Controlled Support MEG imaging

Nagarajan, Srikantan S.; Portniaguine, Oleg; Hwang, Dosik; Johnson, Chris R.; Sekihara, Kensuke

doi:10.1016/j.neuroimage.2006.07.023

Cited by 16 publications

(11 citation statements)

References 24 publications

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“…whose solution is the Minimum Support Estimate (MSE) [20]. In [6,5,7], the authors have shown that, in the context of traditional image processing, the corresponding penalty is related to the Perona-Malik functional [23].…”

Section: Hypermodels: Mce Minimum P and Beyondmentioning

confidence: 99%

“…In this work, we construct a conditionally Gaussian hierarchical parametric model that has the computational advantages of Gaussian prior models but leads to a rich class of MAP estimators that have the desirable qualitative properties of numerous commonly used non-Gaussian models. Using the conditional normality, we construct a fast, efficient and simple MAP estimation algorithm, and show that with proper choices of the few model parameters, the algorithm can be interpreted as a fixed point iteration for solving the minimum norm estimate, the minimum current estimate and, more generally, the minimum p estimate, while with a different choice, the algorithm approximates the minimum support estimate (MSE) [20]. Hence, our approach puts these methods in a unified framework.…”

Section: Introductionmentioning

confidence: 99%

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Conditionally Gaussian Hypermodels for Cerebral Source Localization

Calvetti¹,

Hakula²,

Pursiainen³

et al. 2009

SIAM J. Imaging Sci.

147

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Bayesian modeling and analysis of the magnetoencephalography and electroencephalography modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of the available information into a computational model a challenging task. We propose a generalized gamma family of hyperpriors which allows the impressed currents to be focal and we advocate a fast and efficient iterative algorithm, the iterative alternating sequential algorithm for computing maximum a posteriori (MAP) estimates. Furthermore, we show that for particular choices of the scalar parameters specifying the hyperprior, the algorithm effectively approximates popular regularization strategies such as the minimum current estimate and the minimum support estimate. The connection between priorconditioning and adaptive regularization methods is also pointed out. The posterior densities are explored by means of a Markov chain Monte Carlo strategy suitable for this family of hypermodels. The computed experiments suggest that the known preference of regularization methods for superficial sources over deep sources is a property of the MAP estimators only, and that estimation of the posterior mean in the hierarchical model is better adapted for localizing deep sources.

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Section: Hypermodels: Mce Minimum P and Beyondmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conditionally Gaussian Hypermodels for Cerebral Source Localization

Calvetti¹,

Hakula²,

Pursiainen³

et al. 2009

SIAM J. Imaging Sci.

147

View full text Add to dashboard Cite

show abstract

“…A special example consists in algorithms performing smooth and sparse estimations in separate steps (Liu et al, 2005 ; Palmero-Soler et al, 2007 ) to explicit combining models as the sum of L1 and L2 penalty functions while using iterative algorithms to solve it (Nagarajan et al, 2006 ; Valdés-Sosa et al, 2009 ; Tian and Li, 2011 ).…”

Section: Introductionmentioning

confidence: 99%

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models

et al. 2017

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The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website.

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“…To our knowledge this is the first time that the use of probabilistic Bayesian PCA for data covariance estimation has been demonstrated in the context of MEG beamforming. A related probabilistic regularised estimation of the covariance matrix has been used previously as part of a method for analysing MEG and EEG data (Nagarajan et al (2007, 2006)). In particular, in Nagarajan et al (2007) they propose an interesting generative modelling approach that uses baseline periods to learn noise components (or “interferences”), thereby allowing them to partition noise from signal components in the time period of interest.…”

Section: Discussionmentioning

confidence: 99%

MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization

et al. 2011

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Beamformers are a commonly used method for doing source localisation from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beam-former output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.

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Controlled Support MEG imaging

Cited by 16 publications

References 24 publications

Conditionally Gaussian Hypermodels for Cerebral Source Localization

Conditionally Gaussian Hypermodels for Cerebral Source Localization

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models

MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization

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