Abstract. Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.
A common problem of imaging 3-D objects into image plane is superposition of the projected structures. In dynamic imaging, projection overlaps of organs and tissues complicate extraction of signals specific to individual structures with different dynamics. The problem manifests itself also in dynamic tomography as tissue mixtures are present in voxels. Separation of signals specific to dynamic structures belongs to the category of blind source separation. It is an underdetermined problem with many possible solutions. Existing separation methods select the solution that best matches their additional assumptions on the source model. We propose a novel blind source separation method based on probabilistic model of dynamic image sequences assuming each source dynamics as convolution of an input function and a source specific kernel (modeling organ impulse response or retention function). These assumptions are formalized as a Bayesian model with hierarchical prior and solved by the Variational Bayes method. The proposed prior distribution assigns higher probability to sparse source images and sparse convolution kernels. We show that the results of separation are relevant to selected tasks of dynamic renal scintigraphy. Accuracy of tissue separation with simulated and clinical data provided by the proposed method outperformed accuracy of previously developed methods measured by the mean square and mean absolute errors of estimation of simulated sources and the sources separated by an expert physician. MATLAB implementation of the algorithm is available for download.
In the fall of 2011, iodine-131 (I-131) was detected at several radionuclide monitoring stations in Central Europe.of I-131 to determine the location of the release as well as its magnitude and temporal variation. Although the location of 5 the release became eventually known, its temporal variation is still uncertain and only partial information is available. For our source reconstruction, we use no prior knowledge. Instead, we estimate the source location and emission variation using only the available I-131 measurements. Subsequently, we use the information about the source term for validation of our results. For the source determination, we first perform backward runs of atmospheric transport models and obtain sourcereceptor-sensitivity (SRS) matrices for each grid cell of our study domain. We use two dispersion models, Flexpart and Hysplit, 10 driven with meteorological analysis data from the global forecast system (GFS) weather forecast model. Second, we use a recently developed inverse method, least-squares with adaptive prior covariance (LS-APC), to determine the I-131 emissions and their temporal variation from the measurements and computed SRS matrices. For each grid cell of our simulation domain, we evaluate the probability that the release was generated in that cell using Bayesian model selection. The model selection procedure also provides information about the most suitable dispersion model for the source term reconstruction. Third, we 15 select the most probable location of the release with its associated source term and perform forward calculation to study the consequences of the iodine release. Results of these procedures are compared with the known release location and reported information about its time variation. We find that our algorithm could successfully locate the actual release site. The estimated release period is also in agreement with the values reported by IAEA, while our estimate for the total released activity (490 GBq) is higher than the reported one (342 GBq). Nevertheless, even using our larger source term, dose amounts were very low 20 and never exceeded regulatory limits.1 Atmos. Chem. Phys. Discuss.,
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