Generalized Adaptive Gaussian Markov Random Field for X-Ray Luminescence Computed Tomography

2018 ◽  
Vol 65 (9) ◽  
pp. 2130-2133 ◽  
Author(s):  
Guanglei Zhang ◽  
Stratis Tzoumas ◽  
Kai Cheng ◽  
Fei Liu ◽  
Jie Liu ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Random Field ◽  
Markov Random Field ◽  
X Ray ◽  
Gaussian Markov Random Field ◽  
Markov Random

scholarly journals Mobile Robotic Sensors for Environmental Monitoring using Gaussian Markov Random Field

Robotica ◽  
2020 ◽  
pp. 1-23
Author(s):  
Linh Nguyen ◽  
Sarath Kodagoda ◽  
Ravindra Ranasinghe ◽  
Gamini Dissanayake
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Adaptive Sampling ◽  
Published Data ◽  
Data Sets ◽  
Independence Property ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Sampling Optimization ◽  
Robotic Sensors

SUMMARY This paper addresses the issue of monitoring spatial environmental phenomena of interest utilizing information collected by a network of mobile, wireless, and noisy sensors that can take discrete measurements as they navigate through the environment. It is proposed to employ Gaussian Markov random field (GMRF) represented on an irregular discrete lattice by using the stochastic partial differential equations method to model the physical spatial field. It then derives a GMRF-based approach to effectively predict the field at unmeasured locations, given available observations, in both centralized and distributed manners. Furthermore, a novel but efficient optimality criterion is then proposed to design centralized and distributed adaptive sampling strategies for the mobile robotic sensors to find the most informative sampling paths in taking future measurements. By taking advantage of conditional independence property in the GMRF, the adaptive sampling optimization problem is proven to be resolved in a deterministic time. The effectiveness of the proposed approach is compared and demonstrated using pre-published data sets with appealing results.

scholarly journals Penalized complexity priors for degrees of freedom in Bayesian P-splines

2016 ◽  
Vol 16 (6) ◽  
pp. 429-453 ◽  
Author(s):  
Massimo Ventrucci ◽  
Håvard Rue
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Smooth Function ◽  
Degrees Of Freedom ◽  
Penalized Splines ◽  
Prior Elicitation ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Gaussian Data

Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter [Formula: see text]. Prior elicitation of [Formula: see text] is difficult. To overcome this issue, we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose penalized complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.

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