Getting Used to the Noise
Mark Woolrich
University of Oxford
Oxford centre for Human Brain Activity
Centre for FMRI of the Brain
Gaussianity - The Central Limit Theorem
mixing
balanced sum of a
large number of
independent sources non-Gaussian
noise sources
Gaussian
noise
Overview
•  Outlier subjects in group analysis
➡  Mixture modelling
➡  Permutation testing
•  Dealing with FMRI structured noise at the
first level
➡  Combined ICA and GLM
A Simple Example
subject
true distribution
effect size
Is there a significant population mean effect?
Assume the population distribution is Gaussian
Outliers
subject
true distribution
effect size
Is there a significant population mean effect?
Causes of outliers:
•
•
•
Excessive motion
Misunderstood task
Anatomical variability
Outliers
subject
true inferred distribution
distribution
effect size
Is there a significant population mean effect?
Consequences of outliers:
• Loss of sensitivity and FPR control
Robust Regression
Iteratively reweighted
least squares
Wager et al., NI, 2005
Mixture of Gaussians
subject
non-outlier class
outlier class
effect size
Penny et al., NeuroImage (2007)
Woolrich, NeuroImage (2008)
Mixture of Gaussians
subject
non-outlier class
outlier class
0
1
Prob(Outlier)
effect size
(Non-outlier)
Penny et al., NeuroImage (2007)
Woolrich, NeuroImage (2008)
(Outlier)
Inferring a group mean with a positive outlier
subject
Mixture of Gaussians
Single Gaussian (MOG)
(SG)
effect size
Simulated null data
true
mean
SG
MOG
Inferring a group mean with a negative outlier
subject
Single Gaussian Mixture of Gaussians
(SG)
(MOG)
effect size
Simulated activation data
z-stats
true
mean
SG
MOG
MOG gives
increased
sensitivity
SG
More Assumptions
Parametric
Single Gaussian
- Assumptions violated in
the presence of outliers
Non-parametric
Robust regression
Mixture of Gaussians
permutation tests
- Account for outliers
- Great for controlling
whole-brain FPRs on SPMs
- outliers ?
Permutation Tests •  Sign flipping
[Meriaux et al., HBM, 2007]
Control FPR:
Inferring a group mean from simulated null
data with positive outliers
Permute
Permutation Tests •  Sign flipping
[Meriaux et al., HBM, 2007]
But lose sensitivity:
Inferring a group mean from simulated positive activation data with one positive and one negative outlier
z-stats
z-stats
Best of Both Worlds?
More Assumptions
Parametric
Single Gaussian
- Assumptions violated in
the presence of outliers
Non-parametric
Robust regression
Mixture of Gaussians
permutation tests
- Account for outliers
- Great for controlling
whole-brain FPRs on SPMs
In the presence of
outliers:
- Controls FPR
- Loses sensitivity Best of Both Worlds?
More Assumptions
Parametric
Single Gaussian
- Assumptions violated in
the presence of outliers
Non-parametric
Robust regression
Mixture of Gaussians
permutation tests
- Account for outliers
- Great for controlling
whole-brain FPRs on SPMs
In the presence of
outliers:
- Controls FPR
- Loses sensitivity Could permute MOG approach [Roche et al., NI, 2007]
- BUT very slow
Best of Both Worlds?
Solution (MOG+Permute) - 1. a. Use MOG approach on un-permuted data/design
b. Variance weight data/design using MOG result
2. Permute variance weighted data/design calculating OLS
Best of Both Worlds?
Solution (MOG+Permute) - 1. a. Use MOG approach on un-permuted data/design
b. Variance weight data/design using MOG result
2. Permute variance weighted data/design calculating OLS
Null data
Activation data
z-stats
MOG+perm
z-stats
Overview
•  Outlier subjects in group analysis
➡  Mixture modelling
➡  Permutation testing
•  Dealing with structured noise in FMRI
➡  Combined ICA and GLM
General Linear Model (GLM) design "
matrix"
space
responses"
FMRI data"
="
time"
time"
Scan #k space
spatial
maps
Gaussian
+
Noise
General Linear Model (GLM) design "
matrix"
space
responses"
FMRI data"
="
time"
time"
Scan #k space
spatial
maps
Gaussian
+
Noise
•  Structured noise:
•
•
•
e.g. stimulus correlated motion, physiological noise, networks
of spontaneous neuronal activity can mimic stimulus related activity
can swamp stimulus related activity
Increase False Positives
Nominal rate
Independent Component
Analysis (ICA)
space
space
components"
Data
components"
FMRI data"
="
time"
time"
Scan #k Time
courses
• McKeown et.al. (1998):
spatial
maps
+
Noise
Spatially independent maps (sources)
data is decomposed into a
set of spatially independent component maps and a
set of component time-course
Independent Component
Analysis (ICA)
Scanner-based artefacts
- e.g. Nyquist ghost:
FMRI data
Physiological noise
- e.g. head motion:
ICA denoising
Component 1
FMRI data
Component 2
Component 3
Component 4
Component 5
Component 6
.
.
.
ICA denoising
Component 1
FMRI data
Component 2
Component 3
Identify structured
noise components
Component 4
Component 5
Component 6
.
.
.
ICA denoising
Component 1
FMRI data
Component 2
Component 3
Identify structured
noise components
Component 4
denoised
FMRI data
Component 5
Component 6
.
.
.
Denoising FMRI
before denoising
•  Example:
left
vs right hand
finger tapping
Johansen-Berg et al.
PNAS 2002
LEFT - RIGHT
RIGHT
LEFT
contrast
after denoising
Combined GLM and ICA
design "
matrix"
space
s
u
l
spatial
u ling
m
i
t
el
smaps
d
o
M
GL se m
n
o
p
res
responses"
FMRI data"
="
time"
time"
Scan #k space
+
space
components"
components"
time"
d
e
ur ng
t
independent
c
lli
truspatial
e
s
od maps
A
m
C
I
ise
o
n
Gaussian
+
Noise
Combined GLM and ICA
space
design "
matrix"
components"
Data
="
time"
time"
Scan #k FMRI data"
space
components"
Structured noise
component time
courses
spatial
maps
+
Gaussian
Noise
Spatially independent maps
Makni et al. (In Submission) (see HBM poster #1193 WTh-AM)
Combined GLM and ICA
space
Data
design "
matrix"
components"
FMRI data"
="
time"
time"
Scan #k Mixture model
priors (encode independence)
space
components"
Structured noise
component time
courses
spatial
maps
+
Gaussian
Noise
Spatially independent maps
Bayesian Inference
Makni et al. (In Submission) (see HBM poster #1193 WTh-AM)
Combined GLM and ICA
Automatic Relevance
Determination
(ARD) Priors
components"
space
space
Data
design "
matrix"
components"
FMRI data"
="
time"
time"
Scan #k Structured noise
component time
courses
Mixture model
priors (encode independence)
spatial
maps
+
Gaussian
Noise
Spatially independent maps
Bayesian Inference
Makni et al. (In Submission) (see HBM poster #1193 WTh-AM)
Simulated Data
true
spatial map
GLM-ICA
estimated
spatial map
GLM
estimated
spatial map
component 1
(stimulus related)
component 2
(stimulus related)
component 3
(structured noise)
Makni et al. (In Submission) (see HBM poster #1193 WTh-AM)
False Positives
GLM
Nominal rate
GLM-ICA
Makni et al. (In Submission) (see HBM poster #1193 WTh-AM)
Finger-tapping Task
GLM-ICA
Stimulusrelated
component
Structured
noise
component
Structured
noise
component
GLM
Multimodal data fusion
•  Many subjects, with multimodal data for each one DTI maps from TBSS
Structural GM from VBM
or Freesurfer:
FA
MD
MO
space
Groves et al. (In Submission)(see HBM poster #1091 MT-AM)
modality"
GM density
Cortical thickness
Neuroimaging
data"
PE 2
Multimodal data fusion
⊗
space
space
components"
="
components"
modaility"
modality"
Neuroimaging
data"
modality-
courses
spatial maps
Independent spatial
maps (ICA)
Groves et al. (In Submission)(see HBM poster)
ICA across modalities
Multimodal data fusion
GM
FA
Establish links between
modalities using ICA, then
find group-related
components
Groves et al. (In Submission)(see HBM poster)
MD
MO
Conclusions
•  “Contaminating” outlier subjects or
structured noise can cause:
•  Increased false positives
•  Loss of sensitivity
•  Use a combined approach of Gaussian
MM and permutation testing to handle
outliers at the group level
•  Use combined ICA/GLM to handle
structured noise at the first level
Acknowledgments
•  UK EPSRC
•  Salima Makni
•  Christian Beckmann
•  Adrian Groves
•  Gwenaëlle Douaud
• Michael Chappell
• Morgan Hough
• Tom Nichols
• Stephen Smith