motion correction in fmri time series

IPAM 2004 DSVSHFJ

Motion Correction in fMRI time series

J.-F. Mangin, L. Freire, A. Roche, C Poupon

Service Hospitalier Frédéric Joliot, CEA, Orsay, FranceInstituto de Biofisica e Engenharia Biomedica, FCUL, Lisboa, Portugal

Instituto de Medicina Nuclear, FML, Lisboa, PortugalProjet Epidaure, INRIA, Sophia-Antipolis, France

Medical Vision Laboratory, Oxford, UK

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f MRI time seriesvoxel time series

Motion correction, why?

Task-correlated

motion

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Which solutions?

• Some constraints in the scanner to minimize motion

• Tracking (anatomical or artificial landmarks)

• On line corrections (MR Echo Navigator)

• Postprocessing: image registration

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Image registration

Definition: given two images, find the geometrical transformation that « best » aligns homologous voxels

First 3D image Second 3D image

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Classification of registration problems

• Search space (rigid, non-rigid)

• Monomodal / multimodal

• Intra-subject / inter-subjects

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General formulation of image registration

Given two images I et J,

),,(maxargˆΤ

TJISTT

Similarity measure

Search space (rigid, affine, spline, etc.)

Optimization scheme

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Building a similarity measure

Geometric Approach

• Detect features (points, lines, surfaces,… graphs) • Measure the distance between these features

Iconic Approach

Direct comparison of intensities

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Intuitive example

How to register these images ?

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Geometric/Iconic Approach

Feature detection (here, points with high curvature)

Measure: for instance, k

kkTTS2

)()( yx

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Feature detection (here, points with high curvature)

Measure: for instance, k

kkTTS2

)()( yx


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No segmentation!

Measure: e.g., k

kk jiTS 2)()(

kikj

)( kT x kx

T

))(( kk TJj xInterpolation:


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No segmentation!

T1 =Id

Measure: e.g., k

kk jiTS 2)()(


The simple case of binary images…

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No segmentation!

T2

Measure: e.g., k

kk jiTS 2)()( Partial overlap


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Iconic approach for fMRI!

A typical fMRI imageof the nineties

A lot of widely used softwares:SPM, AIR, AFNI, etc.

Minimize thesum of squared differences

Search through rigid motions(sometimes affine)

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Main differences between softwares?

•Preprocessing (smoothing)•Interpolation

•Optimization scheme (iterative)

nearest neighbor linear spline

•Powell•Levenberg Marquardt•Modified Gauss-Newton

Fighting with local optimaImproving accuracy

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Iterative optimization of smooth measure

Small motion = good initialization

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Is everything fine?

t180 frames

18 frames (2 sec/frame)

Block design, 3T magnet

versus

Activations?

Motion correction

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The consequences of motions

Motion-related artifacts:

– intrascan motion;

– the spin history effect;

– interaction between motion and susceptibility;

– Non perfect estimation and interpolation.

Task-correlated motion =Confounds in cognitive analysis

Use motion estimations as regressors?

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Could activated areas be responsibleFor the task-correlated motion estimation?

BUT!

Is this monomodal situation so secure?

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Classification of standard similarity measures

Assumed relationship:

Sum of squared differencesSum of absolute differences

Adapted measures :

Conservation of intensity

Intensies of image J

Inte

ns

itie

s o

f im

ag

e I

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Affine

Adapted measures

Correlation coefficient

kkk

JIIJ JjIi

nT ))((

1)(




Inte

ns

itie

s o

f im

ag

e I

m

imi

R

RRN 21

Ratio of image uniformity (Woods)

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Woods criterion (1993)Woods variants (Ardekani, 95; Alpert, 96; Nikou, 97)Correlation Ratio (Roche, 98)

Functional

Adapted measures




Inte

ns

itie

s o

f im

ag

e I

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Joint entropy (Hill, 95; Collignon, 95)Mutual Information (Collignon, 95; Viola, 95)Normalized Mutual Information (Studholme, 98)

Statistical

Adapted measures




Inte

ns

itie

s o

f im

ag

e I

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II. Methods Similarity Measures

• LS-SPM (Friston);• LS-AIR (Woods);• GM - custom (INRIAlign);• RIU-AIR (Woods);• CR – custom (Roche)• MI - custom (Wells, Maes, Viola).

Confounds related to interpolation method or search method ?

In some experiments

• LS - Custom;• RIU - Custom;

IPMI’01Do activated areas bias Least Square approaches?

Let us compare various methods…

The “sum of squared differences” measure

assumes Gaussiannoise for the differencebetween both images…

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Entropy for Image Registration

Define a joint probability distribution:

– Generate a 2-D histogram where each axis is the number of possible greyscale values in each image

– Each histogram cell is incremented each time a pair (I_1(x,y), I_2(x,y)) occurs in the pair of images

• If the images are perfectly aligned then the histogram is highly focused. As the images mis-align the dispersion grows

• recall Entropy is a measure of histogram dispersion

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– Define joint entropy to be:

– Images are registered when one is transformed relative

to the other to minimize the joint entropy

– The dispersion in the joint histogram is thus minimized

ji

jipjipBAH,

)],(log[),(),(

Using joint entropy for Image Registration

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Definitions of Mutual Information

Commonly used definitions:

I(A,B) = H(A) + H(B) - H(A,B)Maximizing the mutual info is equivalent to

minimizing the joint entropy (last term)

This definition is related to the Kullback-Leibler distance between two distributions

ba bpap

bapbapBAI

, )()(

),(log),(),(

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Aim of the comparison of methods:

– assess the potential bias in motion parameter estimation due to activation presence, whatever the actual accuracy of each method.

Accuracy study has been done in several works (Jiang, Frouin, West, Holden, etc.), and requires the study and optimization of each parameter influence, which is far beyond the scope of this work.

IPMI’01This is not a robustness or accuracy study !

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II. Methods Image Acquisition

– Brucker scanner operating at 3T using a 30 contiguous slice 2D EPI sequence (slice array of 64x64 voxels).

– Pixel size of 3.75mm and slice thickness of 4mm.

– Various simulated time series.

– Actual time series using a block design.

IPMI’01A few words about the datasets

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IPMI’01Simulated Activation Patterns

Pattern A1 A2 A3Size (%) 12.4 6.2 3.2Mean(%) 1.26 1.19 1.18Max(%) 2.04 2.03 2.03

A first pattern inferred from a simple visual experiment

Two smaller patterns stemming from erosion of the initial largest pattern

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Design of Simulated Time SeriesIPMI’01

3x3x3 median filtering

Tsim applied. 62x62x28 geometry. Gaussian/Rician noise ( = 2.5%)

Activation pattern

Reference image

Test images1 2 n

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Simulated Activations Without Motion

Run the six registration methods and evaluate the transformation parameters (tx, ty, tz, rx, ry, rz) for each package.

40 3-D Frames

Compute cross-correlation between each parameter and A1 time course and infer activated areas.

0 1 2 39

Test,1 Test,2 Test,39

+

I

x

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A couple of estimated motion parameters I

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Spatial Gaussian smoothing - 5mm

Low-pass filtering with 2-frame width

Spurious Clustered Voxels (false positives)

LS-SPM – 227 LS-AIR –16 RIU-AIR and MI - 0

Voxels activated if p-value > 0.001

Detection of “activated areas” using General Linear Model I

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IPMI’01Simulated activations with simulated motion

t = 0.1, 0.2, 0.5, 1.0, 2.0 and 5.0 mm

r = 0.1, 0.2, 0.5, 1.0, and 2.0 deg

t=0.1mm

t=5.0mm

r=0.1deg

r=2.0deg

1 2 20

1 2 20

1 2 20

Tsim

II

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8 Different Reference Images

Nº Pattern Mean Signal Increase (%)

1 NA NA

2 A1 0.63

3 A1 1.26

4 A1 2.52

5 A1 5.04

6 A1 10.08

7 A2 2.52

8 A3 2.52

Simulated activations with simulated motion II

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Influence of motion amplitude

- 2 Reference images:

Pattern Mean Signal Increase (%)1 NA NA2 A1 0.633 A1 1.264 A1 2.525 A1 5.046 A1 10.087 A2 2.528 A3 2.52

- Test images:t = 0.1, 0.2, 0.5, 1.0, 2.0, 5.0 mm.r = 0.1, 0.2, 0.5, 1.0, 2.0 deg.

IPMI’01Simulated activations with simulated motion IIA

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Simulated activations with simulated motion IIA

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IIASimulated activations with simulated motion

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IPMI’01

Influence of activation amplitude



- Test images:t = 0.2 mm.r = 0.2 deg.

Simulated activations with simulated motion IIB

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Simulated activations with simulated motion IIB

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IPMI’01

Influence of activation size



- Test images:t = 0.2 mm.r = 0.2 deg.

Simulated activations with simulated motion IIC

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Simulated activations with simulated motion IIC

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– We have also performed an additional experiment on the influence of the initial spatial smoothing applied by SPM and AIR

– RIU-AIR problems are overcome by a large smoothing, but motion estimates turn out to be biased.

– For SPM, low smoothing implies smaller bias but motion estimates are less accurate.

IPMI’01Evaluation of spatial filtering pre-processing effect III

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III

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IPMI’01Experiment With Actual Time Series

t180 frames

18 frames (2 sec/frame)

IV

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Statistical Inference: Gaussian smoothing (FWHM 5mm); High-pass temporal filtering (period 120s); Low-pass temporal filtering by a Gaussian function (4s).Two explanatory variables: Periodic stimulus convolved with a standard hemodynamic response; Time derivative of hemodynamic response.Voxels reported activated if the p-value > 0.05.

Experiment With Actual Time Series IV

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Experiment With Actual Time Series: “activations”

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IV. Discussion

“Robust” similarity measures have been classicaly used in multimodality registration studies.

In monomodality studies, when the residuals are endowed with a Gaussian distribution, LS-based methods are optimal estimators.

The experiments presented in this work prove that the use of LS-based methods for functional studies may be questioned, due to the presence of activated areas.

Activations can bias “sum of squares” measure

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– In first simulation, the use of the LS-custom method shows that the bias in LS-based similarity measures is related to the nature of the measure and not to the intrinsic computational implementation of each method.

– The bias may induce spurious activations along high-contrast brain edges, in the absence of subject motion.

– RIU-AIR and MI are more robust to activation presence, but presented qualitatively different results.

Accuracy vs. Robustness.

Measure comparison, first simulation

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– The second set of simulations indicates that RIU-AIR and MI accuracy does not depend on the presence of activations.

– Also that the bias magnitude is highly related to the signal change amplitude. This may explain why our 3T magnet led to more difficulties than more usual 1.5T scanners. Indeed, it can be seen that activation level has a more dramatic role on the accuracy decline than activation size.

Measure comparison, other simulations

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– The experiment with actual time series seems to be consistent with our interpretation of the simulation studies.

– LS-SPM and LS-AIR give different results, particularly in pitch. The other two methods do not detect this putative motion.

– Yaw estimations obtained by the four methods do not agree. This may be related to distortions that cannot be corrected with rigid-body transformations.

Actual time series

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– LS-based methods create spurious clusters of activated voxels, whose localization depends, in our opinion, on the brain edge orientation relatively to actual activation localization.

– Spurious activations may appear at the same place across individuals and survive to group analysis

– While we hope that this alarming prediction is too pessimistic, it calls for trying to minimize the risk.

Spurious activations

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V. Conclusion

– Our work has shown that “robust” similarity measures could improve the situation with activation-based outliers

– MI was used for historical reasons, but it may not be the best choice. MI is prone to local maxima problems.

– Could we build a dedicated robust similarity measure?

IPMI’01So what?

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Mutual Information weaknesses (Pluim, Tsao)

Numberof bins

Interpolationmethod

Estimation of the joint histogram (Parzen windows…)

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Taxonomy S. Measure Expression

Intensity Conservation

Least-squares (LS)

Least-squares with a GM estimator (GM)

Affine Dependence

Ratio of Image Uniformity (RIU)

Functional Dependence

Correlation Ratio (CR)

Statistical Mutual Information

Dependence (MI) a b ba

abab pp

pp log

22

2

2

/1 cba

bap

bap

a bab

a bab

m

imi

R

RRN 21

b

BbA

p 22

11

Which similarity measures?

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The influence of the cut-off parameter in GM

In the GM expression:

one shall tune the value of c.

However, the robustness against “outliers” may lead to local optima problems.

2

2

2

1c

ba

bap

a bab

Back to first simulation…

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The influence of spatial smoothing

GM with no smoothing leads to many local minima problems, thus smoothing is required.

In return, the CR and CRsym methods turn out to be more biased as the smoothing level increases.

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Simulated motionless time series.

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The actual time series

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Discussion

- MI and GM methods seem to be the most robust methods relatively to activation presence.

- The GM has a disadvantage, which is related to the tuning of the c parameter. A dynamic strategy to perform this tuning could eventually lead to better results.

- However, some correlations with the activation task persist.

- Build new dedicated measure after activation detection?

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Let us try this simple idea with a couple of measures

• LS – Custom (Friston et al., 1996);

• GM – Custom (Nikou et al., 1998);

• RIU – Custom (Woods et al., 1992);

• CR – Custom (Roche et al., 1998);

• MI – Custom (Collignon et al. 1995, Wells et al., 1996).

Similarity measures implemented according to the conventional (1) and the proposed approach (2), which discards the activation signal.

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Discarding the Activated areas

LS(1) RLS(1) RIU(1) CR(1) MI(1)

Mask LS(2) RLS(2) RIU(2) CR(2) MI(2)

reference test images

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Results (first simulation)

Simulation without motion LS 1 LS 2 GM 1 GM2 RIU 1 RIU 2 CR 1 CR 2 MI 1 MI 2

tx 0.09 0.01 0.06 0.07 0.07 0.14 0.20 0.05 0.04 0.33

ty 0.84 0.38 0.45 0.12 0.82 0.32 0.34 0.03 0.40 0.05

tz 0.84 0.16 0.49 0.12 0.79 0.04 0.18 0.40 0.25 0.09

rx 0.79 0.17 0.03 0.01 0.79 0.24 0.07 0.03 0.23 0.28

ry 0.04 0.17 0.28 0.21 0.19 0.05 0.05 0.13 0.03 0.16

rz 0.25 0.13 0.13 0.20 0.22 0.29 0.10 0.06 0.07 0.01

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Results (actual time series)

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SET 1

LS 1 LS 2 GM 1 GM2 RIU 1 RIU 2 CR 1 CR 2 MI 1 MI 2 tx 0.27 0.27 0.14 0.13 0.29 0.23 0.04 0.05 0.02 0.14

ty 0.65 0.17 0.32 0.12 0.64 0.12 0.27 0.01 0.41 0.06

tz 0.46 0.14 0.16 0.34 0.17 0.25 0.12 0.27 0.19 0.42

rx 0.72 0.10 0.35 0.03 0.74 0.13 0.36 0.01 0.58 0.06

ry 0.02 0.05 0.14 0.09 0.07 0.07 0.06 0.03 0.14 0.07

rz 0.01 0.13 0.18 0.15 0.13 0.18 0.07 0.13 0.18 0.01

SET 2 LS 1 LS 2 GM 1 GM2 RIU 1 RIU 2 CR 1 CR 2 MI 1 MI 2

tx 0.17 0.24 0.03 0.02 0.20 0.30 0.13 0.01 0.01 0.02

ty 0.57 0.27 0.45 0.18 0.58 0.18 0.25 0.09 0.34 0.04

tz 0.63 0.29 0.27 0.02 0.45 0.19 0.11 0.15 0.17 0.05

rx 0.72 0.37 0.53 0.26 0.73 0.33 0.41 0.02 0.57 0.15

ry 0.05 0.16 0.12 0.04 0.21 0.20 0.01 0.02 0.10 0.20

rz 0.20 0.03 0.03 0.02 0.03 0.07 0.01 0.18 0.08 0.06

SET 3 LS 1 LS 2 GM 1 GM2 RIU 1 RIU 2 CR 1 CR 2 MI 1 MI 2

tx 0.36 0.40 0.03 0.15 0.36 0.41 0.03 0.09 0.29 0.21

ty 0.67 0.29 0.51 0.17 0.62 0.22 0.17 0.08 0.32 0.07

tz 0.64 0.11 0.33 0.03 0.46 0.04 0.33 0.06 0.23 0.10

rx 0.69 0.05 0.44 0.01 0.68 0.14 0.23 0.08 0.40 0.13

ry 0.01 0.04 0.06 0.03 0.10 0.02 0.04 0.15 0.07 0.01

rz 0.38 0.17 0.13 0.09 0.29 0.22 0.12 0.19 0.08 0.06

Results (3 actual time series)

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Results (2 actual time series, activations)

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Discussion

- This last work rules out the hypothesis of a true task-related motion. Indeed, discarding about 20% of the voxels almost removes the correlation with the task.

- The dilation of the mask is fundamental in order to avoid contamination of neighbor voxels by activated voxels

- The proposed strategy is easy to implement and suitable for most conventional studies. Improvements may be required when registering complex studies.

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- We have shown that the problem of registration of fMRI time series should be revised in order to take into account the influence of activation.

- We will have to study situations including true task-correlated motion.

- Detecting motion and activation simultaneously ?(Orchard et al., 2003).

- Interactions between motion and distortions!

General Conclusions & Further Work

Be careful!

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Eddy-Current Distortion Correction for MR Diffusion Imaging

+

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Several gradient directions ( at

least 6)

Several gradient strengths and

durations

Diffusion tensor imaging

Diffusion-weighted signal attenuation:

One gradient chronogram

= One b matrix

Chronogram

<x2>1/2

Td

D

50

1750

Tensor estimation:Tensor estimation:

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Eddy current related EPI distortions

Spatial resolution :1,875 mm x 1,875 mm x 2,8 mm

No gradient

Translation Shearing

Scaling

8 mm

Gradient 0 mT/m Gradient 22 mT/m

Diffusion-sensitizing gradientrelated distortion

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Slice by slice estimation of affine transformations

1T

1T

0T

S

Mutual information landscape

Maximum

Parzen window = truncated gaussianLinear resampling

grey value coded with 6 bits

Powellalgorithm

Mutual information maximization

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Results forone slice128 x 128

2mm x 2mm

Reference:T2-weighted4 repetitions

Diffusion gradients:

6 directions5 amplitudes4 repetitions

Higher variabilitywith CR

than with MI

X gradient:shearing

(frequency)

Y gradient:shrinking(phase)

Z gradient:translation (T0)

(slice)

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Improvements achieved by the new estimation scheme

T2-weightedFractional anisotropywithout corrections

Fractional anisotropywith the corrections

Fractionalanisotropy

=variability

ofthe tensor

eigenvalues

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That’s all

A SPM plug-in performing fMRI motion

correction using the Geman McClure robust estimator

is freely distributed by the Epidaure group (INRIA)

INRIAlign…

motion correction in fmri time series

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