A Data-Driven Sparse GLM for fMRI Analysis Using Sparse Dictionary Learning With MDL Criterion

We propose a novel statistical analysis method for functional magnetic resonance imaging (fMRI) to overcome the drawbacks of conventional data-driven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to fMRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studies showing that ICA does not guarantee independence of simultaneously occurring distinct activity patterns in the brain. Instead, sparsity of the signal has been shown to be more promising. This coincides with biological findings such as sparse coding in V1 simple cells, electrophysiological experiment results in the human medial temporal lobe, etc. The main contribution of this paper is, therefore, a new data driven fMRI analysis that is derived solely based upon the sparsity of the signals. A compressed sensing based data-driven sparse generalized linear model is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics. Furthermore, a minimum description length (MDL)-based model order selection rule is shown to be essential in selecting unknown sparsity level for sparse dictionary learning. Using simulation and real fMRI experiments, we show that the proposed method can adapt individual variation better compared to the conventional ICA methods.

[1]  Joseph F. Murray,et al.  Dictionary Learning Algorithms for Sparse Representation , 2003, Neural Computation.

[2]  Roberto Viviani,et al.  Functional principal component analysis of fMRI data , 2005, Human brain mapping.

[3]  Iwao Kanno,et al.  Activation detection in functional MRI using subspace modeling and maximum likelihood estimation , 1999, IEEE Transactions on Medical Imaging.

[4]  A. Andersen,et al.  Principal component analysis of the dynamic response measured by fMRI: a generalized linear systems framework. , 1999, Magnetic resonance imaging.

[5]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[6]  James V. Stone,et al.  Spatiotemporal Independent Component Analysis of Event-Related fMRI Data Using Skewed Probability Density Functions , 2002, NeuroImage.

[7]  A. Dale,et al.  Coupling of Total Hemoglobin Concentration, Oxygenation, and Neural Activity in Rat Somatosensory Cortex , 2003, Neuron.

[8]  E Yacoub,et al.  Detection of the early decrease in fMRI signal in the motor area , 2001, Magnetic resonance in medicine.

[9]  D. Heeger,et al.  In this issue , 2002, Nature Reviews Drug Discovery.

[10]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[11]  C. Koch,et al.  Sparse but not ‘Grandmother-cell’ coding in the medial temporal lobe , 2008, Trends in Cognitive Sciences.

[12]  R. Poldrack,et al.  Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy? , 2003, Physics in medicine and biology.

[13]  David A. Boas,et al.  A Quantitative Comparison of Simultaneous BOLD fMRI and NIRS Recordings during Functional Brain Activation , 2002, NeuroImage.

[14]  Naoki Saito,et al.  Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum-description-length criterion , 1994, Defense, Security, and Sensing.

[15]  S Makeig,et al.  Spatially independent activity patterns in functional MRI data during the stroop color-naming task. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[16]  R. Buxton The Elusive Initial Dip , 2001, NeuroImage.

[17]  Karl J. Friston,et al.  Statistical parametric maps in functional imaging: A general linear approach , 1994 .

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

[19]  Jens Frahm,et al.  The post-stimulation undershoot in BOLD fMRI of human brain is not caused by elevated cerebral blood volume , 2008, NeuroImage.

[20]  Terrence J. Sejnowski,et al.  Learning Overcomplete Representations , 2000, Neural Computation.

[21]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[22]  K. Uğurbil,et al.  The Spatial Dependence of the Poststimulus Undershoot as Revealed by High-Resolution BOLD- and CBV-Weighted fMRI , 2005, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[23]  T. Sejnowski,et al.  Human Brain Mapping 6:368–372(1998) � Independent Component Analysis of fMRI Data: Examining the Assumptions , 2022 .

[24]  R. Turner,et al.  Characterizing Evoked Hemodynamics with fMRI , 1995, NeuroImage.

[25]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[26]  C. G. Phillips,et al.  Localization of function in the cerebral cortex. Past, present and future. , 1984, Brain : a journal of neurology.

[27]  Michael Elad,et al.  Compression of facial images using the K-SVD algorithm , 2008, J. Vis. Commun. Image Represent..

[28]  H. Rauhut,et al.  Atoms of All Channels, Unite! Average Case Analysis of Multi-Channel Sparse Recovery Using Greedy Algorithms , 2008 .

[29]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[31]  Vinod Menon,et al.  Functional connectivity in the resting brain: A network analysis of the default mode hypothesis , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[33]  J. Pekar,et al.  A method for making group inferences from functional MRI data using independent component analysis , 2001, Human brain mapping.

[34]  S Makeig,et al.  Analysis of fMRI data by blind separation into independent spatial components , 1998, Human brain mapping.

[35]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[36]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[37]  H. Akaike A new look at the statistical model identification , 1974 .

[38]  B. Biswal,et al.  Functional connectivity in the motor cortex of resting human brain using echo‐planar mri , 1995, Magnetic resonance in medicine.

[39]  P. Fransson Spontaneous low‐frequency BOLD signal fluctuations: An fMRI investigation of the resting‐state default mode of brain function hypothesis , 2005, Human brain mapping.

[40]  Karl J. Friston,et al.  Analysis of functional MRI time‐series , 1994, Human Brain Mapping.

[41]  C. Koch,et al.  Invariant visual representation by single neurons in the human brain , 2005, Nature.

[42]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[43]  M. McKeown Detection of Consistently Task-Related Activations in fMRI Data with Hybrid Independent Component Analysis , 2000, NeuroImage.

[44]  A. Kleinschmidt,et al.  Simultaneous Recording of Cerebral Blood Oxygenation Changes during Human Brain Activation by Magnetic Resonance Imaging and Near-Infrared Spectroscopy , 1996, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[45]  A. Shmuel,et al.  Investigation of the initial dip in fMRI at 7 Tesla , 2001, NMR in biomedicine.

[46]  Mark W. Woolrich,et al.  Advances in functional and structural MR image analysis and implementation as FSL , 2004, NeuroImage.

[47]  D. V. Cramon,et al.  Investigating the post-stimulus undershoot of the BOLD signal—a simultaneous fMRI and fNIRS study , 2006, NeuroImage.

[48]  Karl J. Friston,et al.  Unified SPM–ICA for fMRI analysis , 2005, NeuroImage.

[49]  I Daubechies,et al.  Independent component analysis for brain fMRI does not select for independence , 2009 .

[50]  Rainer Goebel,et al.  Spatial independent component analysis of functional MRI time‐series: To what extent do results depend on the algorithm used? , 2002, Human brain mapping.

[51]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[52]  B. Biswal,et al.  Blind source separation of multiple signal sources of fMRI data sets using independent component analysis. , 1999, Journal of computer assisted tomography.

[53]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[54]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[55]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited , 1995, NeuroImage.

[56]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[57]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.

[58]  V D Calhoun,et al.  Spatial and temporal independent component analysis of functional MRI data containing a pair of task‐related waveforms , 2001, Human brain mapping.

[59]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[60]  Michael Elad,et al.  Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit , 2008 .