Inverse Problem Research Papers - Academia.edu (original) (raw)

This paper deals with the solution of the stress, displacement, and pore pressure field induced by the drilling and~or the pressurization of a vertical borehole. The rock, which is permeated by fluid, is assumed to behave as a poroelastic material with compressible constituents, following the Biot theory. The analytical solution is derived in the Laplace transform space, and is transformed to the time domain using an approximate numerical inversion technique. The solution reveals a full range of coupled poroelastic effects which provide potential mechanisms for delayed borehole instability and shear fracture initiation inside the rock.

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- Civil Engineering, Rock Mechanics, Stress, Stability

The purpose is to propose an improved method for inverse boundary value problems. This method is presented on a model problem. It introduces a higher order problem. BEM numerical simulations highlight the efficiency, the improved accuracy, the robustness to noisy data of this new approach, as well as its ability to deblur noisy data. Keywords Cauchy problem • inverse problem • boundary values • boundary element method • regularization

- by A. Cimetière
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- Mechanical Engineering, Civil Engineering, Mathematics, Computational Mechanics
- by Jose Herskovits
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- Engineering, Mathematical Programming, Optimization Problem, Shape Optimization

Electrical capacitance tomography (ECT) is considered as a promising process tomography (PT) technology. Image reconstruction algorithms play an important role in the successful applications of ECT. In this paper, a generalized objective functional, which has been developed using the combinational minimax estimation and a generalized stabilizing functional, is proposed. The Newton algorithm is employed to solve the proposed objective functional.

- by JING LEI
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- Mathematics, Applied Mathematics, Computer Science, Process Tomography

This paper is concerned with global in time behavior of solutions for a semilinear, hyperbolic, inverse source problem. We prove two types of results. The first one is a global nonexistence result for smooth solutions when the data is chosen appropriately. The second type of results is the asymptotic stability of solutions when the integral constraint vanishes as t goes to infinity. Bibliography: 22 titles.

- by ALP EDEN
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- Pure Mathematics, Mathematical Sciences, Inverse Problem, Integrity Constraints

We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.

- by Amir Adler
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- Engineering, Image Restoration, Impulse Noise, Time Frequency Analysis

The possibility of developing a photochemical setup on the basis of an optically pumped ammonia laser with an intracavity photoreactor is proved. The obtained values of the cavity 'implication' factor γ are comparable with those of intracavity systems based on a CO2 laser. The conditions for achieving the maximum energy in the focusing cavity are determined and the ways to control the shape of its caustic are indicated.

- by Paula Mendoza
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- Condensed Matter Physics, Laser, Atmospheric Aerosols, Quantum Electronics

... a function that is assumed to have two continuous derivatives, adding the side condition guarantees positivity and produces, uniquely, the Epanechnikov kernel. ... It will be clear from the previous paragraphs that, in the problem of... more

- by Peter Hall
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- Applied Mathematics, Econometrics, Statistics, Inverse Problem

A nonlinear statistical method for the inversion of ocean color spectra is used to determine three inherent optical properties (IOPs), the absorption coefficients for phytoplankton and dissolved and detrital materials, and the backscattering coefficient due to particulates. The inherent optical property inversion model assumes that (1) the relationship between remotesensing reflectance and backscattering and absorption is well known, (2) the optical coefficients for pure water are known, and (3) the spectral shapes of the specific absorption coefficients for phytoplankton and dissolved and detrital materials and the specific backscattering coefficient for particulates are known. This leaves the magnitudes for the three unknown coefficients to be determined. A sensitivity analysis is conducted to determine the best IOP model configuration for the Sargasso Sea using existing bio-optical models. The optical and biogeochemical measurements used were collected as part of the Bermuda Bio-Optics Project and the U.S. Joint Global Ocean Flux Study Bermuda Atlantic Time Series (BATS). The results demonstrate that the lOP ......... ' mouc• is most sensitive to-' ....... useu to mourn changes in me exponential decay constant .............. absorption by dissolved and detrital materials. The retrieved chlorophyll a estimates show excellent correspondence to chlorophyll a determinations (r 2 = 81%), similar to estimates from standard band ratio pigment algorithms, while providing two additional retrievals simultaneously. The temporal signal of retrieved estimates of absorption by colored dissolved and detrital materials is mirrored in ratios of Kd(410) to Kd(488), a qualitative indicator for nonalgal light attenuation coefficients. The backscatter coefficient for particles is nearly constant in time and shows no correspondence with the temporal signal observed for chlorophyll a concentrations. Last, the IOP model is evaluated using only those wavelengths which closely match the Sea Viewing Wide Field of View Sensor wave bands. This results in only a 1 to 6% decrease in hindcast skill with the BATS biogeochemical data set. This is encouraging for the long-range goal of applying the IOP model to data from upcoming ocean color satellite missions. the inversion of ocean color spectra to produce three relevant inherent optical properties (IOPs) for the analysis of biogeochemical variability: the absorption coefficient by phytoplankton, the absorption coefficient by dissolved and detrital materials, and the backscattering coefficient due to Copyright 1997 by the American Geophysical Union. Paper number 96JC03243. 0148-0227/97/96JC-03243509.00 particulates. Methods to invert ocean color observations, such as those employed here, have been extensively explored by Morel and Prieur [1977], Sugihara et al. [1985], Sathyendranath et al. [1989], Gordon et al. [1988], and Roeslet and Perry [1995]. The color of the sea will be related to those photons which are backscattered from within the water column and are not absorbed before entering the atmosphere. Hence changes in the total absorption coefficient, a(;L) (notation list is provided), and the backscattering coefficient, b b (;L), regulate the variations in ocean color spectra or remotely sensed reflectance [Rrs(•.)], where Rrs(•.) is defined as the ratio of upwelled radiance to downwelled irradiance (=Lu(•.)/Ed(•.)). Values of a(;L) an be effectively partitioned into absorption due to water, phytoplankton, and nonalgal materials [e.g.,

- by Sara Garver
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- Remote Sensing, Biogeochemistry, Time Series, Sensitivity Analysis

A new model describing laser noise in terms of non-Markovian stochastic phase jumps has been recently introduced. In this letter an exact expression for the correlation function for the electric field is obtained. This expression, valid for all possible values of the parameters of the stochastic process, reduces to the previously reported approximations. A procedure is described for the inverse problem of determining the stochastic parameters from measured data for real lasers.

- by Alfred Levine
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- Inverse Problems, Stochastic processes, Noise, Shape

Electrical resistivity tomography ͑ERT͒ has shown great promise for monitoring transient hydrologic processes. One advantage of ERT under those conditions is the ability of a user to tailor the spatial sensitivity of an ERT survey through selection of electrode locations and electrode combinations. Recent research has shown that quadripoles can be selected in a manner that improves the independent inversion of ERT data. Our ultimate interest lies in using ERT data along with measurements from other sensors, which typically can provide high-quality data from shallow regions of the subsurface, in a joint inversion. As a result, we do not consider the selection of quadripoles specifically for inde-pendent ERT inversion. Rather, we present an approach to focusthe spatial sensitivity of ERT surveys in specific subsurface regions with the assumption that those data, when interpreted along with other measurements that are sensitive to those regions, will lead to more complete hydrologic characterization. Because we are interested in monitoring rapid processes, our approach is designed to efficiently identify optimal quadripoles. This is achieved by separating the optimization from the inversion grid, significantly reducing computational effort. We extend our previous work to consider the use of both surface and borehole ERT electrodes and to consider the impacts of horizontally layered electrical conductivity conditions. Results confirm the ability of the method to focus survey sensitivity while showing the importance of incorporation of prior knowledge of the subsurface electric conductivity structure in designing optimal ERT surveys.

- by Alex Furman
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- Geophysics, Tomography, Optimization, Surveys

Inversions of borehole temperature profiles that reconstruct past ground surface temperature (GST) changes have been used to estimate historical changes in surface air temperature (SAT). Paleoclimatic interpretations of GST reconstructions are based on the assumption that GST and SAT changes are closely coupled over decades, centuries, and longer. This assumption has been the subject of some debate because of known differences between GST and SAT at timescales of hours, days, seasons, and years. We investigate GST and SAT relationships on daily, seasonal, and annual timescales to identify and characterize the principal meteorological changes that lead to short-term differences between GST and SAT and consider the effects of those differences on coupling between the two temperatures over much longer time periods. We use observational SAT and subsurface data from Fargo, North Dakota; Prague, Czech Republic; Cape Henlopen State Park, Delaware; and Cape Hatteras National Seashore, North Carolina. These records comprise intradaily observations that span parts of one or two decades. We compare subsurface temperature observations to calculations from a conductive subsurface model driven with daily SAT as the surface boundary condition and show that daily differences exist between observed and modeled subsurface temperatures. We also analyze year-to-year spectral decompositions of daily SAT and subsurface temperature time series and show that dissimilarities between mean annual GST and SAT are attributable to differences in annual amplitudes of the two temperature signals. The seasonal partitioning of these amplitude differences varies from year to year and from site to site, responding to variable evapotranspiration and cryogenic effects. Variable yearto-year differences between mean annual GST and SAT are closely estimated using results from a multivariate regression model that associates the partial influences of seasonal meteorological conditions with the attenuation of annual GST amplitudes.

- by Milan Krešl
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- Environmental Science, Climate Change, Interpretation, Czech Republic

Ablative materials can sustain very high temperatures in which surface thermochemical processes are significant enough to cause surface recession. Existence of moving boundary over a wide range of temperatures, temperature-dependent thermophysical properties of ablators, and no prior knowledge about the location of the moving surface augment the difficulty for predicting the exposed heat flux at the receding surface of ablators. In this paper, the conjugate gradient method is proposed to estimate the unknown surface recession and time-varying net surface heat flux for these kinds of problems. The first order Tikhonov regularization is employed to stabilize the inverse solution. Considering the complicated phenomena that are taking place, it is shown via simulated experiment that unknown quantities can be obtained with reasonable accuracy using this method despite existing noises in the measurement data.

- by Sahar Noori
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- Engineering, Heat and Mass Transfer, Tikhonov Regularization, Mathematical Sciences

The potential of a ground-based microwave temperature profiler to combine full tropospheric profiling with highresolution profiling of the boundary layer is investigated. For that purpose, statistical retrieval algorithms that incorporate observations from different elevation angles and frequencies are derived from long-term radiosonde data. A simulation study shows the potential to significantly improve the retrieval performance in the lowest kilometer by combining angular information from relatively opaque channels with zenith-only information from more transparent channels. Observations by a state-of-the-art radiometer employed during the International Lindenberg Campaign for Assessment of Humidity and Cloud Profiling Systems and Its Impact on High-Resolution Modeling (LAUNCH) in Lindenberg, Germany, are used for an experimental evaluation with observations from a 99-m mast and radiosondes. The comparison not only reveals the high accuracy achieved by combining angular and spectral observations (overall, less than 1 K below 1.5 km), but also emphasizes the need for a realistic description of radiometer noise within the algorithm. The capability of the profiler to observe the height and strength of low-level temperature inversions is highlighted.

- by Ulrich Löhnert
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- Geophysics, Algorithms, Information Retrieval, Remote Sensing

We report here on our latest developments in the forward and inverse problems of electrocardiology. In the forward problem, a coupled cellular model of cardiac excitation-contraction is embedded within an anatomically realistic model of the cardiac ventricles, which is itself embedded within a torso model. This continuum modelling framework allows the effects of cellular-level activity on the surface electrocardiogram (ECG) to be carefully examined. Furthermore, the contributions of contraction and local ischemia on body surface recordings can also be elucidated. Such information can provide theoretical limits to the sensitivity and ultimately the detection capability of body surface ECG recordings. Despite being very useful, such detailed forward modelling is not directly applicable when seeking to use densely sampled ECG information to assess a patient in a clinical environment (the inverse problem). In such a situation patient specific models must be constructed and, due to the nature of the inverse problem, the level of detail that can be reliably reproduced is limited. Extensive simulation studies have shown that the accuracy with which the heart is localised within the torso is the primary limiting factor. To further identify the practical performance capabilities of the current inverse algorithms, high quality experimental data is urgently needed. We have been working towards such an objective with a number of groups, including our local hospital in Auckland. At that hospital, in patients undergoing catheter ablation surgery, up to 256 simultaneous body surface signals were recorded by using various catheter pacing protocols. The geometric information required to customize the heart and torso model was obtained using a combination of ultrasound and laser scanning technologies. Our initial results indicate that such geometric imaging modalities are sufficient to produce promising inversely-constructed activation profiles.

- by Nicolas Smith
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- Algorithms, Electrophysiology, Ultrasound, Level Of Detail (LOD)

In this paper, a numerical method for the evaluation of topological derivatives is proposed. The integral shape functional is considered for the Signorini type variational inequality in nonsmooth geometrical domain with a cut. The so-called smooth domain method is used for the purposes of numerical analysis for the variational inequality. The topological derivative of the integral shape functional is defined and computed using the mixed finite elements. Results of computations are presented. The shape topological derivatives can be used for numerical solution of some shape optimization as well as inverse problems.

The uncertain conductivity value of skull and brain tissue influences the accuracy of the electroencephalogram (EEG) inverse problem solution. Indeed, when the assumed conductivity in the numerical procedure is different from the actual conductivity then a source localization error is introduced. When using traditional least-squares minimization methods, the number of electrodes in the EEG cap does not influence the spatial resolution. A recently developed reduced conductivity dependence (RCD) methodology, based on the selection of electrodes, is able to increase the spatial resolution of the EEG inverse problem. This paper presents the implications of the RCD method when using a large number of electrodes in the EEG cap on the spatial resolution of the EEG inverse solutions. We show by means of numerical experiments that in contrast to traditional methods, the RCD method enables to increase the spatial resolution. The computations show that the EEG hardware should be modified with as large as possible electrodes.

- by Bertrand Yitembe
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- Engineering, Electroencephalography, Numerical Analysis, Neurophysiology

In this paper, a crack identification method is developed for axisymmetric and two-dimensional structures. The dual boundary element method is coupled with a quasi-random sequence and the downhill simplex algorithm to minimize the error function, which is expressed as the difference between strains at the boundary sensor points in the guessed crack shape and ones measured in the actual crack identity. The measures are randomly perturbed and the residual norm is regularized to provide an efficient and numerically stable algorithm that leads to stabilized solutions. The accuracy of this method is investigated in the identification of single two-dimensional and axisymmetric cracks on several cases. Through the treated examples, we showed that the quasi-random sequence presents a solid tool, allowing the choice of the optimal initial solution necessary to the convergence of the downhill simplex algorithm.

- by Nasreddine Amoura and +2
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- Mechanical Engineering, Civil Engineering, Applied Mathematics, Boundary Element Methods

A Petschek-type model of magnetic reconnection is used to describe the behaviour of nightside flux transfer events (NFTEs). Based on the Cagniard-deHoop method we calculate the magnetic field and plasma flow time series observed by a satellite. The reconstruction of the reconnection electric field is an ill-posed inverse problem, which we treat with the method of regularisation, since the solution of the Cagniard-deHoop method is given in the form of a convolution integral, which is a well- known problem in the theory of inverse problems. This method is applied to Cluster measurements from September 8 th , 2002, and from August, 13 th , 2002, where a series of Earth-ward propagating 1-minute scale magnetic field and plasma flow variations are observed which are consistent with the theoretical picture of NFTEs. Methods to estimate the satellite position with respect to the reconnection site as well as the Alfven velocity are presented because they are necessary parameters used in the...

- by I. Kubyshkin
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- Time Series, Magnetic field, Magnetic Reconnection, Clustered Data

Projection data obtained through optical techniques for tomographic measurements, such as interferometry for refractive-index-based measurements, are often incomplete. This is due to limitations in the optical system, data storage, and alignment and vignette issues. Algebraic iterative reconstruction techniques are usually favored for such incomplete projections. A number of iterative algorithms, based on additive and multiplicative corrections, are used with a known simulated phantom and noise source to assess the reconstruction performance of incomplete data sets. In addition, we present reconstructions using experimental data obtained from a coherent gradient sensing interferometer for a steady temperature field in a fluid medium. We tested the algorithms using the simulated data set for incompleteness conditions similar to those found in the experimental data, and the best-performing algorithm is identified.

- by raman singh
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- Mechanical Engineering, Image Processing, Inverse Problems, Tomography

The problem of reconstructing locations, shapes, and dielectric permittivity distributions of two-dimensional (2-D) dielectric objects from measurements of the scattered electric field is addressed in this paper. A numerical approach is proposed which is based on a multi-illumination multiview processing. In particular, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a genetic algorithm (GA). The final objective of the approach is the image reconstruction of highly contrasted bodies.

- by Matteo Pastorino
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- Genetic Algorithm, Inverse Scattering, Image Reconstruction, Inverse Problem

In this paper, we investigate the inverse problem of determining the potential of the Schrödinger equation from finite measurements on the boundary. It is well known that this is an ill posed problem in the sense of Hadamard. The stability estimate is proved under the assumption that the potentials have some a priori constraints. Based on this conditional stability result, we propose one kind of Tikhonov regularization and prove the convergence rate for the regularized solution.

- by Gen Nakamura
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- Applied Mathematics, Mathematical Physics, Pure Mathematics, Inverse Problems

This paper investigates the performance of calibration techniques on synthetic Electroencephalography (EEG) data. Brain source localization was performed using an iterative algorithm. A transfer-function-based calibration technique was developed. This technique can be applied in two forms: external calibration and autocalibration. For a low density EEG array system, it was shown that the proposed calibration technique can offer improved performance relative to previously published work.

- by Hasan Al-Nashash
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- Calibration, Inverse Problem

While it is possible to check the energy performance of a given building by means of several available methods, the inverse problem of determining the optimum configuration given a desired performance is more difficult to solve. In the Mediterranean region this problem is more complex due to the following two reasons: the air-conditioning load is as important as the heating load, and the energy needs depend on a high number of architectural parameters which have different, even contradictory, effects on summer and winter loads. In this paper we present an optimization algorithm that couples pseudo-random optimization techniques, the genetic algorithms (GA), with a simplified tool for building thermal evaluation (CHEOPS) for the purpose of minimizing the energy consumption of Mediterranean buildings. Since increasing the energy performance usually requires the use of special devices resulting in a high construction cost, we also propose to use GA for the purpose of economical optimization. #

- by Essia Znouda
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- Engineering, Design, Genetic Algorithms, Energy Efficiency Buildings

Robot arms are used in modern work cells and flexible manufacturing systems (FMS) in handling work pieces and loading/unloading processes. The robot arm links may interfere with the bodies of the system components, which are considered as obstacles in the robot workspace. In order that the robot works in safe conditions, study of robot workspace in a free space and

- by Adel Abbas
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- Engineering, Computer Science, Genetic Algorithm, computer Integrated manufacturing

The Marchenko inversion method of the one-dimensional non-relativistic quantum mechanics is generalised to perturbations. The change in the potential that corresponds to a finite change in the scattering matrix is obtained by formulating a Marchenko-like integral equation. The method used here may be generalisable to higher dimensions because the inversion is formulated in terms of scattering matrices, not only in terms of reflection coefficients.

- by tuncay aktosun
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- Mathematics, Applied Mathematics, Mathematical Physics, Quantum Mechanics

The stress inversion method is developed to find a stress field which satisfies the equation of equilibrium for a body in a state of plane stress. When one stress-strain relation is known and data on the strain distribution on the body and traction along the boundary are provided, the method solves a well-posed problem, which is a linear boundary value problem for Airy's stress function, with the governing equation being the Poisson equation and the boundary conditions being of the Neumann type. The stress inversion method is applied to the Global Positioning System (GPS) array data of the Japanese Islands. The stress increment distribution, which is associated with the displacement increment measured by the GPS array, is computed, and it is found that the distribution is not uniform over the islands and that some regions have a relatively large increment. The elasticity inversion method is developed as an alternative to the stress inversion method; it is based on the assumption of linear elastic deformation with unknown elastic moduli and does not need boundary traction data, which are usually difficult to measure. This method is applied to the GPS array data of a small region in Japan to which the stress inversion method is not applicable. To cite this article: M. Hori et al., C. R. Mecanique 336 (2008). Résumé Méthode d'inversion des contraintes et analyse des données GPS. La méthode d'inversion est développée pour trouver un champ de contraintes satisfaisant les équations d'équilibre pour un corps en situation de contrainte plane. La relation entre contrainte et déformation étant connue et les données de distribution de déformation sur le corps et de traction sur le bord étant fournies, la méthode résout un problème bien posé, qui consiste en un problème aux limites linéaire pour la fonction de contrainte d'Airy, comprenant l'équation de Poisson et des conditions aux limites de type Neumann. La méthode d'inversion est appliquée aux données GPS (Global Positioning System) concernant les îles japonaises. Les incréments de contraintes associés aux incréments de déplacements mesurés par le système GPS sont calculés, et l'on trouve que leur distribution n'est pas uniforme sur les îles, certaines régions présentant un incrément relativement grand. La méthode d'inversion élastique est développée comme alternative à la méthode d'inversion des contraintes ; elle est fondée sur l'hypothèse d'une déformation linéaire élastique avec des coefficients d'élasticité inconnus, et ne requiert pas de données concernant les tractions au bord, généralement difficilement mesurables. La méthode est appliquée aux données GPS d'une petite région du Japon pour laquelle la méthode d'inversion des contraintes n'est pas utilisable. Pour citer cet article : M. Hori et al., C. R. Mecanique 336 (2008).

- by Muneo Hori
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- Mechanical Engineering, Geophysics, Dynamical Systems, Modeling

A new empirical model for the retrieval, at a field scale, of the bare soil moisture content and the surface roughness characteristics from radar measurements is proposed. The derivation of the algorithm is based on the results of three experimental radar campaigns conducted under natural conditions over agricultural areas. Radar data were acquired by means of several C-band space borne

- by Monique Dechambre
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- Algorithms, Remote Sensing, Agriculture, Surface Roughness

Fast magnetic resonance imaging slice acquisition techniques such as single shot fast spin echo are routinely used in the presence of uncontrollable motion. Current applications involve fetal MRI and MRI of moving subjects and organs. Although high-quality slices are frequently acquired by these techniques, inter-slice motion leads to severe motion artifacts that appear in out-of-plane views. Slice sequential acquisitions do not enable 3D volume representation. In this study, we have developed a novel technique based on a slice acquisition model, which enables the reconstruction of a volumetric image from multiple-scan slice acquisitions. The super-resolution volume reconstruction is formulated as an inverse problem of finding the underlying structure generating the acquired slices. We have developed a robust M-estimation solution which minimizes a robust error norm function between the model-generated slices and the acquired slices. The accuracy and robustness of this novel technique has been quantitatively assessed through simulations with digital brain phantom images as well as high-resolution newborn images. We also report here successful application of our new technique for the reconstruction of volumetric fetal brain MRI from clinically acquired data.

- by Judy Estroff
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- Engineering, Algorithms, Obstetrics, Magnetic Resonance Imaging

A numerical approximation of the Green's function equation based on a heat-flux formulation is given. It is derived by assuming as a functional form of the surface heat flux a stepwise variation with space and time. The obtained approximation is very important in investigation of the inverse heat conduction problems (IHCPs) because it gives a convenient expression for the temperature in terms of the heat flux components. Additionally, it is very important for the unsteady surface element (USE) method which is a modern boundary discretization method. Green's function approximate solution equation (GFASE) also creates 'naturally' fixed groups or modules of work elements called ''building blocks'' that may be added together to obtain space and time values of temperature. In the current case, they are subject to a partial heating by an applied surface heat flux. The ''building block'' solution can be derived by using the various analytical and numerical approaches available in heat conduction literature though the exact analysis is preferable, as discussed in the text. Poorly-convergent series deriving from Green's functions approach are replaced by closed-form algebraic solutions.

- by Filippo de Monte
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- Engineering, Inverse Problems, Heat and Mass Transfer, Mathematical Sciences

Many works related learning from examples to regularization techniques for inverse problems, emphasizing the strong algorithmic and conceptual analogy of certain learning algorithms with regularization algorithms. In particular it is well known that regularization schemes such as Tikhonov regularization can be effectively used in the context of learning and are closely related to algorithms such as support vector machines. Nevertheless the connection with inverse problem was considered only for the discrete (finite sample) problem and the probabilistic aspects of learning from examples were not taken into account. In this paper we provide a natural extension of such analysis to the continuous (population) case and study the interplay between the discrete and continuous problems. From a theoretical point of view, this allows to draw a clear connection between the consistency approach in learning theory and the stability convergence property in ill-posed inverse problems. The main mat...

- by Umberto de Giovannini
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- Mathematics, Computer Science, Machine Learning, Support Vector Machines

For many years, applications of the TNDE (Thermographic NonDestructive Evaluation) technique has been limited due to the complex non-linearity nature of related inversion problems such as defect depth estimation. Arti®cial neural networks have recently obtained success in revealing and providing quantitative information concerning defects in TNDE. In this paper, a three dimensional thermal model for nonhomogenous materials such as carbon ®ber reinforced plastic (CFRP) is ®rst given. The modeling results are compared with the analytical solution based on Duhamel's theorem. Two back propagation neural networks (NN) as defect detector and depth estimator are then presented. Finally, simulated and experimental results are presented and discussed.

- by Akbar Darabi
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- Engineering, Neural Networks, Nondestructive Evaluation, Neural Network
- by Jochem Verrelst
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- History, Remote Sensing, Evaluation, Interaction

Local and superficial near-infrared ͑NIR͒ optical-property characterization of turbid biological tissues can be achieved by measurement of spatially resolved diffuse reflectance at small source-detector separations ͑Ͻ1.4 mm͒. However, in these conditions the inverse problem, i.e., calculation of localized absorption and the reduced scattering coefficients, is necessarily sensitive to the scattering phase function. This effect can be minimized if a new parameter of the phase function ␥, which depends on the first and the second moments of the phase function, is known. If ␥ is unknown, an estimation of this parameter can be obtained by the measurement, but the uncertainty of the absorption coefficient is increased. A spatially resolved reflectance probe employing multiple detector fibers ͑0.3-1.4 mm from the source͒ is described. Monte Carlo simulations are used to determine ␥, the reduced scattering and absorption coefficients from reflectance data. Probe performance is assessed by measurements on phantoms, the optical properties of which were measured by other techniques ͓frequency domain photon migration ͑FDPM͒ and spatially resolved transmittance͔. Our results show that changes in the absorption coefficient, the reduced scattering coefficient, and ␥ can be measured to within Ϯ0.005 mm Ϫ1 , Ϯ0.05 mm Ϫ1 , and Ϯ0.2, respectively. In vivo measurements performed intraoperatively on a human skull and brain are reported for four NIR wavelengths ͑674, 811, 849, 956 nm͒ when the spatially resolved probe and FDPM are used. The spatially resolved probe shows optimum measurement sensitivity in the measurement volume immediately beneath the probe ͑typically 1 mm 3 in tissues͒, whereas FDPM typically samples larger regions of tissues. Optical-property values for human skull, white matter, scar tissue, optic nerve, and tumors are reported that show distinct absorption and scattering differences between structures and a dependence on the phase-function parameter ␥.

S U M M A R Y Traveltime calculations in 3-D velocity models have become more commonplace during the past decade or so. Many schemes have been developed to deal with the initial value problem, which consists of tracing rays from a known source position and trajectory usually towards some distant surface. Less attention has been given to the more difficult problem of boundary value ray tracing in 3-D. In this case, source and receiver positions are known and one, or more, minimum time paths are sought between fixed endpoints.

- by Malcolm Sambridge
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- Geology, Geophysics, Algorithms, Algorithm

A new technique is proposed to reconstruct faulty wiring networks from the time-domain reflectometry (TDR) response. The developed method is also for characterization of defects in the branches of the network. The direct problem (propagation along the cables) is modeled by RLCG circuit parameters computed by finite element method (FEM) and the finite-difference time domain (FDTD) method. Genetic algorithms (GAs) are used to solve the inverse problem. The proposed method allows to accurately locate wire faults. Some examples are presented to validate and illustrate the ability of this reconstruction method. Index Terms-Genetic algorithms (GAs), multiconductor transmission lines, network fault diagnosis, time domain reflectometry (TDR).

- by Marc Lambert
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- Engineering, Finite element method, Genetic Algorithm, Fault diagnosis

L'Assimilation de Données est un cadre méthodologique utilisé en sciences de l'environnement pour la prédiction des systèmes complexes, que sont les modèles météorologiques, océanographiques, ou encore de qualité de l'air. L'Assimilation de Données opère en résolvant un systèmeà trois composantes: une premièreéquation décrit l'évolution temporelle du vecteur d'état; une secondeéquation décrit la relation entre le vecteur d'état et l'observation; enfin, une dernièreéquation décrit la condition initiale. Dans ce rapport, nous utilisons ce cadre mathématique pour l'étude des problèmes mal posés du traitement d'image, habituellement résolus par des techniques de régularisation. Pour cela, le problème est formulé au moyen du systèmeà trois composantes de l'Assimilation de Données. Comme illustration, cette approche est appliquée au calcul du flot optique.

- by Isabelle HERLIN
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- Applied Mathematics, Environmental Science, Computer Vision, Air Quality

Objective: Electroencephalography (EEG) is an important tool for studying the temporal dynamics of the human brain's large-scale neuronal circuits. However, most EEG applications fail to capitalize on all of the data's available information, particularly that concerning the location of active sources in the brain. Localizing the sources of a given scalp measurement is only achieved by solving the so-called inverse problem. By introducing reasonable a priori constraints, the inverse problem can be solved and the most probable sources in the brain at every moment in time can be accurately localized.

- by Sara Gonzalez
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- Engineering, Electrophysiology, Neuroimaging, Magnetic Resonance Imaging

This article describes the first attempt to conduct electrical resistivity tomography (ERT) in solid permafrost-affected rock faces. Electrode design, instrument settings, and processing routines capable of measuring under relevant... more

- by Michael Krautblatter
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- Rock magnetism, Heat Transfer, Sea Level, Instrumentation
- by Daniel Rabinovich
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- Engineering, System Identification, Modeling, Vibration

Electrical resistivity tomography was used in order to explore an experimental site of the LaSalle Beauvais Polytechnic Institute (France). The test was conducted along a profile line of 315 m length, using 64 electrodes deployed at an interelectrode spacing of 5 m, and the data were recorded using gradient, Wenner and pole-dipole arrays. The performance of plate electrodes (non-conventional flat-based) is compared with the performance of peak electrodes (conventional spike). The hydrogeophysical investigation of the chalk aquifer system of Beauvais shows that the performance of plate electrodes is satisfactory, leading to inversions of small root-mean-square errors. Peak and the plate electrodes were tested before and after injection of a salt tracer in the piezometer of the experimental site. The study demonstrates the usefulness of plate electrodes (efficient, less time consuming) and the possibility of aquifer characterization by a salt tracer.

- by Lahcen Zouhri
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- Environmental Engineering, Civil Engineering, Groundwater, Performance

A new approach for the estimation of apparent thermal diffusivity of foods at different drying temperatures was explored, analysed and discussed in this work. Temperature versus time was obtained numerically at the center of the food (banana, ''nanicão" variety) using the 1D Fourier equation with drying temperatures in the range between approximately 17-65°C and moisture content in the range between 0.01 and 3.43 (dry basis). The solution of the partial differential equation is made with a finite difference method coupled to an optimization technique of Differential Evolution used in inverse method. The mathematical model proposed considered the effects of shrinkage and convective heat transfer at surface of fruit. Parameters of two functions, the first dependent of the moisture content and the second dependent also of the temperature were obtained by inverse method modelling the apparent thermal diffusivity. Such parameters that provide the best least square fit between the experimental and predicted time-temperatures curves are presented in this work. This study demonstrated that a small change in the temperature and moisture content of banana cause an abrupt change in the apparent thermal diffusivity, which decrease with the decreasing of the moisture. Statistical analysis shows the excellent agreement between reported and estimated curves.

- by leandro coelho
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- Food Engineering, Statistical Analysis, Food, Evolution

Portfolio replication has proven in practice its applicability to enterprise-wide risk problems such as static hedging in complete and incomplete markets and markets that gap; strategic asset and capital allocation; benchmark tracking; design of synthetic products; and portfolio compression. In contrast to mean-variance optimization, the scenario approach allows for general non-normal, discrete and subjective distributions, as well as for the accurate modelling of the full range of nonlinear instruments. It also provides an intuitive, operational framework for explaining basic financial theory. In this paper, we review the basic principles behind this methodology and present several practical examples of its application. We further show how inverse problems in finance can be naturally formulated in this framework. 1. A version of this paper was published in the Annals of Operations Research 85 (1999) 267-284.

- by Dan Rosen and +1
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- Mathematical Sciences, Financial Institutions, Inverse Problem, Capital Allocation

- by Micah M. Murray
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- Engineering, Electrophysiology, Neuroimaging, Statistical Analysis

Two calculation paths for estimating the particle size distribution (PSD) of a polymer latex from single-angle dynamic light scattering (DLS) measurements are evaluated on the basis of a numerical example. In the more common "double-step method," two calculation steps are applied, with the intermediate estimation of the particle light intensity distribution (PLID). In the "single-step method," the calculation is performed in one operation. From the specification of several PSDs, a mathematical model is used to produce the synthetic measurements. An iterative procedure was applied for determining the diameter range and the number of PSD points. The inversion operations were carried out using a regularization technique. For narrow distributions with diameters in the range 100-1000 nm, the PSD and the PLID are similar in shape, and both calculation paths produce similar results. For broad PSDs in the range 100-1000 nm, and for arbitrary PSDs in the range 10-100 nm (i.e., in the Rayleigh region), the single-step method proved preferable. C 2000 Academic Press

- by Jorge Vega
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- Engineering, Light Scattering, Sensitivity Analysis, Physical sciences

This paper discusses the results of geoacoustic inversion carried out using explosive charge data from the Asian Seas International Acoustic Experiment (ASIAEX) East China Sea (ECS) Experiment. A multifrequency incoherent matched-field inversion processor and a genetic algorithm (GA) are used for the inversion. A multistep matched field inversion approach is presented, which makes use of the varying sensitivities of wave fields at various frequencies to reduce the inversion problem into a sequence of smaller inversions with fewer unknowns to estimate at each stage. Different parameters are estimated using data at different frequencies according to their sensitivities. Inversion results for different areas in the ECS region are summarized and compared with core data.

- by Gopu Potty
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- Inverse Problems, Genetic Algorithm, Ocean Waves, Inverse Problem

We formulate the inverse problem of solving Fredholm integral equa- tions of the first kind as a nonparametric Bayesian inference problem, using Levy random fields (and their mixtures) as prior distributions. Posterior distributions for all featues of interest are computed using novel Markov chain Monte Carlo numerical methods in infinite-dimensional spaces, based on generalizations and extensions of the authors' Inverse

- by Robert Wolpert
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- Numerical Method, Bayesian Analysis, Bayesian Inference, Markov Chain Monte Carlo

In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary a priori and would like a solution, e.g. a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic nonlinearity. We prove convergence of a series solution and give a detailed parametric study on the series radius of convergence. Moreover, we prove that the parametrization can indeed can be used for motion planning purposes; computation of the open loop motion planning is straightforward. Simulation results are given and we prove some important properties about the solution. Namely, a weak maximum principle is derived for the dynamics, stating that the maximum is on the boundary. Also, we prove asymptotic positiveness of the solution, a physical requirement over the entire domain, as the transient time from one steady-state to another gets large.

- by N. Petit
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- Applied Mathematics, Calculus, Motion Planning, Free boundary Problem

In an effort to understand the present-day thermal structure of the Jeanne d'Arc Basin, we derive matrix thermal conductivity values, using a geometric mean model, from thermal conductivity values of thirteen lithologic end-members (of which seven are measurements on materials from the Jeanne d'Arc Basin) and lithological data. Temperature corrections to thermal conductivity are made for both matrix and pore water. In-situ thermal conductivities were obtained after correcting for the effect of porosity, which we estimated from both lithological information and digital well logs. Calculated thermal conductivities of the formations range from 1.46 to 2.65 W m -1K -1. The heterogeneity of formation thermal conductivity is caused by at least two factors. The first is lithological variation due to facies change. The second is due to different degrees of compaction. Under-compacted intervals (overpressure zones) are characteristically of lower thermal conductivity. The surface heat flow density calculated with an inverse method in seventeen wells varies from 37.8 to 60.7 mW/m 2. This study indicates that surface heat flow density values estimated without porosity corrections may be 15% higher than those with porosity corrections. We also demonstrate the sensitivity of modelled timing of maturation to thermal conductivity estimations.

- by Zehui Huang
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- Geology, Geochemistry, Geophysics, Density

Results of an analysis of the plane stress state of a thin annular disk subjected to uniform partially distributed heat supply    ) , ( t r f Q  are presented. Some features of the stress distribution are investigated by means of both theoretical technique and numerical testing. Analytical expressions for the components of the displacement and temperature distribution vector that correspond to the stress state under the action of partial distribution are established.

- by Navneet Kumar
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- Mechanical Engineering, Inverse Problem