Robust Regularization for the Estimation of Intra-Voxel Axon Fiber Orientations Also presented at MMBIA Anchorage, Jun, 2008 Alonso Ramirez-Manzanares (PICSL) Hui Zhang (PICSL) Mariano Rivera (CIMAT) James C. Gee (PICSL)

Overview Motivation Statement of the problem Our Proposal Results for in-vivo human data Results for synthetic data Conclusions

MOTIVATION

Motivation (1/3): Intra-voxel fiber orientations. Behrens et al, Neuroimage'07 “We detect complex fibre architecture in approximately a third of voxels with an FA greater than 0.1” DT Multi-DTs

Motivation (2/3): The noisy orientations Because of: - acquisition noise - a reduced # of diffusion encoding orientations (clinical applications)‏ - patient movement

Motivation(3/3): Data averaging and Spatial integration From web site: In our case:

THE PROBLEM

The Problem (1/2): The spatial regularization of directional fields This is a well- known task, for instance, in Optical Flow computation.

The Problem (2/2): The spatial regularization of multi-fiber orientation fields. Problems: a) The need to regularize orientations (not directions)‏ b) The need to match orientations c) The need to use indicator variables of the number of bundles d) The subtle axon fiber structures

OUR PROPOSAL

Proposal(1/5): Observation model, Diffusion Basis Function (DBF) approach. Ramirez-Manzanares et al. IEEE-TMI '07 Tuch et al, MRM '02 Tensor Basis DBFs

Proposal(2/5): The robust spatial regularization term Inspired in statistical robust regression

Proposal(3/5): The robust spatial regularization term Indicator variables Robust Weights Robust regularization

Proposal(4/5): Single DT as a diffusivity profile constraint Plausible Implausible solution solution

Proposal(5/5): The Integration of terms and methods Data and contrast term Ramirez-Manzanares et al TMI’07

RESULTS FOR IN-VIVO HUMAN DATA

Results(1/6): In-vivo human data (b=1000, 60 DWI)‏ Non-Regularized Robust Regularized

Results(2/6): In-vivo human data, a closer view Non-Regularized Robust Regularized DT

Results(3/6): In-vivo human data, a closer view Non-Regularized Robust Regularized DT

RESULTS FOR SYNTHETIC DATA

Results(4/6): Synthetic data Robust Regularized Iteration 1 Robust weights Iteration 1 Robust weights Iteration 3 Non Regularized DT Robust Regularized Iteration 3

Results(5/6): Realistic/complex synthetic data Ground truth non-Regularized SNR=20 DT Iteration 1 Iteration 2 Iteration 3

Results(6/7): Synthetic data, quantitative results

Results(7/7): Comparison: Robust vs. non-Robust Non-Robust Regularized Ramirez-Manzanares et al TMI’07 Robust Regularized

Conclusions

Thank you for your attention! Questions?