White matter fiber analysis using kernel dictionary learning and sparsity priors

Diffusion magnetic resonance imaging, a non-invasive tool to infer white matter fiber connections, produces a large number of streamlines containing a wealth of information on structural connectivity. The size of these tractography outputs makes further analyses complex, creating a need for methods to group streamlines into meaningful bundles. In this work, we address this by proposing a set of kernel dictionary learning and sparsity priors based methods. Proposed frameworks include L-0 norm, group sparsity, as well as manifold regularization prior. The proposed methods allow streamlines to be assigned to more than one bundle, making it more robust to overlapping bundles and inter-subject variations. We evaluate the performance of our method on a labeled set and data from Human Connectome Project. Results highlight the ability of our method to group streamlines into plausible bundles and illustrate the impact of sparsity priors on the performance of the proposed methods.

[1]  Matthew Toews,et al.  Multi-modal brain fingerprinting: A manifold approximation based framework , 2017, NeuroImage.

[2]  Kuldeep Kumar,et al.  Fiberprint: A subject fingerprint based on sparse code pooling for white matter fiber analysis , 2017, NeuroImage.

[3]  Inderjit S. Dhillon,et al.  Kernel k-means: spectral clustering and normalized cuts , 2004, KDD.

[4]  Christophe Lenglet,et al.  Automatic clustering and population analysis of white matter tracts using maximum density paths , 2014, NeuroImage.

[5]  K. Whittingstall,et al.  Tractography in the Study of the Human Brain: A Neurosurgical Perspective , 2012, Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques.

[6]  P. Rousseeuw Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[7]  Hayit Greenspan,et al.  Sparse Representation for White Matter Fiber Compression and Calculation of Inter-Fiber Similarity , 2016, MICCAI 2016.

[8]  Jitendra Malik,et al.  Spectral grouping using the Nystrom method , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  A. Alexander,et al.  White matter tractography using diffusion tensor deflection , 2003, Human brain mapping.

[10]  Peter Savadjiev,et al.  Whole brain white matter connectivity analysis using machine learning: An application to autism , 2017, NeuroImage.

[11]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[12]  Michael Elad,et al.  Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation , 2010, IEEE Transactions on Signal Processing.

[13]  Bernhard Schölkopf,et al.  BundleMAP: Anatomically localized classification, regression, and hypothesis testing in diffusion MRI , 2017, Pattern Recognit..

[14]  Chris H. Q. Ding,et al.  Orthogonal nonnegative matrix t-factorizations for clustering , 2006, KDD '06.

[15]  Dapeng Tao,et al.  Joint medical image fusion, denoising and enhancement via discriminative low-rank sparse dictionaries learning , 2018, Pattern Recognit..

[16]  Fang-Cheng Yeh,et al.  NTU-90: A high angular resolution brain atlas constructed by q-space diffeomorphic reconstruction , 2011, NeuroImage.

[17]  Rachid Deriche,et al.  Unsupervised white matter fiber clustering and tract probability map generation: Applications of a Gaussian process framework for white matter fibers , 2010, NeuroImage.

[18]  Pietro Gori,et al.  Comparison of distances for supervised segmentation of white matter tractography , 2017, 2017 International Workshop on Pattern Recognition in Neuroimaging (PRNI).

[19]  Kuldeep Kumar,et al.  A sparse coding approach for the efficient representation and segmentation of white matter fibers , 2016, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI).

[20]  Guido Gerig,et al.  Towards a shape model of white matter fiber bundles using diffusion tensor MRI , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[21]  Guillermo Sapiro,et al.  Dictionary learning and sparse coding for unsupervised clustering , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[22]  Paul M. Thompson,et al.  Automatic clustering of white matter fibers in brain diffusion MRI with an application to genetics , 2014, NeuroImage.

[23]  Alex Smola,et al.  Kernel methods in machine learning , 2007, math/0701907.

[24]  Maxime Descoteaux,et al.  Real-time multi-peak tractography for instantaneous connectivity display , 2014, Front. Neuroinform..

[25]  Bruce Fischl,et al.  AnatomiCuts: Hierarchical clustering of tractography streamlines based on anatomical similarity , 2016, NeuroImage.

[26]  Carl-Fredrik Westin,et al.  Unbiased Groupwise Registration of White Matter Tractography , 2012, MICCAI.

[27]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Alain Trouvé,et al.  The Varifold Representation of Nonoriented Shapes for Diffeomorphic Registration , 2013, SIAM J. Imaging Sci..

[29]  Paul M. Thompson,et al.  Population learning of structural connectivity by white matter encoding and decoding , 2016, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI).

[30]  Carl-Fredrik Westin,et al.  Clustering Fiber Traces Using Normalized Cuts , 2004, MICCAI.

[31]  Yihong Gong,et al.  Linear spatial pyramid matching using sparse coding for image classification , 2009, CVPR.

[32]  Pietro Gori,et al.  Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles , 2016, IEEE Transactions on Medical Imaging.

[33]  Guy B. Williams,et al.  QuickBundles, a Method for Tractography Simplification , 2012, Front. Neurosci..

[34]  Sang Won Seo,et al.  Sparse SPM: Group Sparse-dictionary learning in SPM framework for resting-state functional connectivity MRI analysis , 2016, NeuroImage.

[35]  W. Eric L. Grimson,et al.  Statistical modeling and EM clustering of white matter fiber tracts , 2006, 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006..

[36]  Maya R. Gupta,et al.  Learning kernels from indefinite similarities , 2009, ICML '09.

[37]  Rama Chellappa,et al.  Kernel dictionary learning , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[38]  David B. Dunson,et al.  Mapping population-based structural connectomes , 2018, NeuroImage.

[39]  Paul M. Thompson,et al.  Segmentation of High Angular Resolution Diffusion MRI Using Sparse Riemannian Manifold Clustering , 2014, IEEE Transactions on Medical Imaging.

[40]  Maxime Descoteaux,et al.  Robust and efficient linear registration of white-matter fascicles in the space of streamlines , 2015, NeuroImage.

[41]  D. Leopold,et al.  Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited , 2014, Proceedings of the National Academy of Sciences.

[42]  J. K. Smith,et al.  Vessel tortuosity and brain tumor malignancy: a blinded study. , 2005, Academic radiology.

[43]  Steen Moeller,et al.  The Human Connectome Project: A data acquisition perspective , 2012, NeuroImage.

[44]  Stephen T. C. Wong,et al.  A hybrid approach to automatic clustering of white matter fibers , 2010, NeuroImage.

[45]  Mark Jenkinson,et al.  The minimal preprocessing pipelines for the Human Connectome Project , 2013, NeuroImage.

[46]  Alain Trouvé,et al.  The Fshape Framework for the Variability Analysis of Functional Shapes , 2014, Found. Comput. Math..

[47]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[48]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[49]  P. Basser,et al.  In vivo fiber tractography using DT‐MRI data , 2000, Magnetic resonance in medicine.

[50]  Felix C. Morency,et al.  A test-retest study on Parkinson's PPMI dataset yields statistically significant white matter fascicles , 2017, NeuroImage: Clinical.

[51]  Fang-Cheng Yeh,et al.  Generalized ${ q}$-Sampling Imaging , 2010, IEEE Transactions on Medical Imaging.

[52]  Gaël Varoquaux,et al.  A Comparison of Metrics and Algorithms for Fiber Clustering , 2013, 2013 International Workshop on Pattern Recognition in Neuroimaging.

[53]  Thomas R. Knösche,et al.  White matter integrity, fiber count, and other fallacies: The do's and don'ts of diffusion MRI , 2013, NeuroImage.

[54]  J. Thiran,et al.  Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond. , 2006, Radiographics : a review publication of the Radiological Society of North America, Inc.

[55]  W. Eric L. Grimson,et al.  A unified framework for clustering and quantitative analysis of white matter fiber tracts , 2008, Medical Image Anal..

[56]  Jian Sun,et al.  Deep ADMM-Net for Compressive Sensing MRI , 2016, NIPS.

[57]  Jean-Francois Mangin,et al.  Automatic fiber bundle segmentation in massive tractography datasets using a multi-subject bundle atlas , 2012, NeuroImage.

[58]  Hayit Greenspan,et al.  White Matter Fiber Representation Using Continuous Dictionary Learning , 2017, MICCAI.

[59]  Kuldeep Kumar,et al.  Brain Fiber Clustering Using Non-negative Kernelized Matching Pursuit , 2015, MLMI.

[60]  Michael Elad,et al.  On the Role of Sparse and Redundant Representations in Image Processing , 2010, Proceedings of the IEEE.

[61]  Jean Gotman,et al.  SPARK: Sparsity-based analysis of reliable k-hubness and overlapping network structure in brain functional connectivity , 2016, NeuroImage.

[62]  Yap-Peng Tan,et al.  Nonlinear dictionary learning with application to image classification , 2018, Pattern Recognit..

[63]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[64]  Yogesh Rathi,et al.  An anatomically curated fiber clustering white matter atlas for consistent white matter tract parcellation across the lifespan , 2018, NeuroImage.

[65]  Essa Yacoub,et al.  The WU-Minn Human Connectome Project: An overview , 2013, NeuroImage.

[66]  V. Wedeen,et al.  Generalized -Sampling Imaging , 2010 .

[67]  Matthew P. G. Allin,et al.  Atlasing location, asymmetry and inter-subject variability of white matter tracts in the human brain with MR diffusion tractography , 2011, NeuroImage.

[68]  W. Eric L. Grimson,et al.  Tractography segmentation using a hierarchical Dirichlet processes mixture model , 2011, NeuroImage.

[69]  Carl-Fredrik Westin,et al.  Fiber clustering versus the parcellation-based connectome , 2013, NeuroImage.

[70]  Kuldeep Kumar,et al.  White Matter Fiber Segmentation Using Functional Varifolds , 2017, GRAIL/MFCA/MICGen@MICCAI.

[71]  Carl-Fredrik Westin,et al.  White Matter Tract Clustering and Correspondence in Populations , 2005, MICCAI.

[72]  Anna Vilanova,et al.  Evaluation of fiber clustering methods for diffusion tensor imaging , 2005, VIS 05. IEEE Visualization, 2005..

[73]  H. Gu,et al.  Detection of transient, randomly occurring neuropsychological events with independent component analysis , 2001, NeuroImage.

[74]  Klaus-Robert Müller,et al.  Feature Discovery in Non-Metric Pairwise Data , 2004, J. Mach. Learn. Res..

[75]  Timothy D. Verstynen,et al.  Deterministic Diffusion Fiber Tracking Improved by Quantitative Anisotropy , 2013, PloS one.

[76]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[77]  Daniel Rueckert,et al.  Segmentation of MR images via discriminative dictionary learning and sparse coding: Application to hippocampus labeling , 2013, NeuroImage.

[78]  C. Westin,et al.  Automated white matter fiber tract identification in patients with brain tumors , 2016, NeuroImage: Clinical.

[79]  Carl-Fredrik Westin,et al.  Automatic Tractography Segmentation Using a High-Dimensional White Matter Atlas , 2007, IEEE Transactions on Medical Imaging.

[80]  Guillermo Sapiro,et al.  Sparse Representation for Computer Vision and Pattern Recognition , 2010, Proceedings of the IEEE.

[81]  Peter F. Neher,et al.  The challenge of mapping the human connectome based on diffusion tractography , 2017, Nature Communications.

[82]  Alain Trouvé,et al.  A Statistical Model of White Matter Fiber Bundles Based on Currents , 2009, IPMI.