Applied Radia ion and Iso opes 155 (2020) 108920
A ailable online 4 Oc obe 2019
0969-8043/© 2019 Else ie L d. All igh s ese ed.
De e mining he p obabili y o loca ing peaks using compu e ized
peak-loca ion me hods in gamma- ay spec a as a unc ion o he ela i e
peak-a ea unce ain y
M.C. Ali San o o
c
, M.J. Anagnos akis
o
, T. Boshko a
a
, A. Camacho
b
, M.C. Fo nacia i Iljadica
c
,
S.M. Collins
d
, R. Diaz Pe ez
e
, J.U. Delgado
, M. Đu a�
sa i�
c
g
, M.A. Duch
b
, V.H. El i a
p
, R.
S. Gomes
, A. Gudelis
h
, D. Gu au
n
, S. Hu ado Be mudez
e
, R. Idoe a
i
, A. Je emo i�
c
g
,
A. Kandi�
c
g
, M. Ko un
j
,
*
, K. Ka opoulos
k
, M. Laubens ein
l
, S. Long
m
, R.M. Ma gineanu
n
,
I. Mi sios
o
, D. Mulas
b
, J.K. Nikoli�
c
, A. Pan elica
n
, V. Pey es Medina
p
, L. Pibida
q
,
C. Po i iadis
k
, R.L. Sil a
, S. Si i
c
, B. �
Se�
slak
g
, L. Ve heyen
, B. Vodenik
j
, I. Vukanac
,
H. Wiedne
s
, B. Zo ko
j
a
Facul y o Physics, S . Klimen Oh idsky Uni e si y o So ia, 5 James Bou chie Bl d., 1164 So ia, Bulga ia
b
Uni e si a Poli �
ecnica de Ca alunya (UPC), Ins i u de Tecniques Ene ge iques, Diagonal 647, 08028, Ba celona, Spain
c
Di isi�
on Radioquimica B�
asica y Da os Nuclea es, Depa amen o Quimica Nuclea , Comisi�
on Nacional de Ene gia A �
omica, A gen ina
d
Na ional Physical Labo a o y, Tedding on, Middlesex, TW11 0LW, UK
e
CITIUS, Uni e sidad de Se illa, A da. Reina Me cedes 4B, 41012, Se illa, Spain
Labo a �
o io Nacional de Me ologia das Radiaç~
oes Ionizan es – LNMRI, Ins i u o de Radiop o eç~
ao e Dosime ia – IRD / CNEN, B asilia, B azil
g
Vin�
ca Ins i u e o Nuclea Sciences, Labo a o y o Nuclea and Plasma Physics, Uni e si y o Belg ade, Belg ade, Se bia
h
Cen e o Physical Sciences End Technology, Sa ano iu A e. 231, Vilnus, Li huania
i
Esquela de Ingenie ia de Bilbao, Uni e sidad del Pais Vasco UPV/EHU, Plaza Ingenie o To es Que edo 1, 48013, Bilbao, Spain
j
“Jo�
ze S e an” Ins i u e, Jamo a Ces a 39, 1000, Ljubljana, Slo enia
k
G eek A omic Ene gy Commission, Agia Pa aske i, A hens, G eece
l
Labo a o i Nazionali del G an Sasso, Ins i u o Nazionale di Fisica Nuclea e, Via G. Aci elli 22, I-67100, Asse gi (AQ), I aly
m
Aus alian Radia ion P o ec ion and Nuclea Sa e y Agency, 619 Lowe Plen y Road, Yallambie, 3085, Aus alia
n
Ho ia Hulubei Na ional Ins i u e o Resea ch and De elopmen in Physics and Nuclea Enginee ing (IFIN_HH), 30 Reac o ului S ., POB MG-6, RO-0077125,
Bucha es -Magu ele, Romania
o
Nuclea Enginee ing Depa men , Na ional Technical Uni e si y o A hens, 15780, A hens, G eece
p
Labo a o io de Me ologia de Radiaciones Ionizan es, A da. Complu ense 40, 28040, Mad id, Spain
q
Na ional Ins i u e o S anda ds and Technology, 100 Bu eau DR, MS8462, Gai he sbu g, MD, 20899-8462, USA
Belgian Nuclea Resea ch Cen e, Boe e ang 200, BE-2400, Mol, Belgium
s
BEV - Bundesam ü Eich- und Ve messungswesen, Physikalisch- echnische P ü diens , A l gasse 35, 1160, Wien, Aus ia
Vin�
ca Ins i u e o Nuclea Sciences, Labo a o y o Radia ion and En i onmen al P o ec ion, Uni e si y o Belg ade, Belg ade, Se bia
ARTICLE INFO
Keywo ds:
Gamma- ay spec ome y
Rela i e peak-a ea unce ain y
Peak loca ion
Decision h eshold
ABSTRACT
The p obabili ies o loca ing peaks wi h a high ela i e peak-a ea unce ain y we e de e mined empi ically wi h
nine ypes o peak-loca ion so wa e used in labo a o ies engaged in gamma- ay spec ome y measu emen s. I
was ound ha i is no possible o loca e peaks wi h a p obabili y o 0.95, when hey ha e a ela i e peak-a ea
unce ain y in excess o 50%. Loca ing peaks a hese ela i ely high peak-a ea unce ain ies wi h a p obabili y
g ea e han 0.95 is only possible in he lib a y-d i en mode, whe e he peak posi ions a e supposed a-p io i. The
de iciencies o he lib a y-d i en mode and he possibili ies o imp o e he p obabili ies o loca ing peaks a e
b ie ly discussed.
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (M. Ko un).
Con en s lis s a ailable a ScienceDi ec
Applied Radia ion and Iso opes
jou nal homepage: h p://www.else ie .com/loca e/ap adiso
h ps://doi.o g/10.1016/j.ap adiso.2019.108920
Recei ed 6 Feb ua y 2019; Recei ed in e ised o m 18 Sep embe 2019; Accep ed 2 Oc obe 2019
Applied Radia ion and Iso opes 155 (2020) 108920
2
1. In oduc ion
In gamma- ay spec ome y measu emen s i is equen ly necessa y
o e alua e peaks ha canno be easily dis inguished om luc ua ions
in he con inuous backg ound on which hey a e supe imposed. Since
he p esence o peaks in he spec um e lec s he p esence o gamma- ay
emi e s, ob ious c i e ia o be used in he loca ion o small peaks, in
o de o signal he p esence o a gamma- ay emi e , should conside he
posi ion o he peak and i s shape. The peak posi ion should co espond
o he ene gy whe e he gamma- ays om he emi e a e egis e ed, and
he peak wid h should ollow he ene gy esolu ion o he spec ome e .
Howe e , since s a is ical luc ua ions in he con inuous backg ound can
a ise a any posi ion in he spec um and can ake on any wid h, hose
wo c i e ia a e no su icien o di e en ia e be ween s a is ical luc-
ua ions and small signals. The e o e, i is necessa y o es ablish a c i-
e ion based on he exp essi eness o he peak. I he peak is small
enough, compa ed o he s a is ical luc ua ions ha can be easonably
expec ed, i is supposed o ep esen a s a is ical luc ua ion and no a
signal due o he p esence o a gamma- ay emi e . The s anda d de i-
a ion o he numbe o coun s in an ene gy in e al, co esponding o he
esolu ion o he spec ome e , is gene ally used o de ine a quan i a i e
c i e ion on he p esence o peaks. This s anda d de ia ion ep esen s
he unce ain y o a peak a ea ha ing a alue o ze o, i.e., he null
measu emen unce ain y (ISO/IEC, 2007). This c i e ion, o mula ed
by Cu ie in 1968, s a es ha excu sions o he con inuous backg ound
ha ing an a ea exceeding he c i ical limi , n*, de ined as
n* ¼k
1-
α
⋅u(n ¼0) (1)
a e classi ied as loca ed peaks, signaling he p esence o gamma- ay
emi e s. In Eq. (1) u(n ¼0) deno es he null measu emen unce ain y
o he indica ion and he p opo ionali y ac o k
1-
α
desc ibes he p ob-
abili y o making e o s o ype I, i.e., co esponding o he alse posi i e,
meaning ha he peak is ac ually caused by a s a is ical luc ua ion.
Usually, c i ical limi s a e calcula ed allowing 5% o alse posi i es,
implying ha k
1-
α
¼1.65.
In he s anda d ISO 11929 (ISO, 2010) he c i ical limi , which e e s
o he numbe o coun s, i.e., he indica ion, is subs i u ed by he deci-
sion h eshold y*, which exp esses he p obabili y o he occu ence o
ype-I e o s wi h he alue o he measu and y as ollows:
y* ¼k
1-
α
⋅u(y ¼0), (2)
whe e u(y ¼0) deno es he null measu emen unce ain y o he
measu and.
The s anda d equi es documen ing whe he he indica ion, signal-
ling he p esence o he measu and, was ecognized o no and doc-
umen ing he co esponding decision h eshold in epo s on
measu emen s o es i ems. The decision h eshold should be epo ed,
ega dless o whe he a peak signalling he p esence o he gamma- ay
emi e was loca ed in he spec um o no . Howe e , he me hod o
he calcula ion o he decision h eshold di e s in bo h cases. In he i s
case (peak p esen ) he heigh o he con inuous backg ound is de e -
mined om he spec al egions ha do no o e lap wi h he peak e-
gion. In he second case he con inuous backg ound is compu ed om a
egion o in e es comp ising he egion whe e he peak is expec ed
(Canbe a, 2004; DIN, 2014). The e o e, he compu ed decision
h eshold can be di e en o he loca ed and o he no -loca ed peaks
esiding on equal backg ounds and ha ing equal a eas. Al e na i ely, o
loca ed peaks, he decision h eshold can be calcula ed om he peak
da a (Ko un e al., 2016).
I is ob ious ha o comply wi h he equi emen o he s anda d, i.e.
o pe o m he calcula ion o he decision h eshold co ec ly, he
loca ion o he peaks, deno ing he p esence o he measu and, should be
pe o med wi h a eliabili y ha is de ined by he p obabili y
α
o
making e o s o ype I. The s a is ical signi icance o he peak ha
should be ecognized wi h his p obabili y is de e mined by he
de ini ion o he decision h eshold. Since he measu e o he s a is ical
signi icance o a peak is he ela i e unce ain y o i s a ea, he ela i e
limi , which s ic ly co esponds o he espec i e decision h eshold
(Boshko a, 2018), may be used. I he ROI (Region o In e es ) me hod is
used o he peak a ea e alua ion, his limi ( ela i e decision h eshold)
ends o 1/k
1-
α
, a a numbe o coun s co esponding o he decision
h eshold, which is much la ge han k
1-
α
2
. Fo a 0.05 p obabili y o ype-I
e o s 1/k
1-
α
akes on a alue o 0.608 (60.8%), while o he numbe o
coun s co esponding o he decision h eshold o 50 coun s, he ela i e
decision h eshold has a alue o 0.628. (Boshko a, 2018). Howe e , i is
no possible o calcula e he decision h eshold and he ela i e decision
h eshold om he peak a ea and i s unce ain y only, since i also de-
pends on he me hod o he peak a ea e alua ion and on he egion o
in e es used o de e mining he con inuous backg ound. The e o e he
app oxima e ela ion nea he decision h eshold
uðyÞ
y¼1
k1
α
(3)
be ween he ela i e peak a ea unce ain y and he decision
h eshold was used, which a ises om he de ini ion o he decision
h eshold, by assuming u(y ¼0) �u(y*). I ollows hen, ha o a 0.05
p obabili y o making ype-I e o s, peaks wi h a ela i e unce ain y o
60.8% should be loca ed wi h a p obabili y o 0.95.
To examine he abili y o he so wa e, ha is cu en ly used in
labo a o ies engaged in gamma- ay spec ome y measu emen s, an
ac ion was ini ia ed wi hin he Low-Le el Measu emen Techniques
Wo king G oup o he ICRM (In e na ional Commi ee o Radionuclide
Me ology), wi h he aim o de e mine he p obabili y o loca ing peaks
in gamma- ay spec a as a unc ion o hei ela i e peak-a ea unce -
ain y. The ac ion ep esen s he ollow-up o a p e ious ac ion pe -
o med wi h he pu pose o de e mining he sys ema ic in luences on
peak a eas when he peaks a e no exp essi e (B uggeman e al., 2018).
The analyses wi hin he ollow-up ac ion we e pe o med on he same
se o spec a as he ac ion on he sys ema ic in luences, a ailable a he
URL add ess h ps://www.d opbox.com/sh/ 9ws2 6g5mn0nqd
/AABiO5-yq1IC 76EYd MCZq6a?dl¼0.
I is he pu pose o his a icle o p esen he esul s o his ollow up
and o d aw some conclusions abou he so wa e and on he way he
labo a o ies use i .
2. Me hods
The pa icipa ing labo a o ies we e asked o analyze a se o 35
spec a and o en e he esul s o he analyses in an Excel ile a ailable
a he same URL add ess as he spec a. Twen y labo a o ies epo ed
wen y- i e se s o esul s. Thi een se s we e ob ained wi h Canbe a’s
peak-loca ion Genie 2000 2nd Di e ences P og am (Canbe a, 2004).
These analyses we e pe o med wi h he alues o he sensi i i y
pa ame e se be ween 2.07 and 2.55. O he ypes o so wa e ha we e
used we e he Genie 2000 VMS S anda d Peak Sea ch P og am (Can-
be a, 2006), wo se s; APTEC (Ap ec, 2000), wo se s; ANGES (Mishe ,
2016), wo se s; Gamma Vision (O ec, 2016), wo se s; Maes o (O ec,
2008), one se ; Silena (2000), one se ; Gamma-W (Gamma-W 2008;
IAEA, 1998), one se ; and SPUNAL (Simopoulos, 1989), one se . The
analyses wi h he Genie 2000 VMS p og am we e made a he sensi i i y
2.2, wi h Silena a he sensi i i y 2.4 and wi h he Gamma-Vision so -
wa e a he mos sensi i e alue o he peak signi icance pa ame e o
uni y (one). Fo o he analyses i can be concluded on he basis o he
numbe o peaks loca ed, ha he peak analyses we e made a simila
sensi i i ies, excep o he ANGES so wa e, whe e he analyses we e
less sensi i e.
The p obabili ies o loca ing a peak a he ene gy E, p(E) we e
calcula ed as
p(E) ¼n(E)/N (4)
M.C. Ali San o o e al.
Applied Radia ion and Iso opes 155 (2020) 108920
3
whe e n(E) deno es he numbe o spec a wi hin a speci ic se o esul s,
whe e a peak a he ene gy E was loca ed, and N is he numbe o spec a
in he se . The unce ain y o his p obabili y was calcula ed as (Gilmo e,
2008; Ko un e al., 2015)
u½pðEÞ� ¼ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i
pðEÞ⋅½1pðEÞ�
N
(5)
The ela i e unce ain y, a ibu ed o he mean peak a ea o a peak
occu ing a an ene gy E, was calcula ed as he mean ela i e unce -
ain y o he peak a eas calcula ed a he ene gy E wi hin a se
u el�npðEÞ�¼1
nðEÞX
nðEÞ
i¼1
u el�npiðEÞ�(6)
whe e n
pi
(E) deno es he numbe o coun s in he peak a he ene gy E in
he i- h spec um wi hin a se o esul s and u
el
[n
pi
(E)] is i s ela i e
unce ain y. The unce ain y was calcula ed as he a-pos e io i unce -
ain y om he wid hs o he dis ibu ions o he ela i e unce ain ies
occu ing a he ene gy E wi hin he se :
u�u el�npðEÞ��¼
i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i
P
nðEÞ
i¼1�u el�npiðEÞ�u el�npðEÞ��
½nðEÞ  1�⋅nðEÞ
2
u
u
u
u
(7)
3. Resul s
The esul s epo ed by he pa icipan s a e p esen ed as he p oba-
bili y o loca e peaks a speci ied loca ions as unc ions o he mean
ela i e unce ain y and a e shown in Figs. 1 and 2 o he a ious ypes
o so wa e used o he peak analysis. I is a common obse a ion ha o
all he da a se s ecei ed, ha a small ela i e peak-a ea unce ain ies
he p obabili y o de ec ion ends o uni y. The dis ibu ion o se s o e
he mean se -speci ic numbe o ene gies in one spec um, whe e a peak
was loca ed, is p esen ed in Fig. 3. Howe e , i is di icul o compa e he
a ious da a se s, because he unce ain ies a ibu ed o he peak a eas
a y signi ican ly. Fig. 4 p esen s he dis ibu ion o he da a se s e-
po ed o e he mean ela i e unce ain y epo ed o his se . I is
ob ious ha when compa ing he esul s om di e en se s he mean
ela i e peak-speci ic peak-a ea unce ain ies epo ed canno be in e -
p e ed di ec ly, bu needs o be e alua ed ela i e o he da a-se -speci ic
mean ela i e peak-a ea unce ain y u el
u el ¼1
MX
M
j¼1
u el�npEj�� (8)
whe e M deno es he numbe o ene gies wi hin a da a se whe e he
peaks we e loca ed and u el½npðEjÞ� is he mean ela i e peak-a ea un-
ce ain y o he peaks loca ed a he ene gy E
j
.
The a iabili y o he da a-se -speci ic mean ela i e peak-a ea un-
ce ain ies canno be explained using he me hods o e alua ion o he
peak a eas only, i.e., depending on whe he he peak a eas we e calcu-
la ed using he ROI me hod o using he leas -squa es me hod. I is
ob ious, he e o e, ha he a iabili y o igina es in he a iabili y o he
spec al egions used o de e mining he backg ound. Howe e , all he
ela i e unce ain ies epo ed exceeded he lowe limi o he ela i e
unce ain y implied by he Poisson s a is ics o he case o a e y wide
spec al in e al used o de e mining he heigh o he con inuous
backg ound, i.e., u
el
>n
g
1/2
, whe e n
g
deno es he g oss numbe o
coun s in he peak egion.
Since he co ela ion be ween he p obabili y o loca e peaks and he
ela i e peak-a ea unce ain y is a he sca e ed, i is di icul o
es ablish a quan i a i e c i e ion o exp ess he uppe limi o he in-
e al o he ela i e unce ain ies whe e he p obabili y o he loca ion
alls below 0.95. I can be obse ed ha a egion o ela i e peak-a ea
unce ain ies exis s, whe e he p obabili ies o he peak loca ion
Fig. 1. Co ela ions be ween he mean ela i e peak-a ea unce ain ies and he
p obabili ies o loca ing he peaks o di e en ypes o so wa e used in he
peak analysis.
Fig. 2. Co ela ions be ween he mean ela i e peak-a ea unce ain ies and he
p obabili ies o loca ing he peaks o da a se s comp ising la ge ela i e peak-
a ea unce ain ies.
M.C. Ali San o o e al.
Applied Radia ion and Iso opes 155 (2020) 108920
4
being equal o uni y a e con iguous, and ha ano he egion o ela i e
unce ain ies exis s whe e he p obabili ies o loca ing peaks, being
smalle han uni y, a e con iguous. The uppe and lowe bounda ies o
hese wo in e als a e deno ed by u
el,Max
and u
el,Min
, espec i ely. In
his way he egion o alues u
el
/u el was di ided in h ee in e als, he
i s one ex ending om ze o o u
el,Max
, he second one ex ending om
u
el,Max
o u
el,Min
and he hi d ex ending om u
el,Min
o in ini y. Fig. 5a
and b p esen he co ela ion be ween u
el,Max
/u el and he numbe o
peaks ha ing u
el
<u
el,Max
and he co ela ion be ween he numbe o
peaks wi h u
el
>u
el,Min
and u
el,Min
/u el, espec i ely. I is ob ious ha
he co ela ions desc ibe he obus ness o he peak analysis. Fig. 5a
p esen s he uppe limi s o he anges o he ela i e unce ain ies
comp ising only peaks wi h a p obabili y o uni y o loca ion. The wide
his ange is, he smalle is he p obabili y o ype-II e o s, i.e., he mo e
obus is he peak-loca ion algo i hm o loca ing exp essi e peaks and
he mo e peaks encompass he in e al [0,u
el, Max
]. Fig. 5b p esen s he
la ges mean ela i e peak-a ea unce ain y o a peak, loca ed wi h a
p obabili y o uni y. The la ge his ela i e unce ain y is, he smalle is
he p obabili y o ype-II e o s in he case o unexp essi e peaks, i.e.,
he mo e sensi i e he peak-loca ion algo i hm is. Also, he la ge u
el,Min
is, he ewe peaks occu wi h he mean peak-a ea unce ain y exceeding
u
el,Min
.
I is ob ious ha he ela i e peak-a ea unce ain y co esponding o
he p obabili y o loca ing a peak wi h he p obabili y o 0.95 mus lie in
he in e al [u
el,Max
, u
el, Min
]. To de e mine his unce ain y, he
dependence o he p obabili y o peak loca ion as a unc ion o he
ela i e unce ain y was smoo hed, and om hese esul s he smalles
ela i e unce ain y was de e mined, a he condi ion whe e he p ob-
abili y o de ec ion d ops below 0.95. The dis ibu ion o he da ase s
o e his ela i e unce ain y is shown in Fig. 6.
4. Discussion
I can be seen in Fig. 6 ha he mean ela i e peak-a ea unce ain ies,
needed o loca ing a peak wi h a p obabili y o 0.95, a e smalle han
60% in all he da a se s, excep one. The main pa ame e , which in-
luences he p obabili y o peak loca ion and he da a-se -speci ic mean
ela i e peak-a ea unce ain y, is he alue o he sensi i i y pa ame e ,
which in luences he peak loca ion p obabili y o he inexp essi e peaks.
High p obabili ies o loca ing peaks inc ease he incidence o he peak
loca ion o unexp essi e peaks, ha ing a high ela i e peak-a ea un-
ce ain y. The e o e, in he da a se s hey inc ease he mean peak-a ea
unce ain y. The co ela ion among he numbe o ene gies whe e he
peaks we e loca ed wi hin a da a se and u el is p esen ed in Fig. 7. He e,
he da a se s whe e he peak a eas we e calcula ed wi h he leas -squa e
me hod and he da a se s calcula ed wi h he ROI me hod a e deno ed
wi h open iangles and ull do s, espec i ely. I can be obse ed ha a
he same numbe o loca ed peaks, i.e., o da a se s analyzed wi h he
same e ec i e alue o he sensi i i y pa ame e , he mean ela i e
unce ain ies ob ained wi h he LSQ me hod a e smalle han hese
Fig. 3. Dis ibu ion o he da a se s o e he se -speci ic mean numbe o en-
e gies in one spec um, whe e a peak was loca ed.
Fig. 4. Dis ibu ion o da a se s o e he se -speci ic mean ela i e unce -
ain y
u el.
Fig. 5. Co ela ion be ween he numbe o peaks ha ing u
el
<u
el,Max
and u
el,
Max
/u el(a) and he co ela ion be ween he numbe o peaks wi h u
el
>u
el,Min
and u
el,Min
/u el (b).
M.C. Ali San o o e al.
Applied Radia ion and Iso opes 155 (2020) 108920
5
ob ained by he ROI me hod, as expec ed (Ko un e al., 2018). Fo he
da a se s comp ising mo e han 100 peaks, he ype o so wa e used is
iden i ied. In Fig. 8 he co ela ion among u el and he ela i e unce -
ain y needed o loca e a peak wi h a p obabili y o 0.95 is p esen ed. I
ollows om Fig. 8 ha some ypes o so wa e achie e a la ge mean
ela i e peak-a ea unce ain y wi h a p obabili y o de ec ion o 0.95,
despi e a smalle u el. By compa ing Figs. 7 and 8 i is clea ha his
occu s al hough he numbe o ene gies whe e he peaks we e loca ed
was app oxima ely he same. The eason o his is he be e selec i i y
o ecognizing inexp essi e peaks. These da a se s a e, in Fig. 6, loca ed
a he mean ela i e peak-a ea unce ain ies, which a e ecognized wi h
a p obabili y o 0.95, in excess o 30%.
I should be men ioned he e ha he da a se ob ained wi h he
Gamma-Vision so wa e di e s quali a i ely om he o he da a se s
(Fig. 2). This se was calcula ed in he lib a y-d i en mode. He e, he
spec um is no scanned o he p esence o peaks, bu he peak a eas a e
only e alua ed a p ede ined ene gies ha a e speci ied in a nuclide li-
b a y. Wi h his app oach he spec um is decomposed in o he con in-
uous backg ound and a peak a each ene gy, speci ied in he lib a y,
using he leas -squa es me hod. In his way, by a-p io i supposing he
p esence o a peak, he so wa e is “ o ced” o calcula e he peak’s
p ope ies. The ad an age o his me hod was ecognized al eady, since
he e he p obabili y o de ec ion is no gi en by he alue o he
sensi i i y pa ame e , bu by he c i e ia o ejec ing he supposed peak
(e.g., on he basis o he ene gy ole ance o he sign o he peak a ea).
In he case o Gamma-Vision i can be seen ha he es ing o whe he
a peak is p esen a a speci ic ene gy was no p e o med op imally. Fig. 9
p esen s he p obabili ies o loca ing he peaks, whe e he peaks loca ed
wi h a p obabili y subs an ially less han uni y a e iden i ied by hei
ene gy. I is ob ious ha he peaks a he highes ene gies we e loca ed
wi h a compa a i ely low p obabili y, which poin s o he c i e ia ha
ejec high-ene gy peaks.
Howe e , he e is a p ice o be paid o he good pe o mance in
ecognizing unexp essi e peaks. By compelling he so wa e o ecog-
nize peaks ha would no be loca ed o he wise he quali y o he esul s
is educed, since in hese cases he shape o he i ed spec um is less
compa ible wi h a peak on a con inuous backg ound. This has he
consequence ha he unce ain ies o he calcula ed peak pa ame e s
inc ease, and wi h hem he ela i e peak-a ea unce ain ies. The e o e,
hei dispe sion inc eases and wi h i also he mean ela i e peak-a ea
unce ain y and i s ep oducibili y. I can be seen in Figs. 1 and 2 ha
he la ges mean ela i e peak-a ea unce ain ies we e ob ained wi h he
Fig. 6. Dis ibu ion o da a se s o e he ela i e peak-a ea unce ain y needed
o loca e a peak wi h a p obabili y exceeding 95%.
Fig. 7. Co ela ion be ween he numbe o ene gies whe e peaks we e loca ed
wi hin a da a se and he se -speci ic mean ela i e unce ain y
u el. The da a
se s calcula ed wi h he ROI me hod a e deno ed wi h ull do s and he da a se s
calcula ed wi h he LSQ me hod wi h emp y iangles.
Fig. 8. Co ela ion be ween he se -speci ic mean ela i e unce ain y and he
ela i e peak-a ea unce ain y needed o loca e a peak wi h a p obabili y o
0.95. The da a se s calcula ed wi h he ROI me hod a e deno ed wi h ull do s
and he da a se s calcula ed wi h he LSQ me hod wi h emp y iangles.
Fig. 9. Co ela ion be ween he mean ela i e peak-a ea unce ain y and he
p obabili y o loca ing a peak in he da a se calcula ed in he lib a y-
d i en mode.
M.C. Ali San o o e al.

Applied Radia ion and Iso opes 155 (2020) 108920
6
lib a y-d i en analysis. This de iciency could be imp o ed by using he
penalized leas -squa es me hod (Kanisch, 2017).
I ollows om Fig. 1, ha mos o he peak-analysis p og ams using
he peak-loca ion me hod do no loca e peaks wi h he mean ela i e
unce ain y o 61% wi h he p obabili y exceeding 0.5. To inc ease his
p obabili y, he ollowing h ee possible ways can be ollowed:
To inc ease he p obabili y o loca ing unexp essi e peaks, a smalle
alue o he peak-signi icance pa ame e should be used, bu his can
cause an unaccep able incidence o spu ious peaks, i.e., ype-I e o s
(Ko un e al., 2017). The e o e his me hod should be complemen ed
wi h il e s o iden i ica ion o alse posi i es on he basis o e.g. he
peak’s ela i e a ea unce ain y and he ag eemen o he peak’s FWHM
wi h he calib a ed FWHM (Ko un e al., 2013). I should be no ed
howe e , ha he alue o he peak signi icance pa ame e can be
dec eased only o a alue, whe e o e lapping o peaks is excluded, since
hen he quali y o he peak-analysis esul s de e io a es.
Ano he way o inc easing he p obabili y o loca ing peaks close o
he decision h eshold is o inc ease he unce ain y o he peak a eas.
This can be done only on he basis o plausibly ounded a gumen s.
Many peak e alua ing algo i hms ake in o accoun only he s a is ical
unce ain y o he numbe o coun s in he peak and he backg ound
whe e he peak is supe imposed, bu do no conside he unce ain y
esul ing om he choice o he peak s a and peak end channels o he
ROI used o he e alua ion o he peak a ea (Ko un, 2008). When his
unce ain y is aken in o accoun mo e eliable decisions on he p esence
o a peak can be made.
To dec ease he occu ence o de ec ion o spu ious peaks, he peak
wid hs, as hey a e obse ed in he spec um, could be inc eased, i.e., by
acqui ing spec a a a highe con e sion gain se ing, co esponding o a
lowe ene gy pe channel alue. Then, o loca e a peak, he con en s o
mo e consecu i e channels mus exceed he a e age channel con en ,
which diminishes he p obabili y o ecognizing s a is ical luc ua ions
as peaks.
I ollows ha by a combina ion o he h ee me hods men ioned i
may be possible o inc ease he p obabili y o loca ing peaks wi h a
la ge ela i e peak a eas unce ain y.
5. Conclusion
I has been shown ha peaks wi h ela i e peak-a ea unce ain ies in
excess o 50% a e no loca ed wi h a p obabili y o 95%, excep in he
lib a y-d i en peak-analysis mode. Howe e , he disad an age o his
mode is ha in he case o unexp essi e peaks he peak-a ea un-
ce ain ies inc ease subs an ially, making hese peak a eas o limi ed use
o u he analysis. An al e na i e possibili y o inc ease he p obabili y
o loca ing small peaks is o use a smalle alue o he sensi i i y
pa ame e , bu his should be used in combina ion by app opia e
il e ing o dec ease he occu ance o spu ious peaks.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
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