12,364 research outputs found
Expectation Propagation for Poisson Data
The Poisson distribution arises naturally when dealing with data involving
counts, and it has found many applications in inverse problems and imaging. In
this work, we develop an approximate Bayesian inference technique based on
expectation propagation for approximating the posterior distribution formed
from the Poisson likelihood function and a Laplace type prior distribution,
e.g., the anisotropic total variation prior. The approach iteratively yields a
Gaussian approximation, and at each iteration, it updates the Gaussian
approximation to one factor of the posterior distribution by moment matching.
We derive explicit update formulas in terms of one-dimensional integrals, and
also discuss stable and efficient quadrature rules for evaluating these
integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem
Holographic particle localization under multiple scattering
We introduce a novel framework that incorporates multiple scattering for
large-scale 3D particle-localization using single-shot in-line holography.
Traditional holographic techniques rely on single-scattering models which
become inaccurate under high particle-density. We demonstrate that by
exploiting multiple-scattering, localization is significantly improved. Both
forward and back-scattering are computed by our method under a tractable
recursive framework, in which each recursion estimates the next higher-order
field within the volume. The inverse scattering is presented as a nonlinear
optimization that promotes sparsity, and can be implemented efficiently. We
experimentally reconstruct 100 million object voxels from a single 1-megapixel
hologram. Our work promises utilization of multiple scattering for versatile
large-scale applications
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EEG-Based Quantification of Cortical Current Density and Dynamic Causal Connectivity Generalized across Subjects Performing BCI-Monitored Cognitive Tasks.
Quantification of dynamic causal interactions among brain regions constitutes an important component of conducting research and developing applications in experimental and translational neuroscience. Furthermore, cortical networks with dynamic causal connectivity in brain-computer interface (BCI) applications offer a more comprehensive view of brain states implicated in behavior than do individual brain regions. However, models of cortical network dynamics are difficult to generalize across subjects because current electroencephalography (EEG) signal analysis techniques are limited in their ability to reliably localize sources across subjects. We propose an algorithmic and computational framework for identifying cortical networks across subjects in which dynamic causal connectivity is modeled among user-selected cortical regions of interest (ROIs). We demonstrate the strength of the proposed framework using a "reach/saccade to spatial target" cognitive task performed by 10 right-handed individuals. Modeling of causal cortical interactions was accomplished through measurement of cortical activity using (EEG), application of independent component clustering to identify cortical ROIs as network nodes, estimation of cortical current density using cortically constrained low resolution electromagnetic brain tomography (cLORETA), multivariate autoregressive (MVAR) modeling of representative cortical activity signals from each ROI, and quantification of the dynamic causal interaction among the identified ROIs using the Short-time direct Directed Transfer function (SdDTF). The resulting cortical network and the computed causal dynamics among its nodes exhibited physiologically plausible behavior, consistent with past results reported in the literature. This physiological plausibility of the results strengthens the framework's applicability in reliably capturing complex brain functionality, which is required by applications, such as diagnostics and BCI
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