Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Foundations of Computational Mathematics
On approximation of orientation distributions by means of spherical ridgelets
IEEE Transactions on Image Processing
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Sparse multi-shell diffusion imaging
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Probabilistic ODF estimation from reduced HARDI data with sparse regularization
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
A new similarity measure for non-local means filtering of MRI images
Journal of Visual Communication and Image Representation
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A spectrum of brain-related disorders are nowadays known to manifest themselves in degradation of the integrity and connectivity of neural tracts in the white matter of the brain. Such damage tends to affect the pattern of water diffusion in the white matter - the information which can be quantified by diffusion MRI (dMRI). Unfortunately, practical implementation of dMRI still poses a number of challenges which hamper its wide-spread integration into regular clinical practice. Chief among these is the problem of long scanning times. In particular, in the case of High Angular Resolution Diffusion Imaging (HARDI), the scanning times are known to increase linearly with the number of diffusionencoding gradients. In this research, we use the theory of compressive sampling (aka compressed sensing) to substantially reduce the number of diffusion gradients without compromising the informational content of HARDI signals. The experimental part of our study compares the proposed method with a number of alternative approaches, and shows that the former results in more accurate estimation of HARDI data in terms of the mean squared error.