Expectation Propagation for Nonlinear Inverse Problems -- with an Application to Electrical Impedance Tomography

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.Comment: Journal of Computational Physics, to appea

An Analysis of Finite Element Approximation in Electrical Impedance Tomography

We present a finite element analysis of electrical impedance tomography for reconstructing the conductivity distribution from electrode voltage measurements by means of Tikhonov regularization. Two popular choices of the penalty term, i.e., $H^1(\Omega)$-norm smoothness penalty and total variation seminorm penalty, are considered. A piecewise linear finite element method is employed for discretizing the forward model, i.e., the complete electrode model, the conductivity, and the penalty functional. The convergence of the finite element approximations for the Tikhonov model on both polyhedral and smooth curved domains is established. This provides rigorous justifications for the ad hoc discretization procedures in the literature.Comment: 20 page

Organic Reference Materials for Hydrogen, Carbon, and Nitrogen Stable Isotope-Ratio Measurements: Caffeines, n-Alkanes, Fatty Acid Methyl Esters, Glycines, L-Valines, Polyethylenes, and Oils

An international project developed, quality-tested, and determined isotope−δ values of 19 new organic reference materials (RMs) for hydrogen, carbon, and nitrogen stable isotope-ratio measurements, in addition to analyzing pre-existing RMs NBS 22 (oil), IAEA-CH-7 (polyethylene foil), and IAEA-600 (caffeine). These new RMs enable users to normalize measurements of samples to isotope−δ scales. The RMs span a range of δ^2H_(VSMOW-SLAP) values from −210.8 to +397.0 mUr or ‰, for δ^(13)C_(VPDB-LSVEC) from −40.81 to +0.49 mUr and for δ^(15)N_(Air) from −5.21 to +61.53 mUr. Many of the new RMs are amenable to gas and liquid chromatography. The RMs include triads of isotopically contrasting caffeines, C_(16) n-alkanes, n-C_(20)-fatty acid methyl esters (FAMEs), glycines, and L-valines, together with polyethylene powder and string, one n-C_(17)-FAME, a vacuum oil (NBS 22a) to replace NBS 22 oil, and a ^2H-enriched vacuum oil. A total of 11 laboratories from 7 countries used multiple analytical approaches and instrumentation for 2-point isotopic normalization against international primary measurement standards. The use of reference waters in silver tubes allowed direct normalization of δ2H values of organic materials against isotopic reference waters following the principle of identical treatment. Bayesian statistical analysis yielded the mean values reported here. New RMs are numbered from USGS61 through USGS78, in addition to NBS 22a. Because of exchangeable hydrogen, amino acid RMs currently are recommended only for carbon- and nitrogen-isotope measurements. Some amino acids contain ^(13)C and carbon-bound organic ^2H-enrichments at different molecular sites to provide RMs for potential site-specific isotopic analysis in future studies

Novel extraction methods and compound-specific isotope analysis of methoxychlor in environmental water and aquifer slurry samples

Multi-element compound-specific stable isotope analysis (ME-CSIA) allows monitoring the environmental behavior and transformation of most common and persistent contaminants. Recent advancements in analytical techniques have extended the applicability of ME-CSIA to organic micropollutants, including pesticides. Nevertheless, the application of this methodology remains unexplored concerning harmful insecticides such as methoxychlor, a polar organochlorine pesticide usually detected in soil and groundwater. This study introduces methods for dual carbon and chlorine compound-specific stable isotope analysis (δ13C-CSIA and δ37Cl-CSIA) of both methoxychlor and its metabolite, methoxychlor olefin, with a sensitivity down to 10 and 100 mg/L, and a precision lower than 0.3 and 0.5 ‰ for carbon and chlorine CSIA, respectively. Additionally, three extraction and preconcentration techniques suitable for ME-CSIA of the target pesticides at environmentally relevant concen- trations were also developed. Solid-phase extraction (SPE) and liquid-solid extraction (LSE) effectively extracted methoxychlor (107 ± 27 % and 87 ± 13 %, respectively) and its metabolite (91 ± 27 % and 106 ± 14 %, respectively) from water and aquifer slurry samples, respectively, with high accuracy (Δδ13C and Δδ37Cl ≤ ± 1 ‰). Combining CSIA with polar organic chemical integrative samplers (POCISs) for the extraction of methoxychlor and methoxychlor olefin from water samples resulted in insignificant fractionation for POCIS-CSIA (Δδ13C ≤ ± 1 ‰). A relevant sorption of methoxychlor was detected within the polyethersulfones membranes of the POCISs resulting in temporary carbon isotope fractionation depending on the sorbed mass fraction during the first deployment days. This highlights the critical role of the interactions of polar analytes with POCIS sorbents and membranes in the performance of this method. Altogether, this study proposes a proof of concept for ME- CSIA of methoxychlor and its metabolites, opening the door for future investigations of their sources and transformation processes in contaminated sites

Dual C and Cl compound-specific isotope analysis and metagenomic insights into the degradation of the pesticide methoxychlor

This study investigates the use of multi-element compound-specific isotope analysis (ME-CSIA) to monitor degradation processes of methoxychlor, a persistent organochlorine insecticide. Laboratory experiments examined the kinetics, release of transformation products, and carbon and chlorine isotope effects during methoxychlor degradation through alkaline hydrolysis, oxidation with alkaline activated persulfate, and biotic reductive dechlorination. Results showed that hydrolysis and oxidation did not cause significant carbon and chlorine isotope fractionation, indicating that C-H rather than C-Cl bond cleavage was the rate determining step. Conversely, biotic reductive dechlorination by a field-derived microcosm under strictly anoxic conditions displayed significant carbon (εC = -0.9 ± 0.3 ‰) and chlorine (εCl = -1.9 ± 1.0 ‰) isotope fractionation. Its corresponding calculated dual isotope slope (ΛC/Cl = 0.4 ± 0.1) and apparent kinetic isotope effects (AKIEC = 1.014 ± 0.005 and AKIECl = 1.006 ± 0.003) indicate a C-Cl bond cleavage as the rate-determining step, highlighting the difference with respect to the other studied degradation mechanisms. Changes in the microbial community diversity revealed that families such as Dojkabacteria, Anaerolineaceae, Dysgonomonadaceae, Bacteroidetes vadinHA17, Pseudomonadaceae, and Spirochaetaceae, may be potential agents of methoxychlor reductive dechlorination under anoxic conditions. This study advances the understanding of degradation mechanisms of methoxychlor and improves the ability to track its transformation in contaminated environments, including for the first time an isotopic perspective