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1 i RBjZ$Bt {B% k PB j$rt8bi {BtR Z{$Bt $t _e]q NZ{ i BZb tr <Bbs I p$&b I G i$, zst I Gsjj ${Ys j V $t G yts{ N 8sY$ Z izi$ V *$ {,- eny * }s 8 t e*yy_ y yqe]< py t =t$% R$k $tt_$ Rt$ ZbR ss ;d T((( py t j$z8 G =t$% R$k BP srrs{yzr R I${sj {YBBj *$%$R$Bt BP WZ{j s I${$t xx Ns, V% WB Y GB { R V =V WZ{j s I${$t * } py t =t$% R$k <BR}$sj * _$t jsst dmx T((( py t j$z8 V qiv]q qy }Z }BR BP Y RZIk bsr B %sjzs Y RBjZ$Bt {B% k $t j$rt8bi {BtR Z{$Bt PB _e]q yt Y$R RZIk b {B8}s Y } PB 8st{ BP Y } B}BR I 8 YBI B BY $ s$% RBjZ$Bt {B% k 8 YBIR $t Y {sr BP I$& t tb$r j % jr G I % jb} I st $ s$% {BtR Z{$Bt 8 YBI by${y ZR R j$rt8bi Iss $tr si BP A$tt I Iss qy t b sjb $Y8 8s, R ZR BP s 8B s{{z s 8BI j BP Y {Bjj$8sB R Z{Z G {B8}s I Y _e]q j$rt8bi {BtR Z{$Bt B Ne!e sti i y sjj $t{jzi$t RBjZ$Bt {B% k 3B Y %sjzs$bt b ZR I pszrr$st RYs} I RBZ { R b$y I$& t 3G< s Y I$& t jb{s$btr sti Y tb$r j % jr 3B Y R I$R $AZ$BtR b {sj{zjs I Y {BtR Z{ I $8s R s I$& t tz8a BP $ s$btr qy sarbjz B PB Y {BtR Z{ I $8s R bsr ZR I B %sjzs Y } PB 8st{ qy } PB 8st{ BP sjj PBZ 8 YBIR $R {B8}s saj PB Y RBZ { R jb{s I $t Y { t BP Y h ji BP %$ b 3B Y RBZ { R jb{s I BZ BP Y { t Y B BP Y j$rt8bi 8 YBI $R R$t$h{stjk jbb Yst Y BY 8 YBIR G I % jb} I s 8 YBI PB RBjZ$Bt {B% k $t _e]q {BtR Z{$Bt ZR$t j$rt8bi Iss qy 8BI j$t BP Y RBjZ$Bt $t Y$R sjb $Y8 j sir B s A RBjZ$Bt {B% k }j$$t Y RkR 8 $tb s R }s s BA` { I } ti t sti I {B I } ti t 8BIZj $% R ZR s 4 -$Aj {BtR Z{$Bt 8 YBI G$Y Y$R b {st % k srk sis} Y RBjZ$Bt {B% k B I$& t {Bjj$8sB k} R kbb IRU N$RT8BI NyiV {BtR Z{$Bt RBjZ$Bt {B% k _e]q d ywqi!*=]qy!w $t{ Y I % jb}8 t BP $tj _YBBt e8$rr$bt ]B8}Z I qb8b s}ykw_e]qd hj I As{, } B` {$Bt YsR A t s RstIs I 8 YBI PB $8s {BtR Z{$Bt qy 8s$t I sbas{, BP Y$R sjb $Y8 $R Ys $ {st tb $t{b }B s Y } B} $ R BP Y s{jz$r$$bt sti Y s{jz$ I Iss $t B I B I sj b$y tb$rk Iss }YBBt $t s{$bt sti I {B {Ys s{ $R${R yt Y R {BtI t s$bt {BtR Z{$Bt sjb $Y8R $ A {s8 }BRR$Aj B 8BI j Y tsz BP Y } B` {$Bt Iss Ak $t{b }B s$bt BP Y _B$RRBt Rs$R${R sti s{{z s 8BI j$t BP Y s{jz$r$$bt RkR 8 Vjj } %$BZR I % jb} I _e]q {BtR Z{$Bt 8 YBIR ZR } B` {$Bt Iss A$tt I $t } I ht I s skr qy$r j sir B s I$R{ $9s$Bt BP Y $tpb 8s$Bt b$y s j$8$ I } {$R$Bt yt _e]q s{jz$r$$bt Y $R I } B` {$Bt s sk $R ZRZsjjk BP Y R$9 dm - dm }$- jr 3B Y stzjs Rs8}j$t Bt BP t $Y ZR R s R } sti RYBB s{jz$r$$bt } BB{Bj s{jz$ $t d( } B` {$BtR B% ne( I R B $Y {Bt$tZ R Bs$t YZR RZ88$t } B` {$Bt $tpb 8s$Bt B% n I R N$RT8BI s{jz$r$$bt BP _e]q } B` {$Bt Iss } B%$I R R % sj si%sts R B% P s8 8BI s{jz$r$$btr 3$ Rjk Bt {st RB Y $t s{$bt jb{s$bt B s Y$Y I BP s{{z s{k w, Ak, PB -s8}j D b$y s ^{$ t{k Yst s{y$ %saj b$y P s8 8BI s{jz$r$$bt {BtIjk Bt IB R tb t I B A$t Y st k stj R $tb } I ht I P s8 R AZ {st {B I Y s{zsj stj Y Ak 8B%$t Y $8}s{ BP stzjs AjZ $t b$y ti {B R}BtI t{ B et8s$ju NZ{ BZb tro Zs{A 4 Medical Imaging 2: Image Processing, Milan Sonka, Kenneth M. Hanson, Editors, Proceedings of SPIE Vol (2) 2 SPIE //$5.

2 {Bt$tZBZR s{jz$r$$bt qy$ Ijk Bt {st {B I Y s{zsj t k BP Y $t s{$bt $tr si BP s $AZ$t Y % t:r t k B Bt BP s j$8$ I tz8a BP } TI ht I b$tibbr y $R BA%$BZR Ys by t $t{ sr$t Y I$8 tr$btsj$k $t Y$R bsk $ $R tb jbt }BRR$Aj B A$t Y Iss $tb s 8s $- qy s sk PB A$tt I Iss $tb s, -, 8s $- PB ne( I {B stj R sti d( t k A$tR bbzji {Bts$t B% dx A$jj$Bt j 8 tr 3B RZ{Y s {sr RB $t Y s{jz$ I % tr b$y Y $ }s s8 R {st RZj $t s IZ{$Bt $t Y JZ$ I Iss R}s{ b$y s Ps{B BP B% x(( 3$tsjjk j$r 8BI {st sjrb RB s$t R$tsjR b$ybz Y t I PB 8}B sj P s8$t BP Y Iss A PB Y$R $tpb 8s$Bt $R {B8}j jk s%s$jsaj qy RZj $R s R$t$h{st $t{ sr $t Y hi j$k BP {B I$t Y } B` {$Bt Iss b$y j$rt8bi s{jz$r$$bt b$ybz s 8 tibzr $t{ sr $t RB s R}s{ yt Y hj I As{, } B` {$Bt 8 YBI I {Bt%BjZ$Bt sti RB s$bt hj R {st A ZR I B {B { PB Y B8 ${ R}BtR dun qy RB s$bt hj R s R}s$sjjk $t%s $st PZt{$BtR I $% I sr st s}} B-$8s$Bt BP Y AjZ $t qy I$Rst{ I } ti t {Bjj$8sB AjZ $t {st sjrb A $t{b }B s I $tb Y 3BZ $ strpb 8 BP Y R$tB s8 8s,$t ZR BP Y P JZ t{kti$rst{ } $t{$}j yt $ s$% {BtR Z{$Bt $ $R }BRR$Aj B $t{b }B s Y I {B R}BtR $tb Y } B` {B \As{,T} B` {B }s$ B {B8} trs PB Y I$Rst{ I } ti t I {B R}BtR IZ $t Y s{jz$r$$bt ; qy s{{z s{k BP Y R {B {$Bt 8 YBIR I } tir Bt Y s{{z s{k BP Y 8BI j qy I {B R}BtR {st A 8 srz I ZR$t }B$t RBZ { R B {st A {sj{zjs I ZR$t Y RYs} sti R$9 BP Y {Bjj$8sB sti -} RR I sr Y }B$t R} si PZt{$Bt BP Y $8s$t RkR 8 yt Y PB bs I B} s$bt Y RBZ { I$R $AZ$Bt s s{y jb{s$bt $R 8Zj$}j$ I b$y Y }B$t R} si PZt{$Bt s Ys I$Rst{ B BAs$t Y } B` { I Iss Bt Y s{jz$r$$bt RkR 8 yt Y$R {sr R Y RBZ { I$R $AZ$Bt $R I$ {jk } B` { I BtB Y Iss R}s{ $88 I$s jk s,$t $tb s{{bzt Y I {B {Ys s{ $R${R yt Y$R }s} Y RBZ { I$R $AZ$Bt $R } B` { I BtB st $t 8 I$s jsk A b t Y BA` { R}s{ sti Y I {B R}s{ V s{y jb{s$bt $t Y RBZ { I$R $AZ$Bt st $RB B}${ 8$RR$Bt BP }YBBtR b$y Y I {sk t k $R t s I pb$t P B8 Y BA` { R}s{ B Y $t 8 I$s jsk Bt Btjk YsR B I sj b$y Y BA` { {Ys s{ $R${R RZ{Y sr }YBBt 8$RR$Bt sti } B}ss$Bt BP }YBBtR Y BZY Y BA` { $t{jzi$t s tzs$bt sti R{s qy R } P B8 Y $t 8 I$s jsk B Y I {B b$jj s, $tb s{{bzt Y } I 8$t I Ys Ibs {Ys s{ $R${R BP Y I {B RkR 8!t $8}B st si%sts BP Y$R s}} Bs{Y $R Ys $ Ps{$j$s R sis}s$bt B I$& t {Bjj$8sB R w{bt TA s8 PstTA s8 }$ttybj D sti k} R BP s{jz$r$$bt w_e]q sti {B$t{$I t{ $8s$t 8BIsj$$ RD *kts8${ s{jz$r$$btr B}$8$9$t {s I$s{ sti R}$ sb k s$t sti % t j$rt8bi s{jz$r$$bt {st A t h P B8 Y$R P sz yt Y$R }s} Y I {B {Ys s{ $R${R RZ{Y sr Y {Bjj$8sB sti s{jz$r$$bt }s s8 R s $t{b }B s I $tb Y $ti$%$izsj R }R Y Ak sjjbb$t RBjZ$Bt {B% k sti B} t$t Z} B ht Rs8}j$t BP Y I {B R}s{ yt Y$R bb, b b$jj -}js$t YBb Y 8BI$h I } B` {B \As{,T} B` {B $R bb,$t sti YBb j$rt8bi {BtR Z{$Bt {st A s{y I ZR$t Y R B} sb R qb %sjzs Y RBjZ$Bt {B% k } PB 8st{ BP Y j$rt8bi {BtR Z{$Bt b ZR I pszrr$st RYs} I RBZ { R b$y I$& t 3G< s I$& t jb{s$btr 3B Y$R %sjzs$bt b t s I Iss R R PB Y I$& t tb$r j % jr 3B Y R I$R $AZ$BtR b {sj{zjs I Y {BtR Z{ I $8s R s I$& t tz8a BP $ s$btr sti ZR I Y sarbjz B B %sjzs Y } PB 8st{ G {B8}s I Y _e]q j$rt8bi {BtR Z{$Bt B Ne!e sti i y sjj $t{jzi$t RBjZ$Bt {B% k d _ B` {B \As{,T} B` {B q<e!io G I$%$I I Y } B` {$Bt B} sb $tb bb R }RU dd {sj{zjs$bt BP Y 8$RR$Bt si$st{ I$R $AZ$Bt sti D Rs8}j$t BP Y I$R $AZ$Bt b$y s {Bjj$8s I I {B qy$r sjjbbr PB Y R }s s$bt BP Y BA` {T I } ti t sti Y I {B TI } ti t sr} {R BP Y } B` {$Bt B} s$bt tbbj I BP Y s tzs$btt {B ^{$ t I$R $AZ$Bt b$jj A srrz8 I Y BZYBZ Y$R }s} VjYBZY sjtbb ji RBZ { I$R $AZ$BtR s {Bt$tZBZR sp } R t$t Y RkR 8 JZs$BtR Y I $% I } B` {B b$jj ZR s I$R{ $9 I } R ts$bt BP ABY Y RBZ { I$R $AZ$Bt sti Y s tzs$bt 8s} Proc. SPIE Vol

3 S θ F(φ, θ) P(r, ϕ) r ϕ φ R E(r,ψ) µ(r,ψ) C 3$Z d 3B bs I } B` {$Bt BP Y RBZ { I$R $AZ$Bt BtB Y $t 8 I$s jsk dd e8$rr$bt si$st{ I$R $AZ$Bt ]BtR$I Y BA` { R}s{ RZ BZtI I Ak s {Bt% - t{jbrz whz dd yt Y$R }s} b ZR s {$ {Zjs t{jbrz AZ Y {sj{zjs$bt {st A {s $ I BZ PB BY RYs} R sr b jj G P B Y$R t{jbrz sr Y $t 8 I$s jsk qy h R R } $t BZ } B` {B $R B {sj{zjs Y 8$RR$Bt si$st{ I$R $AZ$Bt B PB Y$R jsk ]BtR$I Y {Bt$tZBZR RBZ { I$R $AZ$Bt ow, D -} RR I $t }Bjs {BB I$ts R $t s tbttzt$pb 8 s tzs$t BA` { b$y s tzs$bt {B ^{$ t I$R $AZ$Bt w, D qy s 8stk bskr BP }s s8 $9$t Y } B` {$Bt skr Y BZY Y$R RBZ { I$R $AZ$Bt 3B -s8}j Y $R Y RstIs I w&, D }s s8 $9s$Bt BP Y -T sk strpb 8 x b$y & A $t Y st k stj sti Y }BR$$Bt Bt Y {s8 s Ps{ Vj ts$% jk b {YBBR B $I t$pk Y skr Ak Y }s$ BP stj R w*, D RYBbt $t hz d yp Y si$zr BP Y {$ {Zjs t{jbrz $R d Y }B$t C d YsR }Bjs {BB I$ts R wd*d qy stj PB s{y }B$t h w (,D BP Y RBZ { I$R $AZ$Bt ow, D {st A {sj{zjs I sr PBjjBbRU wh, *D ) ylx d ( 3LXw *D d 3 ( 3LXw *D L (, wdd qy$r stj $% R Y I$ {$Bt BP Y }YBBtR {B8$t P B8 _ $t by${y Y k b$jj j s% Y t{jbrz s C d js$% B * qb BAs$t Y si$st{ I$R $AZ$Bt P B8 _ s C d $t I$ {$Bt B w*, D Bt {st ZR Y,tBbt -} RR$BtU 8 Ce B w*, D ) o 3 -} w w, D3QXD, wd b$y o Y %sjz BP Y RBZ { I$R $AZ$Bt s sti w, D Y {Bt$tZBZR s tzs$bt {B ^{$ t I$R $AT Z$Bt qy Bsj 8$RR$Bt si$st{ I$R $AZ$Bt B w*, D s }B$t C d {st A {sj{zjs I Ak $t s$bt BP Y PZt{$Bt B B% Y j$t Y BZY Y BA` { I ht I Ak * sti qb {sj{zjs Y 8$RR$Bt si$st{ I$R $AZ$Bt B w*, D PB s I$R{ } R ts$bt b I$I tb ZR Y {sj{zjs$bt BP B PB s{y $ti$%$izsj }$- j b$y $R s{$%$k { t I s Y 8$IIj }B$t AZ ZR I s skt s{$t 8 YBI b$y Y s{$%$k $t s{y }$- j Zt$PB 8 I$R $AZ I B% Y }$- j s s qy {$ {j I ht I sr Y $t 8 I$s jsk $R Rs8}j I s C d jb{s$btr B } $8s k R{stt$t }B$tR by $R Y $ti - ZR I B tz8 s Y %sjz R BP Y stj R * A b t Y YB $9Btsj Ts-$R sti Y {$ {j si$zr {Bts$t$t Y {B R}BtI$t } $8s k R{stt$t }B$t C d whz D V s{y BP Y } $8s k R{stt$t }B$tR Y }YBBt si$st{ sr s PZt{$Bt BP Y stj js$% B Y tb 8sj B Y {$ {j s C d $R {sj{zjs I P B8 Y RBZ { I$R $AZ$Bt sti s tzs$bt 8s} Ak ZR$t s R BP R {BtI R{stt$t }B$tR C i G$Y Y } $8s k R{stt$t }B$t A $t h- I Y C i :R s sjj Y BY R{stt$t }B$tR Bt Y {$ {j qy si$st{ s jb{s$bt C d $R 42 Proc. SPIE Vol. 4322

4 S i θ F(φ, θ) φ 2 R S 2j φ µ(x,y) 3$Z 3B bs I } B` {$Bt BP Y RBZ { I$R $AZ$Bt BtB Y $t 8 I$s jsk {sj{zjs I PB s{y stj i Ak Rs $t s Y } $8s k R{stt$t }B$t sti } B{ I$t sjbt Y }sy I ht I Ak Y j$t A b t C d sti C i qy si$st{ PB Y$R }sy $R Y RZ8 BP Y s tzs I }$- j s{$%$$ R b $Y I Ak Y }sy j ty Y BZY Y }$- j qy s tzs$bt Ps{B $R Y RZ8 BP Y } BIZ{R BP Y s tzs$bt {B ^{$ t sti Y }sy j ty s% R I Z} B Y$R }B$t sti YsjP Y } BIZ{ BP Y }sy j tyr sti Y s tzs$bt {B ^{$ t PB Y }$- j $t JZ R$Bt qb I 8$t Y s}} B} $s }sy j tyr st $8} B% I $IIBt sjb $Y8 E $R ZR I *B$t Y$R PB Y C d } $8s k R{stt$t }B$tR b b$jj st 8$RR$Bt si$st{ I$R $AZ$Bt B w*, D $t stzjs {BB I$ts R Rs8}j I Bt s Zjs $I $t w*, D R}s{ _ B} jk tb 8sj$9 I Y$R I$R $AZ$Bt {st A R t sr Y } BAsA$j$k I tr$k RZ Ps{ PB I {$t s }YBBt s s { s$t R{stt$t }B$t B$t $t s R} {$h{ I$ {$Bt d s8}j$t si$st{ b$y {Bjj$8s I I {B yt Y$R }s} b {BtR$I Iss s{jz$ I P B8 st BA` { $tb s } B` {$Bt R$tB s8 b$y jb{s$bt BP $t{$i t{ sti st k stj A$t & qy {Bjj$8sB I$R{ZRR I } $8s $jk $t Y$R }s} $R s }s sjj j YBj {Bjj$8sB qy sr BP {Yst$t B PB -s8}j s PstTA s8 {Bjj$8sB b$jj A I$R{ZRR I sp bs IR $t{ b }jst B ZR (;M I {B A$tR PB s{y Rj${ $t Y s{jz$r$$bt M Y$R b$jj j si B s Rs8}j$t ht Yst Y {Bjj$8sB YBj R$9 3B {BtR Z{$Bt b }js{ s {Bjj$8sB YBj B% Y { t BP s{y BP Y I {B A$tR 3 B8 Y ABB8 BP Y {Bjj$8sB YBj Bbs IR Y $t 8 I$s jsk w$ Y {$ {j RYBbt $t hz dd b b$jj R s P s{$bt BP Y {$ {j N$t R I sbt P B8 Y BZ 8BR }s R BP Y {Bjj$8sB YBj R B% Y I R BP Y {Bjj$8sB R }s B Y {$ {j R ${ Y s { R t qy R $t R {$Bt }B$tR {B R}BtI b$y{ d sti { whz nd V Y R R{stt$t }B$tR Y -$RR Btjk Bt 8$RR$Bt stj PB by${y s sk b$jj A s{{ } I $t Y {Bjj$8sB YBj GY t 8B%$t B s R{stt$t }B$t A b t { d B { Y st BP s{{ }saj 8$RR$Bt stj R wi tb I Ak D b$jj $t{ sr GY t s{y$t Y } } ti${zjs } B` {$Bt BP Y {Bjj$8sB YBj b$jj s{y $R 8s-$8Z8 sti b$jj I { sr A kbti Y$R }B$t ]sj{zjs$t Y %sjz BP {B R}BtI$t b$y Y R{stt$t }B$tR jk$t A b t { d sti { b I 8$t Y $Bt \w*, D $t Y w*, DTR}s{ {B R}BtI$t b$y Y }B $Bt BP B w*, D P B8 by${y }YBBtR {st s{y Y I {B jb{s$bt ZtI $t% R$s$Bt whz ;D GY t b $t s Y 8$RR$Bt si$st{ I$R $AZ$Bt B w*, D B% Y $Bt \w*, D b Y {Bt $AZT $Bt BP Y 8$ I }YBBtR P B8 Y Bsj RBZ { I$R $AZ$Bt $tb Y R} {$h{ I {B A$t IZ $t } B` {$Bt qy$r {st sjrb A IBt PB Y $ti$%$izsj }$- j {Bt $AZ$BtR yt Y As{, } B` {$Bt R } \w*, D I ht R Y $Bt BP Y BA` { $tb by${y Y {BZtR $t Y I {B A$t b$jj A As{,} B` { I sti Y PB b$jj I }${ YBb Y I { I }YBBtR PB s R} {$h{ I {B jb{s$bt b$jj {Bt $AZ B Y As{,} B` { I $8s =R$t Proc. SPIE Vol

5 φ δ φ 2 I I 2 θ θ θ 2 t 3$Z n _ B` {$Bt P B8 Y {Bjj$8s I I {B BtB Y $t 8 I$s jsk θ θ θ φ θ 2 φ φ 2 3$Z ; V s } B` { I $t Y w*d R}s{ PB Bt I {B A$t Y$R s}} Bs{Y $t Y } B` {B sti Y As{,} B` {B b Ys% {B8}j jk $t{b }B s I Y I }Y I } ti t RBjZ$Bt BP Y s{jz$r$$bt RkR 8 N$RT8BI {BtR Z{$Bt G Rs I P B8 Y h- IT}B$t $ s$bt R } $t Y j$rt8bi 8s-$8Z8Tj$, j$ybbi {BtR Z{$Bt sjb $Y8 Ys bsr I % jb} I PB _eq Ak _s s sj d( U W w>ldd q ) ]3 i)d w4 i /qd3w w>d q - )d w4 i /D3X 3W w>d wnd yt Y$R JZs$Bt W w>d $R Y -} { I tz8a BP }YBBtR 8$ I P B8 RBZ { A$t } Zt$ BP $8 PB Y > _ $ s$bt sti X $R Y R tr$$%$k PB Ys RBZ { A$t ] $R Y tz8a BP j$rt8bi % tr h w4 i /D $R Y } BAsA$j$k I tr$k Ys s I { I % t t s I $t A$t j sir B s 8 srz 8 t 4 i $t Y I {B Ys $R ZtI $t% R$s$Bt - $R Y tz8a BP RBZ { A$tR qy$r JZs$Bt {st A $t } I sr Y RZ88s$Bt wb% sjj j$rt8bi % trd BP Y } BAsA$j$$ R Ys s }YBBt Ys B $$ts I s jb{s$bt q j sir B Y j$rt 8BI % t i 8Zj$}j$ I Ak Y, _ R$8s BP Y RBZ { %sjz $t q I$%$I I Ak Y Bsj } BAsA$j$k Ys stk }YBBt P B8 Y Bsj R$8s I RBZ { I$R $AZ$Bt j sir B Y$R j$rt8bi % t 44 Proc. SPIE Vol. 4322

6 Uniform source distribution Calculation of radiance distribution F (k) List of data Calculation of A j Calculation of integral of F l (k) over A j Numerical Integration of F (k) over A j j=, N Image updating Result k=, number of iterations 3$Z x 3jBbT{Ys BP Y {BtR Z{$Bt sjb $Y8 qy h R }s BP Y JZs$Bt {st A {sj{zjs I sr PBjjBbR qy RBZ { R$8s s s{y jb{s$bt q b$jj A } B` { I $tb Y w*, D R}s{ k$ ji$t B w*, D q qy$r } B` {$Bt b$jj A R ${ I Ak Y j$rt8bi R} {$h{ s{{ }st{ $Bt \w*, D BP Y {s8 s qy$r {st A $t } I sr Y P s{$bt BP Y $RB B}${ }YBBt 8$RR$Bt P B8 jb{s$bt j Ys {st j si B Y$R j$rt8bi % t qy R {BtI }s BP Y -} RR$Bt {st A I $% I Ak Rs8}j$t Y 8$RR$Bt si$st{ I$R $AZ$Bt B w*, D ZR$t Y $Bt \w*,d by${y b$jj A Y P s{$bt BP Y Bsj }YBBt 8$RR$Bt Ys {st j si B Y$R j$rt8bi % t qy PB Y JZs$Bt {st A b $ t sr PBjjBbRU W w>ldd q ) ]3 $$\ i B w>d q $$ i)d w*, D \ i B w>d w*, D w;d by \ i $R Y j$rt8bi R} {$h{ s{{ }st{ s s B w>d q $R Y si$st{ I$R $AZ$Bt PB }$- j q PB Y > _ R$8s sti B w>d $R Y Bsj si$st{ I$R $AZ$Bt PB Y > _ RBZ { R$8s qy sjb $Y8 Z}Is R Y R$8s BP Y RBZ { I$R $AZ$Bt PB s{y j$rt8bi % t yt Y$R bsk Y bbti$8 tr$btsj $t sjr $t Y tz8 sb {st A {sj{zjs I Bt Y 4k sti IB tb Ys% B A RB I VP s Zt Y BZY Y j$rt8bi Iss R Y 8$RR$Bt si$st{ I$R $AZ$Bt $R {sj{zjs I sti ZR I $t Y t - $ s$btqy } B{ RR BP Y {BtR Z{$Bt sjb $Y8 $R } R t I sr s 4BbT{Ys $t hz x n eq<!* yt Y PBjjBb$t R {$Bt b b$jj -}js$t YBb Y %sjzs$bt BP Y RBjZ$Bt {B% k PB Y I$& t T {BtR Z{$Bt 8 YBIR bsr } PB 8 I 3$ R b I$R{ZRR YBb Y Iss R R b t s I ZR$t Bt ]s j R$8Zjs$BtR {BtIjk b b$jj $% st B% %$ b BP Y {BtR Z{$Bt 8 YBIR 3$tsjjk b -}js$t Y }s s8 R ZR I $t Y Iss stsjkr$r nd Bt ]s jb R$8Zjs$BtR qy yeq Bt ]s jb R$8ZjsB dd bsr ZR I B t s Y Iss R R yt B I B $t% R$s Y } PB 8st{ BP Y RBjZ$Bt {B% k 8 YBIR b t s I R$- RBZ { I$R $AZ$BtR $t s$!t YsjP BP YBR b pszrr$st RBZ { I$R $AZ$BtR b$y s 3Zjj G$IY s <sjp s-$8z8 w3g<d BP d 88 by${y $R js Yst Y RkR 8 RBjZ$Bt qy BY YsjP bsr t s I P B8 s pszrr$st RBZ { I$R $AZ$Bt b$y E 88 3G< YZR R8sjj Yst Y RkR 8 RBjZ$Bt A $t M 88 s s I$Rst{ BP d( {8 P B8 Y Ps{ BP Y {Bjj$8sB 3B s{y R$9 pszrr$st RBZ { I$R $AZ$BtR b { s I PB Y pszrr$st s Y { t Proc. SPIE Vol

7 BP Bs$Bt w]!id sti sti d; {8 BZ P B8 Y$R ]!i qy $t}z B Y Bt ]s jb R$8ZjsB b xd-xd 8s ${ R B 8s, RZ Y pszrr$st RYs} bsr } R % I 3B s{y BP Y R RBZ { I$R $AZ$BtR b t s I Y I$& t R$8Zjs I Iss R R {B R}BtI$t b$y Y I$& t tb$r j % jr qy Bsj tz8a BP I { I }YBBtR $t Y Y BZ}R b x((( d(((( sti dx((( {BZtR qy$r $% R s Bsj BP dm R$8Zjs I Iss R R qy s{jz$ I Iss b RB I sr j$rt8bi Iss b$y s Rs8}j$t BP (;M I {B A$tR BP (dx 88 sti ne( I {B stj R qy$r Iss bsr A$tt I B dm A$tR BP ndx 88 sti d( } B` {$Bt stj R PB ZR b$y Y RstIs I $ s$% {BtR Z{$Bt 8 YBIR n i {BtR Z{$Bt 8 YBIR qy dm Iss R R b {BtR Z{ I b$y Y PBZ I$& t {BtR Z{$Bt sjb $Y8R qy Iss b {BtR Z{ I $tb s dm-dm 8s $- qy j$rt8bi {BtR Z{$Bt 8 YBI NyiV bsr I R{ $A I $t R {$Bt qy s-$8z8 N$, j$ybbi e-} {s$bt s-$8$9s$bt wned ddn sjb $Y8 YsR A t ZR I sti $8} B% I - tr$% jk $t { t k s R! I I ZAR e-} {s$bt s-$8$9s$bt w!ed $t% R$s I Ak <ZIRBt sti Ns,$t d; sti i R{sj I jb{, y s$% Ak k t dx s Y s{{ j s I sjb $Y8R ZR$t RZAR R qy RBjZ$Bt {B% k sjb $Y8 s}}j$ I Ak Y R 8 YBIR bsr }ZAj$RY I Ak {]s Yk sti $jj de sti } %$BZRjk RZI$ I Ak _st sj ; sti _ B $ZR sj d qy }s s8 R I R{ $A$t Y AjZ 8BI j b U isi$zr BP Bs$Bt wi!id ) {8wP B8 { krsj Ps{ D }$- j R$9 ) (ndx {8 Y$Y RBjZ$Bt {Bjj$8sB b$y YBj R$9 ) d;88 YBj j ty ) 88 sti R }s Y${,t RR ) (dm88 qy$r $tpb 8s$Bt RZjR $t Y AjZ 8BI j ) ((ExL((dd~I w{8d 3B s{y BP Y Iss R R x( $ s$btr b {sj{zjs I PB Y I$& t {BtR Z{$Bt 8 YBIR VjYBZY!e sti i y ZR d( B I I R R b sjrb {BtR Z{ I Y RBZ { I$R $AZ$Bt PB x( $ s$btr qy$r $% R ZR Y }BRR$A$j$k B $t% R$s $P Y!e {BtR Z{$BtR s Y z _ $ s$bt {B R}BtI b$y Ne s Y d( z _ $ s$bt nn *ss stsjkr$r yt Y$R bb, b s $t% R$s$t Y sa$j$k BP Y {BtR Z{$Bt sjb $Y8R B {B% Y RYs} BP s $% t RBZ { I$R $AZ$Bt qy BA` { BP Y$R RZIk A $t B $t% R$s Y 8BI j ZR I B I R{ $A Y s{jz$r$$bt RkR 8 $t Y PB bs I sti As{,bs I } B` {$Bt BP Y {BtR Z{$Bt 8 YBIR qb %sjzs Y } PB 8st{ BP Y I$& t 8 YBIR b ZR I Y sarbjz B BP Y {BtR Z{ I $8s % RZR Y P t{ $8s G I ht Y sarbjz B sr Y sarbjz I$& t{ $t % k }$- j RZ88 I B% sjj }$- jr $t Y $8s qy P t{ $8s bsr BAs$t I Ak A$tt$t Y xd-xd RBZ { I$R $AZ$Bt 8s $- B Y 8s $- R$9 BP Y {BtR Z{ I $8s R A $t dm-dm Vjj $8s R b tb 8sj$9 I B Bt GY t Y {BtR Z{$Bt sjb $Y8 $R -s{ Y {BtR Z{ I $8s R $R } P {jk b$y Y P t{ $8s YZR Y sarbjz B JZsjR 9 B GY t Y $R tb 8s{Y A b t Y $8s R Y sarbjz B b$jj A yt sii$$bt b ZR I Y {BtR Z{ I $8s R B RYBb Y jb{sj$9s$bt BP Y B % RZR Y P t{ $8s Vj ts$% jk $ $R sjrb }BRR$Aj B h s * pszrr$st B Y {BtR Z{ I $8s R sti ZR Y tb 8sj$9 I 3G< $t Y sti O I$ {$Bt PB %sjzs$bt <Bb % b -} $ t{ I s js B $t Y hr PB Y RBZ { I$R $AZ$BtR BZ BP { t sti {Bt{jZI I Ys Y$R s}} Bs{Y bsr tb j$saj ; ie=nq qy sarbjz B BP Y {BtR Z{ I $8s % RZR Y P t{ $8s $R $% t $t hz R M BZY dn PB Y I$& t jb{s$btr sti R$9 R BP Y pszrr$st RYs} I RBZ { I$R $AZ$Bt yt % k }jb sjj PBZ 8 YBIR s I$R}jsk I PB Y Y tb$r j % jr 3$Z M RYBbR Y RZjR PB Y E88 RBZ { $t Y { t h ji BP %$ b NyiV sti Ne s JZ$%sj t Z} B x( $ s$btr sti Y $R tb $t4z t{ BP Y tb$r j % j 3B Y$R {sr $ $R $t R$t B s, s jbb, s s Y$Y tz8a BP $ s$btr 3$Z E RYBbR Y j$rt8bi {BtR Z{$Bt $tpb 8s$Bt Z} B dx( $ s$btr G sjrb I$R}jsk I Y Ne $tpb 8s$Bt Z} B x( $ s$btr sti Y $ s$btr d B dx BP!e JZ$%sj t b$y $ s$btr d( ( dx( BP Ne WB${ Ys Y d $ s$bt BP!e $R }js{ I s Y d(y $ s$bt R } Y R{sj BP Y Ts-$R $R Y tz8a BP Ne $ s$btr G {st R Y JZ$%sj t{ A b t Ne sti!e NyiV IB R tb I si sr PsR b$y $t{ sr$t $ s$bt tz8a sab% by Y 8$t$8Z8 B bsr BAR % I 46 Proc. SPIE Vol. 4322

8 LMIRA MLEM OSEM Nr. itera tions 3$Z E VARBjZ B PB Y pszrr$st RBZ { I$R $AZ$Bt $t { t b$y dx {R PB $ s$btr dtdx( NyiV dtx( Ne sti dtdx JZ$%sj t tz8a BP!e $ s$btr GY t b jbb, s hz Y }jbr PB Y E88 RBZ { {8 BZ BP { t b {st R Ys Y B PB NyiV $R R8sjj Yst PB Y BY 8 YBIR qy {BtR Z{ I $8s R RYBb Ys Y R sjb $Y8R PB { s 8$R}BR$$Bt$t BP Y pszrr$st RBZ { B Y b$y PB {$t $ B s 3G< R8sjj Yst Y 3G< BP Y P t{ RBZ { qy$r & { $R % t 8B {j s PB Y E88 RBZ { d;{8 BZ BP Y h ji BP %$ b G {st sjrb R Y tb$r j % j $R Rs $t B Ys% st & { Bt Y s{{z s{k BP Y {BtR Z{$Bt 3$Z R sti d( RYBb Y RZjR PB Y d( sti dx,{r Iss R R s {B8}s saj AZ Y B PB Y x,{r Iss R R $R Y$Y qy RZjR PB Y d88 3G< pszrr$st RBZ { I$R $AZ$Bt s R$8$js B Y } %$BZR RZjR qy I$& t{ A b t NyiV sti Y BY 8 YBIR $R % t 8B R$t$h{st G {st R $t hz dd Ys Y 8$t$8Z8 B PB Y d88 RBZ { $t Y { t h ji BP %$ b $R sj8br Y Rs8 AZ s Y$Y tz8a BP $ s$btr Y B PB Ne!e sti i y $R s}$ijk $t{ sr$t $t {Bt sr b$y Y j$rt8bi {BtR Z{$Bt 8 YBI qy$r $R {szr I Ak PB {$t Y {BtR Z{ I RBZ { I$R $AZ$BtR B s 3G< R8sjj Yst Y 3G< BP Y P t{ RBZ { Y$R & { bsr sjrb R t $t Y RZIk } PB 8 I Ak _st sj ; 3B Y RBZ { R BZ BP Y { t b {st R $t hz R d sti dn Ys Y 8$t$8Z8 B PB Y j$rt8bi {BtR Z{$Bt $R jbb Yst PB Y BY 8 YBIR Vs$t Y R 8 YBIR s 8$R}BR$$Bt$t Y {BtR Z{ I pszrr$st RBZ { YZR $t{ sr$t Y B qy$r 8sk Ys% A t Y RZj BP sj$sr$t $t Y A$tt I s{jz$r$$bt sti bbzji Y PB $t4z t{ Ne!e sti i y {BtR Z{$Bt N$RT8BI {BtR Z{$Bt IB R tb t{bzt Y$R } BAj 8 A {szr BP Y ht Rs8}j$t yt hz Y { BRR R {$Bt $t Y I$ {$Bt BZY Y {BtR Z{ I $8s $R I sbt PB Y E88 3G< RBZ { I$R $AZ$Bt d;{8 BZ BP { t PB dx,{r qb Y b$y Y P t{ {Z % Y j$rt8bi sti Ne {BtR Z{$BtR s RYBbt PB x( $ s$btr sti $t sii$$bt Y!e {BtR Z{$Bt PB d( $ s$btr w)d(( Ne $ s$btrd $R I$R}jsk I!t {st R Ys Y B $R {szr I Ak Y 8$R}BR$$Bt$t sti Y B% {B {$Bt $t Y {BtR Z{ I $8s x *y]=y!w VW* ]!W]N=y!W k 8BI j$t Y I {$Bt RkR 8 BZY ZR BP Y B8 ${ {Ys s{ $R${R BP Y {Bjj$8sB R Z{Z $ $R }BRR$Aj B $8} B% Y s{{z s{k BP Y RBjZ$Bt {B% k yt sii$$bt Y t b } B` {B \As{,} B` {B }s$ 8s, R $ }BRR$Aj B ZR Y Y$Y Rs8}j$t BP j$rt8bi s{jz$r$$bt qy s {Bt$ y $- s88s {s8 s $R {s}saj BP s{jz$ $t j$rt8bi Iss $t (;M A$tR sti Bt IB R tb t I B A$t Y st k stj R $tb } I ht I P s8 R AZ {st {B I Y s{zsj stj Y Ak 8B%$t Y $8}s{ BP stzjs AjZ $t b$y {Bt$tZBZR s{jz$r$$bt y j s% R Bt bbti $t YBb Y A$tt I 8 YBIR bbzji Ys% bb, I b$y htt Rs8}j$t VtI by${y $R 8B $8}B st T R}s$sj B stzjs G,tBb P B8 }sr bb, Ys s d( stj R B% ne( I R b s I ht$ jk ZtI Rs8}j$t s Y I BP Y h ji BP %$ b AZ Bt t IR Btjk s P b Rs8}j R PB st BA` { s Y { t h ji BP %$ b qy RZjR PB Y A$tt I Iss {BtR Z{$BtR I si Proc. SPIE Vol

9 .3.25 Relative # counts.2.5. OSEM iterations MLEM 5 iterations LMIRA 5 iterations Reference.5. X-cross section 3$Z $R}BR$$Bt$t BP Y Ne sti!e ] BRR R {$Bt $t Y I$ {$Bt pszrr$st E88 3G< d;{8 BZ BP ]!i dx,{r <B $9Btsj 8s,R jb{s I $t Y { t BP Y }$- jr_$- j R$9 ndx88 sr Y pszrr$st RBZ { I$R $AZ$Bt 8B% R BZ yt Y$R bb, b ZR I s }s sjj j YBj {Bjj$8sB AZ Y sis}s$bt B PB -s8}j s PstTA s8 {Bjj$8sB {st A s{y$ % I Ak As{,} B` {$Bt BP Y {Bjj$8sB A$t B% Y I R BP Y PstTA s8 R }s yt Y$R {sr Y s s V b$jj tb jbt A s }s sjj jb s8 AZ b$jj Ys% s 8B t sj RYs} qy I }Y I } ti t RBjZ$Bt b$jj A 8BI j I $t Y Rs8 bsk b$y 8$tB si`zr8 tr B Y sjb $Y8 VjYBZY b Btjk $t% R$s I Y A Ys%$B BP Y RBjZ$Bt {B% k $t Y {sr BP pszrr$st RYs} I RBZ { I$R $AZ$BtR Y RZjR strjs B 8B t sj B8 $ R RZ{Y sr PB -s8}j Y Y }} sti NBst }YstB8 W % Y j RR $t PZZ bb, }YstB8 RZIk w<b&8st sti\b ]VqD b$jj Ys% B RYBb Y $8}s{ BP Y $8} B% I sjb $Y8 Bt 8B sj$r${ n* j$rt8bi s{jz$ I Iss E V] W!GNe*peWq qy$r bb, bsr RZ}}B I Ak "ytr$z PB Y _ B8B$Bt BP yttb%s$bt Ak {$ t{ sti q {YtBjBk $t 3jstI R" wygq j$z8d i$, zst I Gsjj $R s }BRTIB{B sj P jjbb BP Y 3ZtI PB {$ t$h{ i R s {YT 3jstI R w3g! j$z8d ie3eiew]e d V $t * q NBt sti V $jj X_e]q %BjZ8 JZst$s$BtU $t4z t{ BP R}s$sj RBjZ$Bt RBZ { R$9 sti RYs} sti %B- j R$9 " I${sj _YkR${R dmwxd }} d(deud(; }\!{ dd B $ZR $t pj${, q _st sti * NZB Xi IZ{$t Y & { BP tbtrs$bts k RBjZ$Bt Bt s{$%$k JZst$s$Bt b$y Y P JZ t{k I$Rst{ js$btry$} $t _e]q" yeee q strs{$btr Bt WZ{j s {$ t{ ;nte }} nnnxunn;d de n z BYj$ $t pj${, sti q _st X]B8}s $RBt BP P JZ t{kti$rst{ js$btry$} sti szrr$stt I$&ZR$BtTAsR I 8 YBIR BP {B8} trs$bt PB I$Rst{ TI } ti t R}s$sj RBjZ$Bt $t _e]q $8s$t" _YkR${R $t I${$t sti $BjBk ;nw;d }} d(xud(n dm ; q _st * NZB z BYj$ sti $t Xyt4Z t{ BP!e jj$}${sj B A$R sti As{, BZtI s{$%$k Bt _e]q n* RBjZ$Bt {B% k" _YkR${R $t I${$t sti $BjBk ; }} xduxn VZZR d x * str qy isibt strpb 8 sti RB8 BP $R s}}j${s$btr FBYt G$j k sti BtR W b OB, dmn E 3 Fs{BAR e ZtI 8st * Z ]Y $R$s tr sti y N 8sY$ Z XV PsR sjb $Y8 B {sj{zjs Y -s{ si$bjb${sj }sy Y BZY s }$- j B %B- j R}s{ " ]B8}Z$t sti ytpb 8s$Bt q {YtBjBk E }} Mu; FstZs k dm i $IIBt X3sR {sj{zjs$bt BP Y -s{ si$bjb${sj }sy PB s Y TI$8 tr$btsj ]q s sk" I${sj _YkR${R d }} xuxx s {Y dmx M N BZb tr i z I Gsjj < p$&b I $t y N 8sY$ Z sti i *$ {,- XNyiV U N$RTBI y s$% i {BtR Z{$Bt VjB $Y8 PB _e]q" RZA8$ I PB }ZAj${s$Bt 48 Proc. SPIE Vol. 4322

10 < s q GY$ sti N _s s XN$RT8BI j$, j$ybbi" FBZ tsj BP Y!}${sj B{$ k BP V8 ${s VT!}${R y8s {$ t{ sti z$r$bt d; }} d;un WB% 8A d d( N _s s sti < s XN$RT8BI j$, j$ybbi U e sjb $Y8 sti $8s JZsj$k R$8s$Bt I 8BtT R s I Bt T* _eq" yeee q strs{$btr Bt I${sj y8s$t d }} Munx V} $j dm dd i <s $RBt sti * <sktb XV }ZAj${TIB8s$t R$8Zjs$Bt RkR 8 PB 8$RR$Bt B8B s}yku }YBBt s{,$t Y BZY Y B t BZR s tzs$bt ZR$t $8}B st{ Rs8}j$t" FBZ tsj BP WZ{j s I${$t n; }E(_skdn d N Y }} sti O zs I$ Xs-$8Z8 j$, j$ybbi {BtR Z{$Bt PB 8$RR$Bt B8B s}yk" yeee q strt s{$btr Bt I${sj y8s$t d }} ddnud dm dn Nst sti i ]s RBt Xe8 {BtR Z{$Bt PB 8$RR$Bt sti str8$rr$bt B8B s}yk" FBZ tsj BP ]B8}Z VRR$R I qb8b s}yk M }} n(eund dm; d; < <ZIRBt sti i Ns,$t XV{{ j s I e {BtR Z{$Bt ZR$t B I I RZAR R BP } B` {$Bt Iss" yeee q strs{$btr Bt I${sj y8s$t dn }} E(duE( d; dx ] k t X jb{,t$ s$% 8 YBIR PB $8s {BtR Z{$Bt P B8 } B` {$BtR" yeee q strs{$btr Bt y8s$t _ B{ RR$t x }} u; sk de de V {]s Yk sti $jj Xs-$8Z8Tj$, j$ybbi _e]q $t {j$t${sj {B8}Zs$Bt $8 R ZR$t 8 RYT {Btt { I }s sjj j {B8}Z R" yeee q strs{$btr Bt I${sj y8s$t d(wnd }} ;Eu;nE dd d B $ZR $t q _st * I z $ R pj${, sti ] Z t Xi IZ{$t Y $t4z t{ BP }s $sj %BjZ8 & { Bt _e]q s{$%$k JZst$h{s$Bt b$y n* 8BI j$t BP R}s$sj RBjZ$Bt $t $ s$% {BtR Z{$Bt" _YkR${R $t I${$t sti $BjBk ;n }} ;(u;( dm Proc. SPIE Vol

11 LM 5k LM k LM 5k ML 5k ML k ML 5k OS 5k OS k OS 5k RBI 5k RBI k RBI 5k Nr. iterations 3$Z M E88 3G< $t { t LM 5k LM k LM 5k ML 5k ML k ML 5k OS 5k OS k OS 5k RBI 5k RBI k RBI 5k Nr. itera tions 3$Z E88 3G< {8 BZ BP { t LM 5k LM k LM 5k ML 5k ML k ML 5k OS 5k OS k OS 5k RBI 5k RBI k RBI 5k Nr. Iterations 3$Z d( E88 3G< d;{8 BZ BP { t 5 Proc. SPIE Vol. 4322

12 LM 5k LM k LM 5k ML 5k ML k ML 5k OS 5k OS k OS 5k RBI 5k RBI k RBI 5k Nr. iterations 3$Z dd d88 3G< $t { t LM 5k LM k LM 5k ML 5k ML k ML 5k OS 5k OS k OS 5k RBI 5k RBI k RBI 5k Nr. iterations 3$Z d d88 3G< {8 BZ BP { t LM 5k LM k LM 5k ML 5k ML k ML 5k OS 5k OS k OS 5k RBI 5k RBI k RBI 5k 3$Z dn d88 3G< d;{8 BZ BP { t Proc. SPIE Vol