kV(p) technique, the x-ray output mustbe increased by factors of 9 and 16 for thedual-filter and sandwich detector techniques,respectively. This would reduce noise levels inthe raw image data and therefore noise levels inthe subtraction images. However, this also leadsto a significantly increased patient exposure.

__~90

0.03

0.02

0.01

140100

110. 120

Copper thickness In em

0.2

0.19

0.18

0.17

~0.16

0.15

f0.14

0.13

0.12

0.11

0.1

0.09

().08

0.07

0.05

0.05

0.04

0.03

0.02

0.01

70

--------80

90-140

0.04 0.06 0.08

Fig 5. Noise level in the tissue image versus copper filterthickness for various kV(p) values. An optimal tungsten filterthickness was computed and used with each different copperfilter thickness.

Copper thiCkness In em

Fig 6. Noise level in the tissue image versus the interdetec­tor copper filter thickness for various kV(p) values.

270

0,05

0.01

Fig 7. Noise level in the tissue image versus kV(p). Thenoise was computed for a fixed patient exposure and mini­mized by choosing the optimal exposure ratio or filter thick­nesses. D, Dual kV(p): +, dual filter; 0, dual detector.

Thus, the dual-kV(p) technique should be thepreferred approach for dual-energy subtractionimaging if noise is the only concern. However,to minimize motion artifacts, the dual-kV(p)technique should be implemented by combiningrapid kV(p) value switching with linear detectorarray imaging. To equalize the low- and high­kV(p) exposures, the high-kV(p) x-rays shouldbe generated at lower current, or alternatively acopper filter can be inserted to attenuate thehigh-kV(p) x-rays. The advantage associatedwith this approach is a further improvement ofthe spectral separation and therefore further

SHAW AND GUR

reduction of the subtraction noise. However,the incorporation of rapid filter change in syn­chronization with the kV(p) value change with aslit-scan imaging system is not a trivial task.

The dual-filter technique results in slightlylower noise than the sandwich detector tech­nique (with a noise level of 0.03 ern v 0.04 em)only at the optimal kV(p) values (110 to 120kV[p]). However, this better performance isachieved at the expense of heavy filtration. Atungsten filter with a thickness of 0.5 mm orgreater and a copper filter with a thickness of 5mm or greater are required for generating thelow- and high-energy x-ray beams. Their usewould require the x-ray tube output to beincreased by a factor of 60 to 65 to achieve thesame exposure level obtained without any filtra­tion. This represents a big disadvantage for thedual-filter technique when it comes to actualimplementation. This disadvantage is furtheraggravated by the fact that the x-ray tube outputmust be further increased by a factor of as highas 200 to accommodate the slit-scan imagingtechnique. The sandwich detector technique,on the other hand, benefits little from prepa­tient filtration and therefore does not requirean increase of the x-ray output. Thus, despite itsslightly poorer noise properties, the sandwichdetector technique seems to be a much morepractical approach.

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