Hierarchical Bayesian Algorithm Research Articles

Robust and Guided Bayesian Reconstruction of Single-Photon 3D Lidar Data: Application to Multispectral and Underwater Imaging

3D Lidar imaging can be a challenging modality when using multiple wavelengths, or when imaging in high noise environments (e.g., imaging through obscurants). This paper presents a hierarchical Bayesian algorithm for the robust reconstruction of multispectral single-photon Lidar data in such environments. The algorithm exploits multi-scale information to provide robust depth and reflectivity estimates together with their uncertainties to help with decision making. The proposed weight-based strategy allows the use of available guide information that can be obtained by using state-of-the-art learning based algorithms. The proposed Bayesian model and its estimation algorithm are validated on both synthetic and real images showing competitive results regarding the quality of the inferences and the computational complexity when compared to the state-of-the-art algorithms.

Rtmpt: An R package for fitting response-time extended multinomial processing tree models.

Response-time extended multinomial processing tree models (RT-MPT; Klauer and Kellen, Journal of Mathematical Psychology, 82, 111-130 2018) provide estimates of process-completion times for cognitive processes modeled by means of multinomial processing tree (MPT) models (Batchelder and Riefer, Psychonomic Bulletin & Review, 6, 57-86 1999). We present the R package rtmpt with which it is possible to fit RT-MPT models easily. The package is free and open source, it can be used with two established MPT syntaxes, and has a number of useful features, such as suppressing process-completion times for specific process outcomes, holding process probabilities constant, and changing some prior parameters. In the background of the R package, an altered version of the original C++ code is used for the MCMC sampling. We provide a guide to using rtmpt, validate the underlying hierarchical Bayesian algorithm of rtmpt using simulation-based calibration and show that previously reported results can be reproduced using rtmpt.

Sensitivity analysis and estimation using a hierarchical Bayesian method for the parameters of the FvCB biochemical photosynthetic model

Photosynthesis is a major process included in land surface models. Accurately estimating the parameters of the photosynthetic sub-models can greatly improve the ability of these models to accurately simulate the carbon cycle of terrestrial ecosystems. Here, we used a hierarchical Bayesian approach to fit the Farquhar-von Caemmerer-Berry model, which is based on the biochemistry of photosynthesis using 236 curves for the relationship between net CO2 assimilation and changes in the intercellular CO2 concentration. An advantage of the hierarchical Bayesian algorithm is that parameters can be estimated at multiple levels (plant, species, plant functional type, and population level) simultaneously. The parameters of the hierarchical strategy were based on the results of a sensitivity analysis. The Michaelis-Menten constant (Kc25), enthalpies of activation (EJ and EV), and two optical parameters (θ and α) demonstrated considerable variation at different levels, which suggests that this variation cannot be ignored. The maximum electron transport rate (Jmax25), maximum rate of Rubisco activity (Vcmax25), and dark respiration in the light (Rd25) were higher for broad-leaved plants than for needle-leaved plants. Comparison of the model's simulated outputs with observed data showed strong and significant positive correlations, particularly when the model was parameterized at the plant level. In summary, our study is the first effort to combine sensitivity analysis and hierarchical Bayesian parameter estimation. The resulting realistic parameter distributions for the four levels provide a reference for current and future land surface models. Furthermore, the observed variation in the parameters will require attention when using photosynthetic parameters in future models.

Brain Activity Mapping from MEG Data via a Hierarchical Bayesian Algorithm with Automatic Depth Weighting.

A recently proposed iterated alternating sequential (IAS) MEG inverse solver algorithm, based on the coupling of a hierarchical Bayesian model with computationally efficient Krylov subspace linear solver, has been shown to perform well for both superficial and deep brain sources. However, a systematic study of its ability to correctly identify active brain regions is still missing. We propose novel statistical protocols to quantify the performance of MEG inverse solvers, focusing in particular on how their accuracy and precision at identifying active brain regions. We use these protocols for a systematic study of the performance of the IAS MEG inverse solver, comparing it with three standard inversion methods, wMNE, dSPM, and sLORETA. To avoid the bias of anecdotal tests towards a particular algorithm, the proposed protocols are Monte Carlo sampling based, generating an ensemble of activity patches in each brain region identified in a given atlas. The performance in correctly identifying the active areas is measured by how much, on average, the reconstructed activity is concentrated in the brain region of the simulated active patch. The analysis is based on Bayes factors, interpreting the estimated current activity as data for testing the hypothesis that the active brain region is correctly identified, versus the hypothesis of any erroneous attribution. The methodology allows the presence of a single or several simultaneous activity regions, without assuming that the number of active regions is known. The testing protocols suggest that the IAS solver performs well with both with cortical and subcortical activity estimation.

Concurrent EEG and Functional MRI Recording and Integration Analysis for Dynamic Cortical Activity Imaging

Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) are two of the fundamental noninvasive methods for identifying brain activity. Multimodal methods have sought to combine the high temporal resolution of EEG with the spatial precision of fMRI, but the complexity of this approach is currently in need of improvement. The protocol presented here describes the recently developed spatiotemporal fMRI-constrained EEG source imaging method, which seeks to rectify source biases and improve EEG-fMRI source localization through the dynamic recruitment of fMRI sub-regions. The process begins with the collection of multimodal data from concurrent EEG and fMRI scans, the generation of 3D cortical models, and independent EEG and fMRI processing. The processed fMRI activation maps are then split into multiple priors, according to their location and surrounding area. These are taken as priors in a two-level hierarchical Bayesian algorithm for EEG source localization. For each window of interest (defined by the operator), specific segments of the fMRI activation map will be identified as active to optimize a parameter known as model evidence. These will be used as soft constraints on the identified cortical activity, increasing the specificity of the multimodal imaging method by reducing cross-talk and avoiding erroneous activity in other conditionally active fMRI regions. The method generates cortical maps of activity and time-courses, which may be taken as final results, or used as a basis for further analyses (analyses of correlation, causation, etc.) While the method is somewhat limited by its modalities (it will not find EEG-invisible sources), it is broadly compatible with most major processing software, and is suitable for most neuroimaging studies.

Concurrent EEG and Functional MRI Recording and Integration Analysis for Dynamic Cortical Activity Imaging

Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) are two of the fundamental noninvasive methods for identifying brain activity. Multimodal methods have sought to combine the high temporal resolution of EEG with the spatial precision of fMRI, but the complexity of this approach is currently in need of improvement. The protocol presented here describes the recently developed spatiotemporal fMRI-constrained EEG source imaging method, which seeks to rectify source biases and improve EEG-fMRI source localization through the dynamic recruitment of fMRI sub-regions. The process begins with the collection of multimodal data from concurrent EEG and fMRI scans, the generation of 3D cortical models, and independent EEG and fMRI processing. The processed fMRI activation maps are then split into multiple priors, according to their location and surrounding area. These are taken as priors in a two-level hierarchical Bayesian algorithm for EEG source localization. For each window of interest (defined by the operator), specific segments of the fMRI activation map will be identified as active to optimize a parameter known as model evidence. These will be used as soft constraints on the identified cortical activity, increasing the specificity of the multimodal imaging method by reducing cross-talk and avoiding erroneous activity in other conditionally active fMRI regions. The method generates cortical maps of activity and time-courses, which may be taken as final results, or used as a basis for further analyses (analyses of correlation, causation, etc.) While the method is somewhat limited by its modalities (it will not find EEG-invisible sources), it is broadly compatible with most major processing software, and is suitable for most neuroimaging studies.

Adaptive Markov Random Fields for Joint Unmixing and Segmentation of Hyperspectral Images

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm.

Nonlinear Unmixing of Hyperspectral Images Using a Generalized Bilinear Model

Nonlinear models have recently shown interesting properties for spectral unmixing. This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization not only of the accepted linear mixing model but also of a bilinear model that has been recently introduced in the literature. Appropriate priors are chosen for its parameters to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. Unfortunately, this posterior is too complex to obtain analytical expressions of the standard Bayesian estimators. As a consequence, a Metropolis-within-Gibbs algorithm is proposed, which allows samples distributed according to this posterior to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.

Knowledge-Aided STAP in Heterogeneous Clutter using a Hierarchical Bayesian Algorithm

The problem of estimating the covariance matrix of a primary vector from heterogeneous samples and some prior knowledge is addressed, under the framework of knowledge-aided space-time adaptive processing (KA-STAP). More precisely, a Gaussian scenario is considered where the covariance matrix of the secondary data may differ from the one of interest. Additionally, some knowledge on the primary data is supposed to be available and summarized in a prior matrix. Two KA-estimation schemes are presented in a Bayesian framework whereby the minimum mean square error (MMSE) estimates are derived. The first scheme is an extension of a previous work and takes into account the nonhomogeneity via an original relation. In search of simplicity and to reduce the computational load, a second estimation scheme, less complex, is proposed and omits the fact that the environment may be heterogeneous. Along the estimation process, not only the covariance matrix is estimated but also some parameters representing the degree of a priori and/or the degree of heterogeneity. Performance of the two approaches are then compared using STAP synthetic data. STAP filter shapes are analyzed and also compared with a colored loading technique.

Estimating the Number of Endmembers in Hyperspectral Images Using the Normal Compositional Model and a Hierarchical Bayesian Algorithm

This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images.