Image Reconstruction in Photoacoustic Tomography taking acoustic attenuation into account

Transcription

1 Imag Rcostructio i Photoacoustic Tomography takig acoustic attuatio ito accout Ptr Burghozr Rsarch Ctr for No Dstructiv Tstig GmbH, Liz, Austria Ti Fbruary 9: Uppr Austria Rsarch GmbH, Liz, Austria Sit RECENDT 9 Ptr Burghozr Outi! Photoacoustic Imagig! Acoustic attuatio! Stoks quatio! Attuatio i tissu: powr aw dpdc! Ivrsio! Hat diffusio quatio! Soutio i k-spac! Ivrsio! Rguarizatio mthods! Etropy productio ad iformatio oss! Cocusio ad Outook Sit RECENDT 9 Ptr Burghozr

2 Imagig tchiqus X-ray utrasoud ight Sit 3 RECENDT 9 Ptr Burghozr Sit 4 RECENDT 9 Ptr Burghozr

3 Sit 5 RECENDT 9 Ptr Burghozr Mod basd tim rvrsa mthod P. Burghozr, G. J. Matt, M. Hatmir, ad G. Patauf, Exact ad approximativ imagig mthods for photoacoustic tomography usig a arbitrary dtctio surfac, Physica Rviw E 75, 7 Sit 6 RECENDT 9 Ptr Burghozr 3

4 Stoks quatio i! Kx% $ t" ikx % i$ t %# x " pa wavs: p & p & p " With compx K(!) = k(!) + i "(!) =!/c(!) + i "(!) " k(!), "(!) hav to satisfy Kramrs-Kröig-Ratios ".g. Stoks quatio: dsity chag foows prssur chag with a raxatio tim # ( p % c ' ' t p ) ' p ( & ' t p c '* ( ' t Stoks quatio + Rxatio tim # $ 3 # & c k $ 3 & c %. A A / ). A A / with A - ) $ + for $+,, : $ + # 4 c $ % k $ +. c 8 / Sit 7 RECENDT 9 Ptr Burghozr Photoacoustic imagig with tim rvrsa accoutig for acoustic attuatio " (a) Prssur simuatio rsuts for # =. ad c= " (b), (c) Rcostructios with tim rvrsa without ad with compsatio of attuatio " (d) Rcostructio profi aog horizota dashd i P. Burghozr t a., Compsatio of acoustic attuatio for high-rsoutio photoacoustic imagig with i dtctors usig tim rvrsa Proc. SPIE , Photoics Wst, BIOS 7 Sit 8 RECENDT 9 Ptr Burghozr 4

5 Examp for Stoks quatio: Oi # = 7 ps Micha J. Buckigham., Causaity, Stoks wav quatio, ad acoustic pus propagatio i a viscous fuid, Phys. Rv. E 7, 5 Sit 9 RECENDT 9 Ptr Burghozr PA sigas i oi mm from icusio $ ~ 5 6 ick ( ) t p( r, $ ) & pida! r, t" $ c K % 6 ( $ ) dt Rivir, Zhag, ad Aastasio, Optics Lttrs (6). Diamtr. mm c t p ( r ) p( r, 3D Sit RECENDT 9 Ptr Burghozr 5

6 Ivrsio: rguarizatio with SVD for oisy sigas % ois.% ois.% ois.% ois Sit RECENDT 9 Ptr Burghozr Tim dampd soutios Two possib soutios of th wav quatio ar: "! ra, K(!) = k(!) + i "(!) =!/c(!) + i "(!) compx, dscribs a statioary wav dampd i spac. " k ra, $ (k) =!(k) - i!(k) compx, dscribs a stadig wav (.g. i a asr rsoator) dampd i tim. p ( r ) p( r, Ra spac FT IFT pˆ ( r) Tim t pˆ ( r) % i$ t %7 t Fourir spac Sit RECENDT 9 Ptr Burghozr 6

7 Exprimta Dtrmiatio of Attuatio Sit 3 RECENDT 9 Ptr Burghozr Attuatio i tissu " For tissu: # y! $ " 8 # $ with y 8 Kda R. Watrs, Micha S. Hughs, Jo Moby & Jams G. Mir; Diffrtia Forms of th Kramrs-Kröig Disprsio Ratios; IEEE Trasactios o Utrasoics, Frroctrics, ad Frqucy Cotro, Vo. 5, No., Jauary 3, c! $ " c! $ " y% y! $ % $ " 3 9 % & ) # ta y. / for y= c & c % # $ $! $ "! $ " 9 Sit 4 RECENDT 9 Ptr Burghozr 7

8 Ifuc of Attuatio i D, D ad 3D Attuatio i huma fat:.6 db MHz - cm - ; dtctor distac is mm (3 db MHz - cm - i huma drmis) p ( x ) Layr with thickss. mm k x p ( r ) Diamtr. mm Diamtr. mm c t p ( r ) c t D c t p( x, p( r, D p( r, 3D Sit 5 RECENDT 9 Ptr Burghozr Acoustic attuatio i various dimsios D D 3D Sit 6 RECENDT 9 Ptr Burghozr 8

9 Th ifuc of disprsio! Iitia prssur distributio: sphrica absorbr (diamtr.mm)! Simuatio rsuts at a distac of mm i huma fat gctig disprsio (gr) ad takig disprsio ito accout (rd)! Rcostructio of th iitia prssur distributio from abov dtctor sigas gctig disprsio (gr) ad takig disprsio ito accout (rd) Sit 7 RECENDT 9 Ptr Burghozr Ivrsio: rguarizatio with SVD for oisy sigas % ois.% ois.% ois thrma ois Sit 8 RECENDT 9 Ptr Burghozr 9

10 D hat diffusio quatio ' T & # ( T ' t Fourir 83, or.g. Madis t a. "..thrma diffusivity Iitia vaus: T ( x, t & ) & T ( x) ' Numa boudary coditios: T & for x & ad x & ' x Usuay sovd by tmpora Fourir trasform # Hmhotz quatio with soutios: < cos( ; x % $ # or spatia Fourir trasform, (costrasform).g. by Brosti: T ( x, & : b cos( kx), with 6 % k # t k b & 5 T ( x dx ) & b & 5T ( x)cos( kx) dx, &,,3,... $ x # T ~ $! 9 & Sit 9 RECENDT 9 Ptr Burghozr T ( x, t & ) & T ( x) T ( x, Costrasform b Tim t A U b Ivrs Cos-trasform % k # t 9, with k & T ( x &, & T ( S Sit RECENDT 9 Ptr Burghozr

11 D hat diffusio quatio: tim rvrsa T ( x, t & ) & T ( x) T ( x, Ivrs Cos-trasform b ) k # t 9, with k & Iv(U) Tim t Iv(A) b Costrasform Sit RECENDT 9 Ptr Burghozr SVD ad Tikhoov rguarizatio mthod i k-spac k # t b t & % ( ) b (), with k & bt & Atb A & diag(xp( % k SVD: = C b () & B =A 9 ) k # t b (, for D i? s => t # ) Tikhoov: t t mi(( A t b % b t ) ) 7b ) At bt & ( At At ) 7E) b % k # t b ( ) & b ( % k # t ) 7 Sit RECENDT 9 Ptr Burghozr

12 SVD ad Tikhoov rguarizatio mthod i k-spac () (b Tmpratur (ad aso prssur) ar ma vaus Statistica fuctuatios: (( T ) & kbt C Sit 3 RECENDT 9 Ptr Burghozr Cocusios Dissipatio causs: $ Etropy productio $ Fuctuatios: usig ths as ois v th rcostructd imag shows a oss of iformatio which is qua to th tropy productio (at ast for th D hat diffusio quatio). Sit 4 RECENDT 9 Ptr Burghozr

13 Outook! Hat diffusio quatio: D ad 3D! Prssur wavs takig acoustic attuatio ito accout! fuctuatio dissipatio thorm from statistica physics dscribs i a vry gra way how fuctuatios ad tropy productio ar ratd. Thrfor it shoud b possib to graiz th rsuts foud for D tmpratur profis. Sit 5 RECENDT 9 Ptr Burghozr Ackowdgmts This work has b supportd by th Austria Scic Fud (FWF), projct umbrs S53-N ad S5-N, by th Europa Rgioa Dvopmt Fud (EFRE) i th framwork of th EU-programm Rgio 3, ad th fdra stat Uppr Austria. Sit 6 RECENDT 9 Ptr Burghozr 3

14 thak you for your atttio Sit 7 RECENDT 9 Ptr Burghozr 4