Lotfi Chaari

Fast Joint Detection-Estimation of Evoked Brain Activity in Event-Related fMRI Using a Variational Approach

In standard within-subject analyses of event-related functional magnetic resonance imaging (fMRI) data, two steps are usually performed separately: detection of brain activity and estimation of the hemodynamic response. Because these two steps are inherently linked, we adopt the so-called region-based joint detection-estimation (JDE) framework that addresses this joint issue using a multivariate inference for detection and estimation. JDE is built by making use of a regional bilinear generative model of the BOLD response and constraining the parameter estimation by physiological priors using temporal and spatial information in a Markovian model. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to sample the resulting intractable posterior distribution, we recast the JDE into a missing data framework and derive a variational expectation-maximization (VEM) algorithm for its inference. A variational approximation is used to approximate the Markovian model in the unsupervised spatially adaptive JDE inference, which allows automatic fine-tuning of spatial regularization parameters. It provides a new algorithm that exhibits interesting properties in terms of estimation error and computational cost compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model misspecification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery.

Flexible multivariate hemodynamics fMRI data analyses and simulations with PyHRF

As part of fMRI data analysis, the pyhrf package provides a set of tools for addressing the two main issues involved in intra-subject fMRI data analysis: (1) the localization of cerebral regions that elicit evoked activity and (2) the estimation of activation dynamics also known as Hemodynamic Response Function (HRF) recovery. To tackle these two problems, pyhrf implements the Joint Detection-Estimation framework (JDE) which recovers parcel-level HRFs and embeds an adaptive spatio-temporal regularization scheme of activation maps. With respect to the sole detection issue (1), the classical voxelwise GLM procedure is also available through nipy, whereas Finite Impulse Response (FIR) and temporally regularized FIR models are concerned with HRF estimation (2) and are specifically implemented in pyhrf. Several parcellation tools are also integrated such as spatial and functional clustering. Parcellations may be used for spatial averaging prior to FIR/RFIR analysis or to specify the spatial support of the HRF estimates in the JDE approach. These analysis procedures can be applied either to volume-based data sets or to data projected onto the cortical surface. For validation purpose, this package is shipped with artificial and real fMRI data sets, which are used in this paper to compare the outcome of the different available approaches. The artificial fMRI data generator is also described to illustrate how to simulate different activation configurations, HRF shapes or nuisance components. To cope with the high computational needs for inference, pyhrf handles distributing computing by exploiting cluster units as well as multi-core machines. Finally, a dedicated viewer is presented, which handles n-dimensional images and provides suitable features to explore whole brain hemodynamics (time series, maps, ROI mask overlay).

Sparse EEG Source Localization Using Bernoulli Laplacian Priors

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 ℓ₂ 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 ℓ₂ norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the ℓ₁ norm that are easy to handle with optimization techniques. In this paper, we consider the use of an ℓ₀ + ℓ₁ 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 ℓ₀ pseudonorm handles the position of the nonzero elements while the ℓ₁ norm constrains the values of their amplitudes. We use a Bernoulli-Laplace prior to introduce this combined ℓ₀ + ℓ₁ 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 ℓ₂ and ℓ₁ norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted.

Hemodynamic-informed parcellation of fMRI data in a joint detection estimation framework.

Identifying brain hemodynamics in event-related functional MRI (fMRI) data is a crucial issue to disentangle the vascular response from the neuronal activity in the BOLD signal. This question is usually addressed by estimating the so-called hemodynamic response function (HRF). Voxelwise or region-/parcelwise inference schemes have been proposed to achieve this goal but so far all known contributions commit to pre-specified spatial supports for the hemodynamic territories by defining these supports either as individual voxels or a priori fixed brain parcels. In this paper, we introduce a joint parcellation-detection-estimation (JPDE) procedure that incorporates an adaptive parcel identification step based upon local hemodynamic properties. Efficient inference of both evoked activity, HRF shapes and supports is then achieved using variational approximations. Validation on synthetic and real fMRI data demonstrate the JPDE performance over standard detection estimation schemes and suggest it as a new brain exploration tool.

A Hamiltonian Monte Carlo Method for Non-Smooth Energy Sampling

Efficient sampling from high-dimensional distributions is a challenging issue that is encountered in many large data recovery problems. In this context, sampling using Hamiltonian dynamics is one of the recent techniques that have been proposed to exploit the target distribution geometry. Such schemes have clearly been shown to be efficient for multidimensional sampling but, rather, are adapted to distributions from the exponential family with smooth energy functions. In this paper, we address the problem of using Hamiltonian dynamics to sample from probability distributions having non-differentiable energy functions such as those based on the l1 norm. Such distributions are being used intensively in sparse signal and image recovery applications. The technique studied in this paper uses a modified leapfrog transform involving a proximal step. The resulting nonsmooth Hamiltonian Monte Carlo method is tested and validated on a number of experiments. Results show its ability to accurately sample according to various multivariate target distributions. The proposed technique is illustrated on synthetic examples and is applied to an image denoising problem.

Improving Spacecraft Health Monitoring with Automatic Anomaly Detection Techniques

Health monitoring is performed on CNES spacecraft using two complementary methods: an utomatic Out-Of-Limits (OOL) checking executed on a set of critical parameters after each new telemetry reception, and a monthly monitoring of statistical features (daily minimum, mean and maximum) of another set of parameters. In this paper we present the limitations of this monitoring system and we introduce an innovative anomaly detection method based on machine-learning algorithms, developed during a collaborative R&D action between CNES and TESA (TElecommunications for Space and Aeronautics). This method has been prototyped and has shown encouraging results regarding its ability to detect actual anomalies that had slipped through the existing monitoring net. An operational-ready software implementing this method, NOSTRADAMUS, has been developed in order to further evaluate the interest of this new type of surveillance, and to consolidate the settings proposed after the R&D action. The lessons learned from the operational assessment of this system for the routine surveillance of CNES spacecraft are also presented in this paper.

Sparse signal recovery using a Bernoulli generalized Gaussian prior

Bayesian sparse signal recovery has been widely investigated during the last decade due to its ability to automatically estimate regularization parameters. Prior based on mixtures of Bernoulli and continuous distributions have recently been used in a number of recent works to model the target signals, often leading to complicated posteriors. Inference is therefore usually performed using Markov chain Monte Carlo algorithms. In this paper, a Bernoulli-generalized Gaussian distribution is used in a sparse Bayesian regularization framework to promote a two-level flexible sparsity. Since the resulting conditional posterior has anon-differentiable energy function, the inference is conducted using the recently proposed non-smooth Hamiltonian Monte Carlo algorithm. Promising results obtained with synthetic data show the efficiency of the proposed regularization scheme.

Parameter estimation for hybrid wavelet-total variation regularization

In many image restoration/reconstruction problems, using redundant linear decompositions also named as frames may be fruitful. Moreover, Total Variation (TV) is also widely used in the edge-preserving regularization literature. Associating these two tools in a joint regularization framework may be of great interest since they are somehow complementary. However, estimating the regularization parameters in this case becomes a tricky issue which cannot be performed by using standard estimators. In this work, a hierarchical model is introduced to solve this problem within a fully Bayesian framework. A hybrid MCMC algorithm is subsequently proposed to sample from the derived posterior distribution. We show that this algorithm allows the regularization parameters to be determined accurately. We finally investigate its application to parallel MRI reconstruction, where the use of a joint wavelet-TV regularization is also novel.

A hierarchical sparsity-smoothness Bayesian model for ℓ0 + ℓ1 + ℓ2 regularization

Sparse signal/image recovery is a challenging topic that has captured a great interest during the last decades. To address the ill-posedness of the related inverse problem, regularization is often essential by using appropriate priors that promote the sparsity of the target signal/image. In this context, ℓ₀ + ℓ₁ regularization has been widely investigated. In this paper, we introduce a new prior accounting simultaneously for both sparsity and smoothness of restored signals. We use a Bernoulli-generalized Gauss-Laplace distribution to perform ℓ₀ + ℓ₁ + ℓ₂ regularization in a Bayesian framework. Our results show the potential of the proposed approach especially in restoring the non-zero coefficients of the signal/image of interest.

Hybrid sparse regularization for magnetic resonance spectroscopy

Magnetic resonance spectroscopy imaging (MRSI) is a powerful non-invasive tool for characterising markers of biological processes. This technique extends conventional MRI by providing an additional dimension of spectral information describing the abnormal presence or concentration of metabolites of interest. Unfortunately, in vivo MRSI suffers from poor signal-to-noise ratio limiting its clinical use for treatment purposes. This is due to the combination of a weak MR signal and low metabolite concentrations, in addition to the acquisition noise. We propose a new method that handles this challenge by efficiently denoising MRSI signals without constraining the spectral or spatial profiles. The proposed denoising approach is based on wavelet transforms and exploits the sparsity of the MRSI signals both in the spatial and frequency domains. A fast proximal optimization algorithm is then used to recover the optimal solution. Experiments on synthetic and real MRSI data showed that the proposed scheme achieves superior noise suppression (SNR increase up to 60%). In addition, this method is computationally efficient and preserves data features better than existing methods.