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Advances in Applied Mathematics
Greedy algorithms and M-term approximation with regard to redundant dictionaries
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Atomic Decomposition by Basis Pursuit
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IEEE Transactions on Visualization and Computer Graphics
High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution
Journal of Mathematical Imaging and Vision
Fast Directional Continuous Spherical Wavelet Transform Algorithms
IEEE Transactions on Signal Processing
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
An affine scaling methodology for best basis selection
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Spatially regularized q-ball imaging using spherical ridgelets
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Fast and accurate reconstruction of HARDI data using compressed sensing
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Locally weighted regression for estimating and moothing ODF field simultaneously
MIAR'10 Proceedings of the 5th international conference on Medical imaging and augmented reality
Sparse multi-shell diffusion imaging
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Function-valued mappings, total variation and compressed sensing for diffusion MRI
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part II
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Visualization and analysis of the micro-architecture of brain parenchyma by means of magnetic resonance imaging is nowadays believed to be one of the most powerful tools used for the assessment of various cerebral conditions as well as for understanding the intracerebral connectivity. Unfortunately, the conventional diffusion tensor imaging (DTI) used for estimating the local orientations of neural fibers is incapable of performing reliably in the situations when a voxel of interest accommodates multiple fiber tracts. In this case, a much more accurate analysis is possible using the high angular resolution diffusion imaging (HARDI) that represents local diffusion by its apparent coefficients measured as a discrete function of spatial orientations. In this note, a novel approach to enhancing and modeling the HARDI signals using multiresolution bases of spherical ridgelets is presented. In addition to its desirable properties of being adaptive, sparsifying, and efficiently computable, the proposed modeling leads to analytical computation of the orientation distribution functions associated with the measured diffusion, thereby providing a fast and robust analytical solution for q-ball imaging.