A MATLAB implementation of the minimum relative entropy method for linear inverse problems
Computers & Geosciences
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Applied Stochastic Models in Business and Industry
Detection and localization of vapor-emitting sources
IEEE Transactions on Signal Processing
Source localization by spatially distributed electronic noses for advection and diffusion
IEEE Transactions on Signal Processing
Landmine detection and localization using chemical sensor arrayprocessing
IEEE Transactions on Signal Processing
Biochemical Transport Modeling and Bayesian Source Estimation in Realistic Environments
IEEE Transactions on Signal Processing
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Recovering the origin of an incident after detection of a polluting substance in the environment is crucial to start the remediation procedures. The lack of observations, the measurement errors and the model uncertainties make the problem of source estimation an ill-posed inverse problem that requires regularization to determine a solution. The two most frequent methods of regularization are source parametrization and penalization of undesirable solutions. In this paper, the proposed approach combines both methods in order to obtain a strong regularization that is efficient in case of few and erroneous observations. Point sources with parametric temporal releases and parameter penalizations are incorporated in a Bayesian framework where observations and prior information are combined in a hierarchical probabilistic model and the posterior law is explored with a Markov Chain Monte Carlo sampling algorithm. Estimation of the source parameters is provided by the posterior mean and uncertainties are provided by the posterior variance. To validate the method, several simulated cases with different emission events are considered. Quality of the estimate as well as impact of source model errors are also investigated. Then, a comparison with two existing least squares methods is conducted, in various configurations of sensors and noise level. Finally, the behavior of the method is described on a strongly underdeterminate real case where only one sensor recorded the pollution.