Robust Regularization for the Estimation of IntraVoxel Axon

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. DT Multi-DTs Behrens et al, Neuroimage'07 “We detect complex fibre architecture in approximately a third of voxels with an FA greater than 0. 1”

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: www. iua. upf. es/activitats/semirec/semi-rderiche/ In our case:

THE PROBLEM

The Problem (1/2): The spatial regularization of directional fields This is a wellknown 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. Tuch et al, MRM '02 DBFs Ramirez-Manzanares et al. IEEE-TMI '07 Tensor Basis

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 solution Implausible 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 Non Regularized DT Robust Regularized Iteration 1 Iteration 3 Robust weights Iteration 1 Robust weights Iteration 3

Results(5/6): Realistic/complex synthetic data Ground truth Iteration 1 non-Regularized SNR=20 Iteration 2 DT 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? alram@cimat. mx