Denoising Intra-voxel Axon Fiber Orientations by Means of ECQMMF Method

Diffusion weighted magnetic resonance imaging is widely used in the study of the structure of the fiber pathways in brain white matter. In this work we present a new method for denoising intra---voxel axon fiber tracks. In order to improve local (voxelwise) estimations, we use the general---purpose segmentation method called Entropy---Controlled Quadratic Markov Measure Field Models. Our proposal is capable of spatially---regularize multiple axon fiber orientations (intra-voxel orientations). In order to provide the best as possible local axon orientations to our spatial regularization procedure, we evaluate two optimization methods for fitting a Diffusion Basis Function model. We present qualitative results on real human Diffusion Weighted MRI data where the ground---truth is not available, and we quantitatively validate our results by synthetic experiments.

[1]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

[2]  Yijun Liu,et al.  Recovery of intra-voxel structure from HARD DWI , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[3]  Edgar Arce Santana,et al.  Hidden Markov Measure Field Models for Image Segmentation , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  David E. Breen,et al.  Level Set Segmentation and Modeling of DT-MRI human brain data , 2003 .

[5]  Zhizhou Wang,et al.  A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field from DWI , 2003, IPMI.

[6]  Zhizhou Wang,et al.  A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI , 2004, IEEE Transactions on Medical Imaging.

[7]  Zhizhou Wang,et al.  Tensor Field Segmentation Using Region Based Active Contour Model , 2004, ECCV.

[8]  Rachid Deriche,et al.  DTI segmentation by statistical surface evolution , 2006, IEEE Transactions on Medical Imaging.

[9]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[10]  Zhizhou Wang,et al.  DTI segmentation using an information theoretic tensor dissimilarity measure , 2005, IEEE Transactions on Medical Imaging.

[11]  Baba C. Vemuri,et al.  A Unified Computational Framework for Deconvolution to Reconstruct Multiple Fibers From Diffusion Weighted MRI , 2007, IEEE Transactions on Medical Imaging.

[12]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[13]  David H. Laidlaw,et al.  Visualization and image processing of tensor fields , 2006 .

[14]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[15]  Mariano Rivera,et al.  Diffusion Basis Functions Decomposition for Estimating White Matter Intravoxel Fiber Geometry , 2007, IEEE Transactions on Medical Imaging.

[16]  Mariano Rivera,et al.  Entropy-Controlled Quadratic Markov Measure Field Models for Efficient Image Segmentation , 2007, IEEE Transactions on Image Processing.

[17]  Zhizhou Wang,et al.  An affine invariant tensor dissimilarity measure and its applications to tensor-valued image segmentation , 2004, CVPR 2004.

[18]  James C. Gee,et al.  Non-rigid registration of diffusion tensor MR images , 2002, Proceedings IEEE International Symposium on Biomedical Imaging.

[19]  Mark W. Woolrich,et al.  Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? , 2007, NeuroImage.

[20]  David E. Breen,et al.  Level Set Modeling and Segmentation of DT-MRI Brain Data , 2001 .

[21]  Daniel C. Alexander,et al.  Probabilistic Monte Carlo Based Mapping of Cerebral Connections Utilising Whole-Brain Crossing Fibre Information , 2003, IPMI.

[22]  David E. Breen,et al.  Level set modeling and segmentation of diffusion tensor magnetic resonance imaging brain data , 2003, J. Electronic Imaging.

[23]  P. Basser,et al.  MR diffusion tensor spectroscopy and imaging. , 1994, Biophysical journal.

[24]  Rachid Deriche,et al.  Vector-valued image regularization with PDE's: a common framework for different applications , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[25]  R. Buxton.  Introduction to Functional Magnetic Resonance Imaging: Principles and Techniques , 2002 .

[26]  Jiří Matas,et al.  Computer Vision - ECCV 2004 , 2004, Lecture Notes in Computer Science.

[27]  B. Vemuri,et al.  Fiber tract mapping from diffusion tensor MRI , 2001, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision.

[28]  Rachid Deriche,et al.  Vector-valued image regularization with PDEs: a common framework for different applications , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Juan Ruiz-Alzola,et al.  Nonrigid Registration of 3D Scalar, Vector and Tensor Medical Data , 2000, MICCAI.

[30]  Alan Connelly,et al.  Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution , 2004, NeuroImage.

[31]  Rachid Deriche,et al.  A Riemannian Approach to Diffusion Tensor Images Segmentation , 2005, IPMI.

[32]  Nicholas Ayache,et al.  Clinical DT-MRI estimation, smoothing and fiber tracking with Log-Euclidean metrics , 2006, 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006..

[33]  P. Basser,et al.  Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. 1996. , 1996, Journal of magnetic resonance.

[34]  Daniel C. Alexander,et al.  An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond , 2006, Visualization and Processing of Tensor Fields.