Hierarchical Bayesian sparse image reconstruction with application to MRFM

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of our hierarchical Bayesian sparse reconstruction method is illustrated on synthetic and real data collected from a tobacco virus sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

7T functional MRI finds no evidence for distinct functional subregions in the subthalamic nucleus during a speeded decision-making task

The subthalamic nucleus (STN) is a small, subcortical brain structure. It is a target for deep brain stimulation, an invasive treatment that reduces motor symptoms of Parkinson’s disease. Side effects of DBS are commonly explained using the tripartite model of STN organization, which proposes three functionally distinct subregions in the STN specialized in cognitive, limbic, and motor processing. However, evidence for the tripartite model exclusively comes from anatomical studies and functional studies using clinical patients. Here, we provide the first experimental tests of the tripartite model in healthy volunteers using ultra-high field 7 Tesla (T) functional magnetic resonance imaging (fMRI). Thirty-four participants performed a random-dot motion decision-making task with a difficulty manipulation and a choice payoff manipulation aimed to differentially affect cognitive and limbic networks. Moreover, participants responded with their left and right index finger, differentially affecting motor networks. We analysed BOLD signal in three subregions of the STN along the dorsolateral-ventromedial axis, identified using manually delineated high resolution anatomical images and based on a previously published atlas. Using these paradigms, all segments responded equally to the experimental manipulations, and the tasks did not provide evidence for the tripartite model