1Depa

INTRMR pamappiing (Cthis wmappicantly METHConsidimagedata caly proping [3

assum

formed

as P =

coefficthe spdesignspace equivastraint

sU for

where zation VARP RESUThe prin a bscannetimes. ing, anunderspling preconsseparanique. reconsThe Thigher DISCSeveraPCA iand spphysic CONCA newmetho REFE[1] Liapp. 1591973. p

Hig

artment of Electrica

RODUCTION arametric mappinng has been limit

CS) [2] have showwork, we present

ng. The proposedreduced imaging

HODS der T2 mapping s with variable Tan incur severe arposed reconstruc][4]. The same a

mes ( , )ntρ =∑r

d from samples o

s tU V , where tV

cients. Under thearse sampling op

ned to determine data is used as

alent to solving Uts can effectively r the PS model, a

TV(·) representswith continuatio

PRO (variable pro

ULTS roposed techniqu

brain T2 study. Ted at 3T with a sThe imaging par

nd 256x208 matrisampled at an acpattern shown in structed with (1)able model [6]; a Figure 2 compa

structions using (2 map estimated

r spatial resolution

USSION al sparse samplinis based on the bparsity constraintscally acquired trai

CLUSION w image reconstru

d shows superior

ERENCES ang Z-P, IEEE-ISB93-1596. [5] Donepp. 413-432, 1973

ghly Accelerat

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wn great potentiala new method to

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approach can be

1( ) ( )

Ll l nl

u v t=

r , w

of ( , )ntρ r such t

represents the te

e PS model, the mperator and ξ is Vt. In Fig.1, wetemporal traininsU . However, dirstabilize the ill-c

and the reconstruc

s the spatial total on [3][4]. After ρojection) [8].

ue, named as PS-The brain of a hspin-echo sequencrameters are 2s Tix size. The data

cceleration factor Fig. 1. The down

) compressed senand (3) the propares the T2 map(1) CS, (2) PS, afrom fully samp

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wn to achieve muc

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onstructed imageng joint PS and seasily adapted fo

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emporal subspac

measured data cathe measurement

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-Sparse, was valihealthy volunteece at 32 different

TR, 17.2 ms echo set was retrospecof 10 using the

n-sampled data sensing [5]; (2) paposed PS-Sparse ps estimated fromand (3) the PS-Spled 32 echoes is the CS and PS co

ametric mappingnd suffers from thestimated from a h can more faithfu

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pling, direct inveres and subsequentsparsity constrainor parametric ma

model order. Co

, )nt . The PS mo

e, and sU repres

an be written as t noise. Multipleampling pattern,

being determineg sU from measu

rse problem. Specn be formulated a

rization. The aboed, the desired p

idated r was t echo spac-

ctively sam-

et was artial-tech-

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g methods have bhe ill-conditioninpre-fixed parame

ully capture under

ial separability anusing a single PS

, MRM 2007. pp. [6] Petzschner F,

Fig. 2. of 10, r

s

arg min ||= − ΩU

d

th Joint Partiamiao Lu2, and Zhi-t Urbana-Champaat Urbana-Champ

ssue properties, wmethods based o

sition. Some of thusing the PS and

e T2 maps than ex

,N represents a sersion of the (k, ttly the T2 map. Wnts for acceleratinapping. Specifica

onsidering the C

del can be equiv

ents the correspo

s s t( ) ξ= Ω +d F U V

e data acquisitionin which fully s

ed, the reconstruured data can suffcifically, we use as,

ve convex optimparameter map is

rence. As can be he CS showing si

been proposed recng issue illustrateetric signal moderlying temporal e

nd sparsity constrS or sparsity cons

1182-1195. [3] Zh, MRM 2011. pp.

a) Estimated T2 mrespectively; b) Er

2s s t 2( ) || + λΩ F U V

al Separability-Pei Liang1,2 aign, Urbana, IL, Upaign, Urbana, IL

which are useful bon the theory of phe methods have d sparsity constrxisting methods u

et of T2-weightet)-space measureWe have previousng dynamic imag

ally, the PS mode

Casorati matrix P

valently expressed

onding the spatia

ξ , where ( )Ω ⋅ isn schemes can besampled central kuction problem isfer from severe ila spatial finite di

mization problem s obtained using

seen in Fig. 2 (aignificant spatial

cently, such as thed in Fig. 2. REPel. The proposed evolution of relax

raints has been prstraint for reconst

hao B, IEEE-EMB706-716. [7] Huan

maps from CS, PS,rror maps of estima

sTV( ) λ U

y and Sparsity

United States, 2BeL, United States

biomarkers. Howpartial separable f

been extended toraints jointly andusing a single PS

ed ed s-g-el

P

d

al

s e k s ll-conditioning isfference to regula

can be efficientlya nonlinear least

a), the proposed Pblurring and the

he k-t PCA methPCOM uses a sim

method uses the xation process.

roposed to acceletructing highly un

BS 2010. pp. 3390ng C, MRM 2011

, and PS-Sparse reated T2 maps usin

Fig. 1. A samSparse, whictemporal trapled imagin

y Constraints

ckman Institute of

wever, the utility functions [1] and o parametric map

d illustrates its pe or sparsity const

sue. Imposing sparize the inverse

y solved by half-t squares fitting p

PS-Sparse producPS low SNR.

hod [6] and REPCmilar formulation

temporal subspa

erate MR paramendersampled data

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i-as

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2233Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)