Non Fourier Encoding For Accelerated MRI. Arjun Arunachalam Assistant Professor Electrical engineering dept IIT-Bombay

Transcription

1 Non Fourir Encoding For Acclratd MRI Arjun Arunachalam Assistant Profssor Elctrical nginring dpt IIT-Bombay

2 Outlin of th Prsntation An introduction to Magntic Rsonanc Imaging (MRI Th nd for spd in MRI Rcnt advancs in acclratd MRI A currnt ampl of Comprssd Snsing (CS in MRI CS and Radio frquncy ncoding Simulations and Rsults Futur work

3 MRI is an intr-disciplinary Signal gnration fild Signal ncoding Signal rcption Spin physics Puls squnc Imag rconstruction MRI Instrum ntation Magnts/ Cryognics Rf antnnas Gradint coils Digital Signal Procssing Embddd programming Physics Mchanical Eng. Chmical Eng. Powr lc. Rf nginring Elctromagntics Physics

4 Magntic Rsonanc Imaging Fundamntals Powrful non invasiv imaging modality Suprior soft-tissu contrast Imaging plans in an arbitrary orintation Applications Diagnostic imaging studis of th CNS and musculoskltal systm MR angiography, functional MRI, ral tim MR... Emrging- Carbon 13 imaging tc..

5 MRI Fundamntals MRI Signal formd by localizing th NMR signal by frquncy Mdical MRI uss 1 H (th proton Protons intract with static magntic fild B 0 radiofrquncy fild B 1 linar gradint fild G

6 MRI Fundamntals 1. Static magntic fild B 0 Rsonanc at Larmor frquncy Z Longitudinaldirction B 0 M Transvrs(y plan Y X Ais convntion

7 MRI Fundamntals 2. Radiofrquncy (RF Fild B 1 M y dtctd by rcivr coil -Fr Induction Dcay(FID Longitudinal rlaation tim constant (T 1 B 0 Z M Y Transvrs rlaation tim constant (T 2 Introducd by Rf puls S( t X = M (, y Sin( α (, y z jγg B 1 y yt p jγg t ddy Gradint magntic fild trms

8 MRI sampling using gradints k k ky ky

9 Th nd for spd in MRI Dynamic Imaging Contrast nhancd MR angiography Cardiac Imaging Trad off btwn spatial and tmporal rsolution Acquir a sris of 2D/3D imags ovr tim (tim frams Tmporal rsolution: Rat of acquisition of tim frams Spatial rsolution: Imag rsolution of ach tim fram

10 Problm Dfinition Convntional MRI data acquisition spd is limitd (physical and physiological constraints To spdup acquisition sub-sampling k-spac is ncssary Th consqunc is aliasing &/or rsolution loss Nd for bttr mthods to spdup th acquisition without dgrading th imag quality

11 Paralll Imaging Spatially sparatd multipl RF rcivr coils Indpndnt spatial snsitivity profils of th RF coils Coils must hav som snsitivity diffrnc in th sub-sampling dirction Can b usd for th primary in-plan phas ncoding(2d scans & scondary phas ncoding(3d scans

12 Paralll Imaging (PMRI Paralll Rconstruction Algorithms Rconstruction algorithm Coil rfrnc data Imag -basd Sub-sampld targt data SENSE imag domain imag domain k-spac basd (Fourir spac SMASH imag domain k-spac Gnralisd SMASH k-spac k-spac AUTO-SMASH K-spac K-spac GRAPPA k-spac k-spac

13 Paralll Rconstruction Algorithms Eampl: Snsitivity Encoding (SENSE Rcivr coil snsitivitis ncod th objct in complmntary way to Fourir ncoding Undrsampl k-spac for vry coil Aliasing in objct domain (for vry coil Us snsitivity information of th coils to & rconstruct th original imag

14 Eampl-SENSE stp 1: crat aliasd rducd FOV imag for ach array lmnt using DFT stp 2: crat a full-fov imag from th st of intrmdiat imags. A I alias,1 =s 1,A 1,A I A + s 1,B 1,B I B s1 IA B A IB s2 B I alias,2 =s 2,A I I A + s 2,B 2,B I B W know s 1, s 2 (snsitivity maps; w masur I alias,1, I alias,2 ; so w can calculat I A,

15 Eampl-Comprssiv Snsing Again, gradints ar usd to prform random sampling Spars MRI: Lustig t al: Availabl on Ric univrsity CS wbpag

16 A Non Fourir ncoding approach Non-sinusoidal spatial ncoding profils inducd via RF citation S( t S( t = M (, y Sin( α (, y = M (, y α (, y jγg y yt jγg Can b approimatd as p y yt p jγg t jγg t ddy ddy Can b drivd from wll known fid mathmatical basis sts: Wavlts, Noislts tc

17 Non Fourir Encoding ddy y y M t S t G j yt G j p y γ γ α =, (, ( ( = = ddy y M k K S k j y k j M m m l l m π π α 2 2 1, (, (,..., ( 1 M k k K =, (, ( 1 m M m m l l k k s k K S = = α Th non-fourir signal quation is a combination of th typical Fourir mods Acquird through convntional mans in MRI MRI Imags ar comprssibl in th wavlt domain. An appropriat masurmnt domain can b introducd during Rf citation Th masurmnts ar linar combinations of typical Fourir mods,..., 1 l =( N

18 Non-Fourir PMRI acclration Whn using multipl coils ɣ, th quation if th following: M l Sγ ( Kl, k = α msγ ( km, k m= 1 Haar Encoding R=6 Random Encoding R=6

19 otntial for comprssiv snsing and PMRI Th masurmnt matri is not rstrictd to Fourir domain alon Currnt CS approachs ar unprdictabl whn applid on multi-snsor MRI data Th solution can b in th imag domain or th Fourir domain Non Fourir acclration mthods can ploit ral tim k-spac data proprtis