Sequential Monte Carlo samplers for semi-linear inverse problems and application to magnetoencephalography

Sommariva, Sara; Sorrentino, Alberto

doi:10.1088/0266-5611/30/11/114020

Cited by 31 publications

(51 citation statements)

References 35 publications

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“…In [19] the authors assume a uniform prior for the number of dipoles, and use reversible-jump Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. In [39,37], the authors assume a Poisson prior for the number of dipoles, and use sequential Monte Carlo (SMC) samplers [11] to approximate the posterior distribution; as SMC samplers employ multiple Markov Chains running in parallel, they are less likely to remain trapped in local maxima.…”

Section: Bayesian Monte Carlo Methods For Static Dipolesmentioning

confidence: 99%

Inverse Modeling for MEG/EEG Data

Sorrentino

Piana

2017

Mathematical and Theoretical Neuroscience

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We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.

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Section: Bayesian Monte Carlo Methods For Static Dipolesmentioning

confidence: 99%

Inverse Modeling for MEG/EEG Data

Sorrentino

Piana

2017

Mathematical and Theoretical Neuroscience

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“…The next sections explain how to sample from the conditional distributions of the unknown parameters and hyperparameters associated with the posterior of interest (8). The resulting algorithm is also summarized in Algorithm 1.…”

Section: Markov Chain Monte Carlo Methodsmentioning

confidence: 99%

“…Because of the complexity of this posterior distribution, the Bayesian estimators of {θ, Φ} cannot be computed with simple closed-form expressions. Section IV studies an MCMC method that can be used to sample the joint posterior distribution (8) and build Bayesian estimators of the unknown model parameters using the generated samples.…”

Section: Posterior Distributionmentioning

confidence: 99%

“…To solve this problem, the MUSIC algorithm [4] and its variants R-MUSIC [5], RAP-MUSIC [6], and FINES [7] were developed. Another recent dipole-fitting model whose parameters are estimated using sequential Monte Carlo [8] formulates the EEG source localization as a semilinear problem due to the measurements having a linear dependence with respect to the dipole amplitudes and a nonlinear one with respect to the positions. If few and clustered sources are present in the underlying brain activity, the dipole-fitting algorithms generally yield good results [9], [10].…”

Section: Introductionmentioning

confidence: 99%

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Sparse EEG Source Localization Using Bernoulli Laplacian Priors

Costa

Batatia

Chaâri

et al. 2015

IEEE Trans. Biomed. Eng.

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 14691 Abstract-Source localization in electroencephalography has received an increasing amount of interest in the last decade. Solving the underlying ill-posed inverse problem usually requires choosing an appropriate regularization. The usual 2 norm has been considered and provides solutions with low computational complexity. However, in several situations, realistic brain activity is believed to be focused in a few focal areas. In these cases, the 2 norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the 1 norm that are easy to handle with optimization techniques. In this paper, we consider the use of an 0 + 1 norm to enforce sparse source activity (by ensuring the solution has few nonzero elements) while regularizing the nonzero amplitudes of the solution. More precisely, the 0 pseudonorm handles the position of the nonzero elements while the 1 norm constrains the values of their amplitudes. We use a Bernoulli-Laplace prior to introduce this combined 0 + 1 norm in a Bayesian framework. The proposed Bayesian model is shown to favor sparsity while jointly estimating the model hyperparameters using a Markov chain Monte Carlo sampling technique. We apply the model to both simulated and real EEG data, showing that the proposed method provides better results than the 2 and 1 norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted.Index Terms-Electroencephalography (EEG), inverse problem, 0 + 1 norm regularization, Markov chain monte carlo (MCMC), source localization, sparse Bayesian restoration.

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“…These can be classified into two groups: (i) the dipole-fitting models that represent the brain activity as a small number of dipoles with unknown positions; and (ii) the distributed-source models that represent the brain activity as a large number of dipoles in fixed positions. Dipole-fitting models (Sommariva and Sorrentino, 2014;da Silva and Van Rotterdam, 1998) try to estimate the amplitudes, orientations and positions of a few dipoles that explain the measured data. Unfortunately, the corresponding estimators are very sensitive to the initial guess of the number of dipoles and their initial locations (Grech et al, 2008).…”

Section: Introductionmentioning

confidence: 99%