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From Spatial Regularization to Anatomical Priors in fMRI Analysis. Fragmented Map. Regularized Map. Wanmei Ou William Wells Polina Golland. Core 1 Meeting – May 23 rd , 2006. Main Contributions. Propose new spatial regularization method: Incorporating Anatomical Information

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from spatial regularization to anatomical priors in fmri analysis

From Spatial Regularization to Anatomical Priors in fMRI Analysis

Fragmented Map

Regularized Map

Wanmei Ou William Wells Polina Golland

Core 1 Meeting – May 23rd, 2006

main contributions
Main Contributions
  • Propose new spatial regularization method: Incorporating Anatomical Information
  • Empirically Compare proposed methods with traditional methods
road map
Road Map
  • Background and Motivation
  • Markov Random Field (MRF) and Anatomical Guided MRF Model
  • Mean Field Approximation Solver
  • Experimental Evaluation
  • Conclusions
road map1
Road Map
  • Background and Motivation
  • Markov Random Field (MRF) and Anatomical Guided MRF Model
  • Mean Field Approximation Solver
  • Experimental Evaluation
  • Conclusions
from fmri images to fmri analysis
From fMRI Images to fMRI Analysis

Image Acquisition

MRI

fMRI

Task protocol: Auditory, Vision, etc.

Spatial

Regularization

Voxel-by-voxel detector

Threshold

Activation Map

Scatter activation

road map2
Road Map
  • Background and Motivation
  • Markov Random Field (MRF) and Anatomical Guided MRF Model
  • Mean Field Approximation Solver
  • Experimental Evaluation
  • Conclusions
goal and approaches
Goal and Approaches

Goal: Recover True Activation through Spatial Regularization

Our Approach:

  • Incorporate MRF into General Linear Model (GLM) Statistic
  • Include Anatomical Information into MRF
detailed approaches
Detailed Approaches

Our Approach:

  • 1. Incorporate MRF into GLM Statistic
    • Capture spatial dependency
    • Overcome over-smoothing effect
  • 2. Include Anatomical Information into MRF
    • Activation is more likely in gray matter
    • Spatial dependency is strong within tissue type

Activation Maps

MRF

MRI

Synthetic Ground Truth

Segmentation

Gray, White, Other

general linear model glm
General Linear Model (GLM)

Protocol-Independent Signal

Two Hypotheses

Not-active voxel

Active voxel

Protocol-Dependent Signal

GLM

ML Estimate

F or T statistic

P-value

Traditional Approach

General Log Likelihood Ratio (Cosman, 04)

Our Approach

markov random field
Markov Random Field

Spatial Priors:

Likelihood:

-- Hidden Activation State

-- Noisy Observation/Statistic

MAP Estimate:

incorporating anatomical information
Incorporating Anatomical Information

Combine activation state & tissue type

MRI

Segmentation

-- Hidden Activation State

-- Tissue Type

MAP Estimate:

-- Segmentation Label

-- Noise Statistic

markov random fields solvers
Markov Random Fields Solvers
  • Binary MRF Min-Cut/Max-Flow (Min-Max) Binary MRF Only
  • Gibbs Sampling Slow
  • Simulated Annealing Slow
  • Belief Propagation Fast, Approximation
  • Mean Field Fast, Approximation
road map3
Road Map
  • Background and Motivation
  • Markov Random Field (MRF) and Anatomical Guided MRF Model
  • Mean Field Approximation Solver
  • Experimental Evaluations
  • Conclusion and Future work
mean field
Mean Field
  • Approximate by
  • Iterative up-date rule

Belief: Prob. Of voxel is active

  • Approximated MAP
slide15
Mean Field

Similar up-date rule while incorporating anatomical information

Approximated MAP

alternative anatomically guided filters
Alternative Anatomically Guided Filters
  • No smoothing with Anatomical Information
    • Suppress all activation in the non-gray matter.
  • Anatomically Guided Gaussian Filter
    • Adjust weights based on segmentation labels.
road map4
Road Map
  • Background and Motivation
  • Markov Random Field (MRF) and Anatomical Guided MRF Model
  • Mean Field Approximation Solver
  • Experimental Evaluation
    • Synthetic Data
    • Real fMRI Data
  • Conclusions
low snr fragmented activation maps
Experiments – Synthetic Data SetsLow SNR Fragmented Activation Maps

Noise

SNR = -6.3dB

Noise

SNR = -9.3dB

Activation Maps

Threshold:

False positive = 0.05%

Forward

Model

GLM

Detector

+

Synthetic Ground Truth

slide19
Experiments – Synthetic Data Sets

Noise

Forward

Model

GLM with different

smoothing methods

+

Synthetic Ground Truth

  • No Smoothing
  • No Smoothing w/ Anatomical Info
  • Gaussian Smoothing w/o Anatomical Info
  • Gaussian Smoothing w/ Anatomical Info
  • MRF w/o Anatomical Info
  • MRF w/ Anatomical Info
roc analysis
ROC Analysis

Without Anatomical Information

Min-Max (Exact Solver) vs. Mean Field (Approximation)

SNR = -6dB

SNR = -9dB

roc analysis1
ROC Analysis

Without Anatomical Information

MRF (Mean Field) vs. Gaussian Smoothing

SNR = -6dB

SNR = -9dB

roc analysis2
ROC Analysis

With Anatomical Information

MRF (Mean Field) vs. Gaussian Smoothing

SNR = -6dB

SNR = -9dB

road map5
Road Map
  • Background and Motivation
  • Markov Random Field (MRF) and Anatomical Guided MRF Model
  • Mean Field Approximation Solver
  • Experimental Evaluation
    • Synthetic Data
    • Real fMRI Data
  • Conclusions
evaluation on real data
Evaluation on Real Data

“Ground Truth”

GLM

Majority Voting

GLM

8 task epochs

comparisons

GLM with various spatial regularizers

2 task epochs

activation maps comparison
Activation Maps Comparison

Anat No Smoothing Gaussian MRF

“Ground Truth” No Smoothing+Anat Gaussian+Anat MRF+Anat

Three Epochs

sm007ep3

activation maps comparison1
Activation Maps Comparison

Anat No Smoothing Gaussian MRF

“Ground Truth” No Smoothing+Anat Gaussian+Anat MRF+Anat

Three Epochs

sm007ep3

activation maps comparison2
Activation Maps Comparison

Anat No Smoothing Gaussian MRF

“Ground Truth” No Smoothing+Anat Gaussian+Anat MRF+Anat

Three Epochs

sm007ep3

slide28
Conclusions
  • New Spatial Regularization method
    • Anatomical Bias
  • Empirical Evaluation
    • ROC analysis
    • Activation maps
  • MRF + Anatomical Information
    • Increase detection accuracy with reduced-length signal
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