Accelerated DESPOT1

Jason SuOct. 10, 2011

DISCOPOT

• View sharing of k-space between a sequence of angles• Fully sampled center of k-space, under sampled outer• Outer k-space pattern is pseudo-random but

complementary with shared angles• Mixing scheme:

– AB1.*fa_{i} + B2.*fa_{i-1} + B3.*fa_{i+1}– Edge cases are slightly different

• Tested on raw SPGR P-file data with fa1-13• Many angles collected with the goal of mcDESPOT in

mind

DISCOPOT Sampling

DISCOPOT – fa1

Errors Due to offline.recon

DISCOPOT – fa8

DISCOPOT – T1

Why are fa1&2 the worst?

0 5 10 15 20 25 300

0.01

0.02

0.03

0.04

0.05

0.06SPGR Curves for T1=500:100:1500, TR=3.5ms

Flip Angle (deg.)

Sig

nal

Solutions• Use the signal equation to scale the mixed k-space data

– Can calculate scale factors a priori assuming a uniform T1– Can scale by the ratio of energy in the centers of k-space

between images• What errors do we expect we use a constant scale factor?

– At higher flips, the SPGR curves are nearly parallel regardless of T1, this means that a constant scale factor should work very well

– At lower flips, performance will be worse– Consider the SPGR signal as a time signal, the lower flips is

where things diverge and we get different behavior with T1. After the Ernst angle, the signal decays predictably

0 1000 20001.6

1.8

2

Slo

pe

T1 (ms)

fa2/fa1Diff: 0.33228

0 1000 20001

1.5

Slo

pe

T1 (ms)

fa3/fa2Diff: 0.31334

0 1000 20001

1.2

1.4

Slo

pe

T1 (ms)

fa4/fa3Diff: 0.28675

0 1000 20000.5

1

1.5

Slo

pe

T1 (ms)

fa5/fa4Diff: 0.25407

0 1000 20000.5

1

1.5

Slo

pe

T1 (ms)

fa6/fa5Diff: 0.22141

0 1000 20000.5

1

1.5

Slo

pe

T1 (ms)

fa7/fa6Diff: 0.19157

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa8/fa7Diff: 0.1654

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa9/fa8Diff: 0.14288

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa10/fa9Diff: 0.12364

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa11/fa10Diff: 0.10727

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa12/fa11Diff: 0.093343

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa13/fa12Diff: 0.081483

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa14/fa13Diff: 0.071363

0 1000 20000.8

1

1.2

Slo

pe

T1 (ms)

fa15/fa14Diff: 0.06271

0 1000 20000.9

0.95

1

Slo

pe

T1 (ms)

fa16/fa15Diff: 0.055289

0 1000 20000.9

0.95

1

Slo

pe

T1 (ms)

fa17/fa16Diff: 0.048908

0 1000 20000.9

0.95

1

Slo

pe

T1 (ms)

fa18/fa17Diff: 0.043405

0 1000 20000.95

1

Slo

pe

T1 (ms)

fa19/fa18Diff: 0.038643

0 1000 20000.95

1

Slo

peT1 (ms)

fa20/fa19Diff: 0.034511

0 1000 20000.95

1

Slo

pe

T1 (ms)

fa21/fa20Diff: 0.030914

0 1000 20000.95

1

Slo

pe

T1 (ms)

fa22/fa21Diff: 0.027773

0 1000 20000.95

1

Slo

pe

T1 (ms)

fa23/fa22Diff: 0.025022

0 1000 20000.95

1

Slo

pe

T1 (ms)

fa24/fa23Diff: 0.022605

0 1000 20000.95

1

Slo

pe

T1 (ms)

fa25/fa24Diff: 0.020476

0 1000 20000.95

1

Slo

peT1 (ms)

fa26/fa25Diff: 0.018595

DISCOPOT, use full fa1 – T1

DISCOPOT, a priori scaling – fa1

DISCOPOT, energy scaling – fa1

DISCOPOT, energy scaling – fa8

DISCOPOT, energy scaling – T1

Comments

• fa1 makes a greater max error than fa8 but its distribution is tighter overall, standard deviation is lower– Perhaps central k-space energy is not a good

measure at higher flips due to higher contrast• Errors are worst around CSF: periphery and

ventricles

LCAMP

• Compressed sensing reconstruction• Same undersampling pattern as DISCO, but do not

mix data• Uses the constraint of known non-zero wavelet

coefficient locations based on a prior– We use the view shared volume as this prior

• Remaining questions:– How sensitive is the solution to the initial guess?– How sensitive is the solution to the location constraint?

DESPOT – fa1

DISCOPOT – fa1

LCAMP+DISCO – fa1

LCAMP+DISCO, energy scaling – fa1

DESPOT – fa8

DISCOPOT – fa1

LCAMP+DISCO – fa1

LCAMP+DISCO, energy scaling – fa8

LCAMP+DISCO, energy scaling – T1

Comments

• Something is going wrong with the LCAMP reconstruction

• LCAMP output seems to closely match the initial guess for fa1, is it helping much?

Conclusions and Future Work

• DISCOPOT with energy scaling provides a compelling way to accelerate a DESPOT collection

• Future work to apply this to a SSFP set and mcDESPOT