a£esian a elet#%ased 1oisson intensit ... - Michel Desvignes

s cale parameter s . sing th is pr ior, we have s hown that the marg i nal pdf of of ..... er 100 trial simulation in estimating the Hoffman phantom intensity image as a .... D ata q uantiles v s G aussian q uantiles for each residual image before the in ...
473KB taille 3 téléchargements 45 vues
   " !  ! #  $   %&'( *)+,( ! ! -. *)+/ 10 * 2/ (3546  78 9( 2 -:! 9()+,( ! ;=@ACBED FHGJI KI:LNMO;,QNP RT&S U6Q AV.åo!@+†&Y%!/O4 0h|, &çå )9\-X$h!(*[åO)"~!@+(„b13&€&Y+@µ4,"æ5,SæI&\%!(ôY)æ(&! PI*%æU!@+@¾Y0&å:)*[,/;%ßY&g0æ(åô+/æQ;_;‰+(4N™æ2)a"!@!(©+ Y%å:,uo&-!@â! ;_"å +@13)‡&+rPI!âIå Y%,S"m)^+UPR!/!@Y%åO)."OåO,"S)O!(g!@T{"æ©V)æ6gæ©&0æUå 1-=!29$';qµ& åO045åÑOæ©Xæ(0&&X+©)_  å !(*%åÑY%æI+@4 &]h],")%*13&&æâæUPI+_™ )^™æ"æ2A !@!âK&5å 45&VP0$ !©åOæ()%4WXl+&]#!@&0&Y%!()%5YrO9QA8;-S!@ˆ‰!@Y%"& +@+@4”K‡åO+()¾0=åÑ+6,Sæ2!â"VåO),Nµ !@æ© ;‚åô9æ6åÑ# æ(,,"ä%0+(+@)."|9 !©V[ç"åôç"O†"=P\ ;ðæ(å: ,åO)çm; !@åO0"¡) ))åæ©; â! å !2æ…M 9^0µ O13Xæ(\%&&))©+ ,uå !(!⁠Y%å }&40) „ &0 8C ½ ºÌL ½ F H  F GZÌL º]L F " ,J º]L F "C»   ¼L2EG ¼ ”•æ()g*0!(%+ Y%æUq)%78*æâæb9&0™æÌ1Zå:0!@Y%)eWPR*%*%+@&"OS,/!.YeS`-j**%+©)åOæÌ&åO+5&)r;‚AåÑæUd8!(+âY%å V%N\%13!©&åO&O ).&Påôæ£åO)%åOXJ4WæU*=&N,u!âæUå=&;e)ø&åÑ)‹æå !()Y!@q")PR;-=;‰"!@OS&^!N*%,"+(&]&S|–lå:;-, €åO"))ø!âæ£åO)åO) !(+@&-&;-+/;-\",u+€!âå &!(&z)c!@,"&f*-7R!(\™+(æ©fæ("D!(Y>  130&O+@+@4 æ;%9€;‚åÑ&æUV!(+âæUå V%+(\%!©åO;N&)!@æm&1ŠV[0¡4£æ(å YO9ó0+@æU*%\¾O9€å !@*[V%O5h=!(&c;l0,/Y)0;l+/Y%,u!@"|+âåOåÈ ç9NN!@!(µY%å O ;6PRA'ˆc"0OS)]!95æU,/\Y%V%&µVå:,S0™)æD;‹13&,S+&]!(SY–låôæ,å *%+â)å !%&æm+;-Y)æÌQå !©V[åO*"æ€") PI*%Y¾+@å:&,/Yz*[&gYæ(;£5åO)lV["!(Y)  ô åo!@"+/!(\+(V ¡æ@," N£4 åo`]!(\+(W&01!2P&f)%&+(450D‚; åÑæU!(â+ å V%\%©! åO&) æ  } „'&+.&)%W)%&+(450D‚; åÑæU!(â+ å V%\%©! åO&)0);a *[µ& åO)!‡4Wg æ©æ.0! ç"+@&  }}ƒ%“‚k#"}} Œ „„{#AM;-K&&\%PV%Om"S+=`-#k*[4W&)%&gæU)!_©! &å:01Z6!(*%Yâ+ *åOæ(&N+Q*P +©å åO!(&Y‰+%æ,Wæ(*[\-µ&wkåO")+.!K1345+@&µ 4 æâæQ b! Oç,/"hq+@& &018 } ,"’ 0„*%#%!(!(\%Y+â€å )n_X ;5äo!(Yåôæ8‡k4NæU&-\¾;-å !@‡V%)OK;f4W &-*-;-!("&kh*%\+@+U&â! åO|,åOA';-=d8;NY!(bYx0â+!æU!@!8Y%!2_P+(&5™æU,S\%& )!©‚;åO)%å ©!X€åO&PR) æI"+(OS_!P ,"&å:;-""–lO9.&=:,u!(, &ç"+N9]h !@0 |h ~0åO„_)%oXYg å æ^)!(0&zÑ æU&g,",S*%&+(\%&)*!€N& æU!@=Y%;˜^g*04N+(©! "å:!(,SY%\&-O; +NV)µ æ(!(\; +(f&&0)˜1b!@!(Y%Y%ó qæU$'Y%µ& â+ åÑåOæâ)%æUh&0)‹Xa)%µ& &0åÑi1æ(fb); + *%åO4W;+@&-2\,SXæ2*  !%æâæ8æ(åÑ*æQ!(æYh]IA ‡)%Q&!(PIY%&+@PR)f*"æ(!(Y%& ä 789™ æÌå:0)^;-")µ& åÑæU+K;-* æ@,Sâ+ åOV=;fV& åÑæR!(Y%)‰0*%*%ô åO; &) !(¾Y åÑæ8!(+/0?) æ213&+(4W; åO4WXA

    !#"#$% &('"*)+$!,-'.% !(¡n YåOC" 0)€| !(Yä( åÑæÌå ç_45!(0+/X08)?æ2&0131[&,"+(&45\%)!â%! å æ&) 8 %(' X#&PI+âåo¾Y !@å:Y%,/4 kY åÑåÑæyæI!(µYæRI13+(&=O0O&ô åÈPç=æ©! åO&)€&0=1 å );-"*[");%")!†+@);-&4 $'µ& åÑæ©æ(&)©+ å:0V ™ æ./ %('1032 -s  %(' tu# }AIa4 }6K5& b) *%j *%O}69N5 8m7Z&0)%)b ; æU!(4 }6*55 #PR)"}95 " *O7áS!Då )!@æU+@!(=) æ2;N13&&0+(1[4 !(Y\ Iæ©å \)%æUX.\!@0Y%!O bb0+y+†xPR!(+âæ"ADOSd8!=AY%QQ;-&"PR!@"åO"+=,"#0&PR"–lQ, \ åOæ("I)!â!(æHY%b`c%([ )%'&)%0T{!†)%&+(45,/YN&È åô+âç"åO=";m)!@x0 !©!(åO&â+ ) æ _0); O&-,"0©! åO&)s +,)-rt80);l!@Y%m0*%*+(&‚` åO4W0©! åO&)f,S&]S–l , åO"); ! :*%(A@ R R F F @ R H F F >G@ R F F @ F `#IJ %(I' .K>G@ $ B R D& C $E R & @ $B C $-E F & H >G@ $RB &DC $E @ $-B C $R E F F F `#IJ %(G@ $B R &DC $E R & @ $ B RC $-E H & F >G@ $B &C R $-E F @ $-B C $E F ` %( $B &DC $E & $B &C $-E $B C $-E & $-B C $E

sŠ“t

%AIa‡)%&P +(*%:,Sb!(Ym;-S!/åOr,S&]S–l,å )!%æå )^=,/Yf&+âå )!/!âå &) µæR13& O&Pæ1  å P1 :*%R6@",AB"!'.C"ED996F!GIH&>.!4"0J$ >.J$">.!+K4LEKM?NO6"1,-9">.!P6""AJ$Q>.J$R">.!S6T?",LU2'6!'NO6"V7T..2W"O,.'G XP   SYcD)[Z;\$!  ]^]J$!

$

j*["?!P()*.8"R2#NT. ,.-9">?!S/4?2' ! ,6O,?2'!#LU8"5,?NO*'?F  !'2'.- 2#NT. "5,?87 ,L 96",.I$C"> ,6T?R-?!'?.F !#">.@-  7,&">?!4:4,6B" 9,F!42',T??"!J-BD), .!1$">0S2J,N.F 7 62#", ,7  G  NJ$ 2'T?@" WGH&>. ! .8"+.,?!'N -?!'?O2W"P">.! 6OF,,N  2J,N!J- POB"!'?C"ED 9,F!96- "S?8D !# !'2'.- 6.!'N WG 1!'T.NC",7)">? ! &'DB!'O6  +( -?!'?!#46!S ">?!P!'2',-0J $ ?T.?! !#,N > 5- ,.- ,7 "">?!'>?NO-?.F 6!P!'!'2W"! !'NCD 0">?! ">.C5-0,-97 ,T?"> J$'G

 H&>?!9 !#5,F,!   - M !#  0"O,N 3T.NO "O,  !'8"9 "O?F0">?! :;66B" B"!'?"%D O96F!6  7 T?.2#",3,7?">.!INO,F  ">?[,742J6NO?F;7 62#", @DS$>?2W>+">.!IOB"!'?C"ED+9,F,!$R6 3T.NC".N!J-+ 65-?!# ";,!' ">.!I!#7 69,?2'! ,7">?! !#">?@-? ,"> ">.!+NJ$RL1,.- >.F> L%2#T.B"4!#"".F GPH&>?! ?8" 6.!'N42'.6!S">.! ()* "56.87 696"  ,NOO- NO?! " ">.!+/1.2',3!;"56.87,96",  -?,>?!J- N.! &7 6;!J62W> - !'.,O?F!#">.@-=G&H&>?!+N 68"4"%$&.,.!#NO!'!'2W"! !'NCD 2',6!P">?! ,6T?4- !'.,O?F3"!'25>.? BT?!'&7 6;!J62W>0"5,.87,9 "O, G

XP bc

 "#$)+] L$ \ `$ %.-' ",$  

”•+@)‰"*%!@+@Y¾*åÑæ(æ¡")æ(!âæK,S!©!(åOY&N)6#[)]!@\%Y%4€€V*+(+‡&*&01&NæU =;^*%4NY&0"!(!(&Y%)&-æ.;Ÿ,Såô&æ.\%0)*!(*%;jÈåO;q!_!(!(&YN Q*T+@åo`-9f"D4WO&-,";‚0å:!©,"åO&y)c&)%)‰XµåO&!@Y%X+@æU*%Y])92æU&åO4W+A”X!™æ"åÑæ_A.Pd8Y% 'h])%&\%PIN)c&01†!(Y=0! ,/Y‰æ(\*,/åoYj`-"  ,S &\%\ )æ©©!å )åO)%X€XW!@*%Y%+@‡&]*%,"*+@&æâæR*[g&!29]æ(¾* ; *),,F! +,.-0/12354-76 L98 0: .? G=?@A;>?B? CC;?G  =3G.!GDP?>? ,-E#5G  G.%,>..8",.! F'8/4-., ".F " T.&) ?J$ B,">.?!' @O $R !#NO!W"V>?*),,F,! +HG6O6 ?,.-^3G2J65- '`_  !'N!#"&>?*),,F,!Ba /48D ?",.OAb +^G"cedfcT&3 L 35-gVW3c T/S\c,hcjik `= ?. G&: @>:B:  CCAB? G  ;l =Gm] G  ,NNO6" n'8/ ">.!'6D 7,S T.NC"C!'NT?", F,,N - !'2',C"O,aR">?! $& !'N!#";!' !'!'B"56", +UoNpqp psr*4 L J*VXcut Rv o    .? G*w l;\@2 L -QJ?F_ N!#D€ @? *‚4!#$„ƒ6W) …CBCBC@G  w\3G4G )!W2' 6N6- /+G.H;G"_ 6NO-?!' } L 2 L 23 v 23QP&/zVqM…/4$r†-Q1$2Te24K-`2V R J LL | VW-gV =&63  - F!P !' e=    G  9 / G /1@",.O-  *% G F,," .,- H;G ?,.6"6 q'_  !#NO!W"!'8"96",R .,. 5,!#"2;!#F,!'mIa / 2', 56" !P3T?NO6L " 8"T.- D +FG?+ 61LU5'D !J- 2J,N ,?FF65,?>@D 67">?!  !J,8"JG;?NCD  *#B , 9!'2' .2 !'F,O, P>?J$ G H&>.! .8";O96F! O4">.! ,F6N*'B!J-V!'F,O, 67 B"!#!'8"JG0H&>.!?8" 2#NT.  2 ! F O96F!' P>? $+">.! !'T.NC" ,71- !'.,O?FVT..F ">?!()*"5,.87,9 "O, ,.- ">.!!#2'.2',NOT?   - 7 > 9,F,!' &2',!',- 1"3">?!+/4?2' !4"5,?87 696" $C"> ">?!P,!+- !'.,O?F9,NF6">?'G   %L  +(G  2 %L  - LU8"5,.N!G  ! %L  7 &>.65-0T?. !#6N "> !'>.,NO-?.F G  F %L  > ,7 "1T.. !W,N=">?!'>?NO-?.F G

pb+âåOXµåO)0

 i S6"5 BT,B"N!' @]P,T.O6 BT6@"N!' 7 , !J,25> !# - T6NSO96F! !#7 6! ">.!  !#! "5,.87,9 "O,  ()* , /4?2' ! P6..N!J-=GH&>.!.8"49,F,! >?J$1">?!3K4LEK .N6";67 ">.!S!'O-?T.,N96F!S$C">.T "P6BD0"56.87 696" 6..N!J- , ">.! .,O8D 6F6NI9,F,!G3H&>.! ?8"+2'NT?   2 ! F 9,F!# ;>.J$P">.! K4L8K .N,"ST?.F9">.! ()*3"56.87,96", ,.- ">?! !'2',-2',NOT?  - 7 >99,F,!' I2'6!'.-?"S">.!4/4?2' !R"5,.87,9 "O,$">9">.!1,!4-?!#..F ,NF,,C">.'G   %L   +(G  2 %L  - LU8"56.N!G  ! %L  7 > 5-0T?. !#6N "> !'>.,N - .F?G  F %L  > ,7 "4T?. !#6N "> !'>.,NO-?.F G

 C\G SNO,2#*#D") '_  !'N!#" >?*),,F,!R!'8"96"672'!#"56O,B"!'.C"ED F.,NIT?.FS2'6!'2#"!J- "> !'>.,NO-? +T*3 L 35-gVW35-0S L T*-gJ&-0S Y .. G  C\@:B? CCBC@G   \ )G=(?DL *'N!#$2'* 6- ] G )G‚P6 .'8/ $R !'N!#"L .* ,NF,,C">.^7 ,P @"!#.C"EDV!#8"O9 " +9"!'25> G!' G ;!' "!'B" ,7   ">.!'9 "2' 4. !#C"ED 67I8"N m=  A=BG    =Gj] G  6NN  " R } L 2 L 23 3`/lI"4/NMVW-7{J LBL 4 /SK2VWVK-QJ..96 RG SNO,2'*WD&) 16- +G  2JT.NNB2W> Z'E/;-?,?" ! 'DB!'O, $R !'N!#"0>?*),,F,! + G"c R 1cnT*3 L 35-gVW3c R VWVXcDY . G X; …:\ @ X;>=  CC @G  :\  G@NCD?-?! .,NO-?.F @   .'DB!'O,0,?? 62W> +FG"cd9cT*3 L 35-gVW3c†Tj/S\c , ˆ*[ ?. G =B?…@ l;BC …CBCB@x G  \? 4Gl;y O-.l)  @O2,.-3(G 4T?FF,!# ' &, !#">?@-ma H&>.!'6D ,-+3T?N  ". P+ "!'25> GJ!# G A#%.8"C"T?"!I,7 B"56"8"2' ,.- P!#2'O,  2'!'?2'!' &PT*) !;?! !#C"ED &=   @G  w\ G)G @O,.2'!#NON=6-G@: G@/;- !'N '(;‚ ,!;!' 6N @O .JD !'O,$R !'N!#"&2',.F +  rP>-g4 z oKJ&3  L  /JMh/JZoK1 L {>2t 4 /S ?. G&: C\@>:BxB= e#     F B2  B2'!#"%D 0! ,T?,?.! CCBw G    =GI>.,.F 4G Iƒ T ,-  GqIy !W""!#N 8' /4-., " !0$& !'N!#"">?!'>?NO-??F 7 699,F! -?!'?.F 6- 2' !' +oNpqp p r*4 J*V SX35-0/J&V/JoK1 {>2tD4N/SK2VKVW-gJ>{ Y 0C .? G \?=B=… @ \?l:  †=    G  x\ =G.L >6L .F 4G?!'>?NO-??F $C"> 2',@"!  "&@-?!'N.F 7 ,19,F,!S-?!#.8L .F +ZoNpqp p r*4 J&VXc oK1 {>2nt 4 /SK2VWVW-gJ. R/+G L !'*'!#O6L . ;,.- )GH&,) ,NO-?!' ^'(4‚  !'N1'DB!'O, 3T.NC"2J6NO!V!W">.@- 7, !'2K@) NO! !# ,,N !J- 2J,N T.NC"5,,T..- 9,F!# +$oNp pqp r*4 J*VXc v 2WzAcoK1 {>c [ .? G =@ lxB: =   G  = \ 4G†! Gm;‚  @)  6 ,-  G  >6 T*-7L {J LBL t 4 /SK2VWVW-gLJ=C =  G  =B=9 / G @ 68"5   GA! T @6- G@"!WD? ,.-ZW# G D?*#>. ) r L h L 2/(M9-QJ*320{4 LBL V  V…24K-`2V L Jz  4 /zI&SX35V /42'-?!#O2 !' . G8!#