Bayesian Inversion of Piecewise Affine Operators in a Gaussian Framework

Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, are of this type. In a piecewise affine inverse problem a parameter is to be reconstructed when its mapping through a piecewise affine operator is observed, possibly with errors. A piecewise affine operator is defined by partitioning the parameter space and assigning a specific affine operator to each part. A Bayesian approach with a Gaussian random field prior on the parameter space is used. Both problems with a discrete finite partition and a continuous partition of the parameter space are considered.

The main result is that the posterior distribution is decomposed into a mixture of truncated Gaussian distributions, and the expression for the mixing distribution is partially analytically tractable. The general framework has, to the authors' knowledge, not previously been published, although the result for the finite partition is generally known.

Inverse problems are currently of large interest in many fields. The Bayesian approach is popular and most often highly computer intensive. The posterior distribution is frequently concentrated close to high-dimensional nonlinear spaces, resulting in slow mixing for generic sampling algorithms. Inverse problems are, however, often highly structured. In order to develop efficient sampling algorithms for a problem at hand, the problem structure must be exploited.

The decomposition of the posterior distribution that is derived in the current work can be used to develop specialized sampling algorithms. The article contains examples of such sampling algorithms. The proposed algorithms are applicable also for problems with exact observations. This is a case for which generic sampling algorithms tend to fail.     

Aliasing Error of Sampling Series in Wavelet Subspaces

Alising error arises whenever a sampling formula, valid for a prescribed space, is applied to a function in a bigger space. In this work, we estimate the aliasing error of classic and average sampling expansions in wavelet subspaces of a multiresolution analysis.     

Suitability of different containers for the sampling and storage of biogas and biomethane for the determination of the trace-level impurities – A review

The traceable and accurate measurement of biogas impurities is essential in order to robustly assess compliance with the specifications for biomethane being developed by CEN/TC408. An essential part of any procedure aiming to determinate the content of impurities is the sampling and the transfer of the sample to the laboratory. Key issues are the suitability of the sample container and minimising the losses of impurities during the sampling and analysis process. In this paper, we review the state-of-the-art in biogas sampling with the focus on trace impurities. Most of the vessel suitability studies reviewed focused on raw biogas. Many parameters need to be studied when assessing the suitability of vessels for sampling and storage, among them, permeation through the walls, leaks through the valves or physical leaks, sorption losses and adsorption effects to the vessel walls, chemical reactions and the expected initial concentration level. The majority of these studies looked at siloxanes, for which sampling bags, canisters, impingers and sorbents have been reported to be fit-for-purpose in most cases, albeit with some limitations. We conclude that the optimum method requires a combination of different vessels to cover the wide range of impurities commonly found in biogas, which have a wide range of boiling points, polarities, water solubilities, and reactivities. The effects from all the parts of the sampling line must be considered and precautions must be undertaken to minimize these effects. More practical suitability tests, preferably using traceable reference gas mixtures, are needed to understand the influence of the containers and the sampling line on sample properties and to reduce the uncertainty of the measurement.     

Sampling numbers and function spaces

We want to recover a continuous function using only its function values. Let us assume, that f is from the unit ball of some function space (for example a fractional Sobolev space or a Besov space) and the precision of the reconstruction is measured in the norm of another function space of this type. We describe the rate of convergence of the optimal sampling method (linear as well as nonlinear) in this setting.     

TDI CCD成像系统的研究

采用IL E2TDICCD作为传感器 ,与计算机构成了成像系统 ,并在计算机CRT上显示出图像。解决了CCD的时序电路及功率驱动电路设计问题。采用相关双采样技术滤除CCD输出信号复位噪声 ,提高了视频信号的信噪比。CCD的数据传送速度达到 10MHz ,行扫描速度达到 3.5kHz。     

Metrological estimation of sampling and sample preparation procedures as applied to analytical testing of technogenic origin raw material containing recoverable precious metal

 Different schemes of analytical testing including the sampling, sample preparation and sample analysis operations are considered as applied to a lot of raw material containing recoverable precious metal. The errors resulting from the step-by-step operations of the analytical testing are estimated. Sampling and sample preparation operations are found to be significant contributors to the total error of determination of the percentage and /or weight of a precious metal of interest in a lot. Some ways to diminish both the sampling error and the total error of the analytical testing procedure are recommended. Received: 28 December 1998 · Accepted: 22 February 1999     

A Sampling Theory for Compact Sets in Euclidean Space

We introduce a parameterized notion of feature size that interpolates between the minimum of the local feature size and the recently introduced weak feature size. Based on this notion of feature size, we propose sampling conditions that apply to noisy samplings of general compact sets in euclidean space. These conditions are sufficient to ensure the topological correctness of a reconstruction given by an offset of the sampling. Our approach also yields new stability results for medial axes, critical points, and critical values of distance functions. The authors were partially supported by DARPA under grant HR0011-05-1-0007 and by ANR under grant “Topologie, Géométrie Différentielle et Algorithmes.”     

The potential of Raman spectroscopy for characterisation of the fatty acid unsaturation of salmon

Raman spectroscopy has been evaluated for characterisation of the degree of fatty acid unsaturation (iodine value) of salmon (Salmo salar). The Norwegian Quality Cuts from 50 salmon samples were obtained, and the samples provided an iodine value range of 147.8-170.0 g I₂/100 g fat, reflecting a normal variation of farmed salmon. Raman measurements were performed both on different spots of the intact salmon muscle, on ground salmon samples as well as on oil extracts, and partial least squares regression (PLSR) was utilised for calibration. The oil spectra provided better iodine value predictions than the other data sets, and a correlation coefficient of 0.87 with a root mean square error of cross-validation of 2.5 g I₂/100 g fat was achieved using only one PLSR component. The ground samples provided comparable results, but at least two PLSR components were needed. Higher prediction errors were obtained from Raman spectra of intact salmon muscle, and this may partly be explained by sampling uncertainties in the relation between Raman measurements and reference analysis. All PLSR models obtained were based on chemically sound regression coefficients, and thus information regarding fatty acid unsaturation is readily available from Raman spectra even in systems with high contents of protein and water. The accuracy, the robustness and the low complexity of the PLSR models obtained suggest Raman spectroscopy as a promising method for rapid in-process control of the degree of unsaturation in salmon samples.     

无富集进样原子荧光光谱法测定地表水中的痕量汞

通过增大样品进样量的方式,样品进样量是标准进样量的10-100倍,降低了汞的检出限,从而达到了无富集直接进样测定地表水中痕量汞.其检出限为0.008μg/L;浓度为0.05μg/L和0.10μg/L左右的有证标准物质测定均值分别为0.0483μg/L和0.1016μg/L,加标回收率为92.3％和95.2％.灵敏度高,精密度好,能达到准确定量Ⅰ类和Ⅱ类地表水汞(0.05μg/L以下)的要求.对汉江湖北段水样进行测定,在较洁净的地表水分析中,氧化还原处理后与酸化水样测定结果差异不大,处理后水样结果略微增大.建议对较洁净的地表水样品将氧化还原预处理步骤省略掉,直接进样.     

Integrating Sampling Methods for Trace Metal Analysis of Natural Water Systems: Ion Exchange Membrane Targets for Proton-Excited X-Ray Fluorescence Analysis

Abstract

An initial investigation of ion-exchange membranes as trace metal concentrating devices in natural water systems and their suitability as targets for proton-excited x-ray flurorescence (PEXF) is reported. Element maps (Z=19 to Z=85) for various locations along a river were obtained with acceptable sensitivity in an irradiation period of 300 sec. The membrane used is mechanically stable in situ and is not destroyed by the 3 Mev (50 na) proton beam used in the study.