From spatial regularization to anatomical priors in fmri analysis
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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

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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 23rd, 2006


Main Contributions

  • Propose new spatial regularization method: Incorporating Anatomical Information

  • Empirically Compare proposed methods with traditional methods


Road Map

  • Background and Motivation

  • Markov Random Field (MRF) and Anatomical Guided MRF Model

  • Mean Field Approximation Solver

  • Experimental Evaluation

  • Conclusions


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

Image Acquisition

MRI

fMRI

Task protocol: Auditory, Vision, etc.

Spatial

Regularization

Voxel-by-voxel detector

Threshold

Activation Map

Scatter activation


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: Recover True Activation through Spatial Regularization

Our Approach:

  • Incorporate MRF into General Linear Model (GLM) Statistic

  • Include Anatomical Information into MRF


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)

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

Spatial Priors:

Likelihood:

-- Hidden Activation State

-- Noisy Observation/Statistic

MAP Estimate:


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

  • 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 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

  • Approximate by

  • Iterative up-date rule

Belief: Prob. Of voxel is active

  • Approximated MAP


Mean Field

Similar up-date rule while incorporating anatomical information

Approximated MAP


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 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


Experiments – Synthetic Data Sets

Low 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


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

Without Anatomical Information

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

SNR = -6dB

SNR = -9dB


ROC Analysis

Without Anatomical Information

MRF (Mean Field) vs. Gaussian Smoothing

SNR = -6dB

SNR = -9dB


ROC Analysis

With Anatomical Information

MRF (Mean Field) vs. Gaussian Smoothing

SNR = -6dB

SNR = -9dB


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

“Ground Truth”

GLM

Majority Voting

GLM

8 task epochs

comparisons

GLM with various spatial regularizers

2 task epochs


Activation Maps Comparison

Anat No Smoothing Gaussian MRF

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

Three Epochs

sm007ep3


Activation Maps Comparison

Anat No Smoothing Gaussian MRF

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

Three Epochs

sm007ep3


Activation Maps Comparison

Anat No Smoothing Gaussian MRF

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

Three Epochs

sm007ep3


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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