Fast Dynamic magnetic resonance imaging using linear dynamical system model - PowerPoint Presentation

Slide1

Fast Dynamic magnetic resonance imaging using linear dynamical system model

Vimal Singh, Ahmed H. TewfikThe University of Texas at Austin

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Slide2

Outline

IntroductionAlgorithm

Results

Conclusions

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Introduction

Algorithm

Results

Conclusions

Slide3

Significance

Fast magnetic resonance imaging (MRI

) of

physiological

functions

high temporal and/or spatial resolution

improved

sensitivity and specificity of

the diagnosisperfusion studies: brain, myocardialless enhanced hypo-perfused tissuerelative enhancement changes in image timeseriesLinear dynamical systems (LDS) based dynamic MRI formulationusing true physical evolution model ()sparse innovations ()

 

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Mean signal intensity curves from myocardial perfusion MRI test of a normal subject

http://

www.ncbi.nlm.nih.gov/pubmed/17578718

Slide4

Prior work

Parallel imaging: SENSE,

GRAPPA

Exploiting data redundancy

spatial : partial Fourier, reduced FOV

temporal : k-t BLAST,

HYPR, k-t FOCUSS

Compressed

sensingsparsity priors: wavelets, total-variational norm, dictionaries sensing/sampling: signal encoding formulationLow-rank matrix completionLow-rank plus sparse matrix completion 4

Slide5

Innovation

The novelty of the fast MRI technique is based on the insight of using measurable system dynamics

combines

linear dynamical system model with sparse recovery techniques

explicitly

uses the available physical dynamical

models

improved

redundancy encoding results in high compressibility of images to be recovered using sparse recovery methods unifies prior information based methods which implicitly use the dynamics of underlying physiological functions 5

Slide6

Background

Classic dynamical system

:

dynamic state at

time point

time-evolution

function of the underlying

states: modeling error or innovations: k-space measurements for the state : linear measurement matrix: measurement noise

L

inear dynamical systems (LDS) based dynamic MRI formulation

: underlying evolving images

:

k

-space samples

, a linear image evolution model

 

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Slide7

Outline

IntroductionAlgorithm

Results

Conclusions

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Introduction

Algorithm

Results

Conclusions

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LDS based fast dynamic MRI

Proposed formulation

under-sampled acquisitions,

i.e.,

sparse/compressible innovations,

i.e.,

prior knowledge of ’ssolve:

versus Kalman filter which solves:

 

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LDS based fast dynamic MRI

State transition matrices

’s

based on true physical evolution models

perfusion, angiography

contrast changes between time frames

temporal difference:

cardiac CINE MRI

pseudo-periodic cardiac motionsecond order Autoregressive (AR2) model

 

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LDS based fast dynamic MRI

Solution

solve for innovations

u

se them to explicitly estimate

r

earrange

the innovations as

l

2

-norm fidelity term as

reformulate the problem to recover the sparse innovations

 

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Slide11

LDS based fast dynamic MRI

Recover the sparse innovations

sliding window with size

u

sing previous estimates to calculate

Numerical method

n

on-linear conjugate gradient descent algorithm with backtracking line search [

Lustig et al., 2008]converges for diagonal ’serror-propagation for non-diagonal ’s 11M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182–1195, 2007.

Slide12

Outline

IntroductionAlgorithm

Results

Conclusions

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Introduction

Algorithm

Results

Conclusions

Slide13

Myocardial perfusion imaging (MPI)

Dataset

in-vivo data

90 (phase) x 190 (frequency) x 70 (time)

Saturation-recovery sequence

TR/TE: 2.5/1

ms

saturation recovery:100

msEvolution functioncontrast changes between timeframestemporal difference:   13SamplesAbs. innovation

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Under-sampled MPI experiment

Acceleration (R) : 4

Window size (

): 4

Initialization (

): sliding window

 

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Slide15

Comparison – MPI

Kalman

filter

i

nnovation

k-t FOCUSS

prediction + residual prediction: temporal averageresidual: sparse imagek-t Sparsedual sparsityspatial dimension – Waveletstemporal dimension – 1D FourierLow-rank plus sparse matrixlow-rank: temporal correlationssparse: temporally varying 15

Signal-to-noise

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Comparison – MPI

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19.1 dB, 0.88

19.6 dB, 0.91

16.4 dB, 0.88

17.6 dB, 0.91

Linear dynamical

s

ystemk-t FOCUSSk-t SparseKalman filterLow-rank plus sparse matrix

13.4 dB, 0.84

15.8 dB, 0.78

18.0 dB, 0.89

15.6 dB, 0.88

16.6 dB, 0.81

19.0 dB, 0.92

Reference

#17

Zoom Ref.

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Innovation

#18

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MPI time-series plots

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Time-series plot

averaged signal intensity

acceleration R = 6

Red : Blood Pool (BP)

Green: Myocardium (MYO)

t

ime framessignal intensity

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Cardiac CINE MRI

Dataset

in-vivo data

256 (phase) x 256 (frequency) x 25 (time)

b

alanced steady-state free precession

flip

angle:

50 degTR = 3.45 ms Modificationextended to 100 time-pointsinterpolation, concatenationadded slow, fast & faster phases18

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Cardiac CINE MRI

Evolution function

temporal difference

second

order Autoregressive (AR2) model

l

earn

and

first 25 samples of the modified datasetleast square estimate 19TemporaldifferenceTemporalAR2Imagetime-series

Samples

Absolute innovation

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CINE results (R = 4)

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Ref. #53

Ref. #54

Innv

. #54

24dB, 0.96

24.5dB, 0.96

Ref. #53Ref. #54Innv. #5420.8dB, 0.9622.1dB, 0.96

Temporal AR2

Temporal Difference

Recovered (R)

Recovered (R)

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Comparison – cardiac CINE

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S

ignal-to-noise

Structural Similarity Index Measure

Slide22

Outline

IntroductionAlgorithm

Results

Conclusions

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Introduction

Algorithm

Results

Conclusions

Slide23

Conclusions

Improving temporal resolution in dynamic MRI applications

perfusion studies: ischemia detection, tumour detection

c

ardiac cine MRI: cardiac function evaluation

A novel fast dynamic MRI formulation

combines a linear dynamical system model with sparse recovery techniques

u

nifies previous implicit spatio-temporal dynamics based formulation Improved imaging speeds up to 6xhigh temporal resolutions23

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