Search results for "inverse problem"
showing 10 items of 163 documents
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds
2022
In this article we study the linearized anisotropic Calderon problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderon problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the tra…
Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier
2015
Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane–Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler–Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical result…
The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG
2015
The estimation of neuronal activity in the human brain from electroencephalography (EEG) and magnetoencephalography (MEG) signals is a typical inverse problem whose solution pro- cess requires an accurate and fast forward solver. In this paper the method of fundamental solutions is, for the first time, proposed as a meshfree, boundary-type, and easy-to-implement alternative to the boundary element method (BEM) for solving the M/EEG forward problem. The solution of the forward problem is obtained by numerically solving a set of coupled boundary value problems for the three-dimensional Laplace equation. Numerical accuracy, convergence, and computational load are investigated. The proposed met…
Optimal measurement setup for damage detection in piezoelectric plates
2009
[EN] An optimization of the excitation-measurement configuration is proposed for the characterization of damage in PZT-4 piezoelectric plates, from a numerical point of view. To perform such an optimization, a numerical method to determine the location and extent of defects in piezoelectric plates is developed by combining the solution of an identification inverse problem, using genetic algorithms and gradient-based methods to minimize a cost functional, and using an optimized finite element code and meshing algorithm. In addition, a semianalytical estimate of the probability of detection is developed and validated, which provides a flexible criterion to optimize the experimental design. Th…
Color and multispectral image processing for the detection of inflammatory lesions of the stomach
2019
The work presented in this manuscript is part of the ANR project EMMIE. This project aims to develop an innovative multimodal system for the detection of inflammatory lesions in the stomach. To this purpose, a prototype has been developed to be able to acquire NBI endoscopic images and multispectral images during human's antrum exploration. The prototype is made of a standard endoscope and multispectral images.The prototype can acquire two types of data: NBI images and spectra. These two modalities are processed independently. Common image processing features are used to recognize four kind of diseases: active gastritis, chronic gastritis, metaplasia and atrophy. In addition, visual based f…
Stiffness design of laminates using the polar method
2001
This paper is devoted to the analysis of elastic properties of anisotropic laminas using the so-called polar representation method: this is an effective mathematical tool to analyse two-dimensional elastic problems. By this method, the authors have been able to find a particular class of solutions to some special inverse problems concerning laminates made by anisotropic layers. The properties of these solutions are described and discussed, along with some general results.
Conservative Averaging Method for Solutions of Inverse Problems for Heat Equation
2004
Inverse problems arise in various fields of science, technology and agriculture where from measurements of state of the system or process it is required to determine a certain typesetting of the causal characteristics. It is known that infrigement of the natural causal relationships can entail incorrectness of the mathematical formulation of inverse problem. Therefore the development of efficient methods for solving such problems allow us to simplify experimental research considerably and to increase the accuracy and reliability of the obtained results due to certain complication of algoritms for processing the experemental data. The problem of the determination of the coefficient of therma…
COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS
2005
We propose a new method to calibrate the local volatility function of an asset from observed option prices of the underlying. Our method is initialized with a preprocessing step in which the given data are smoothened using cubic splines before they are differentiated numerically. In a second step the Dupire equation is rewritten as a linear equation for a rational expression of the local volatility. This equation is solved with Tikhonov regularization, using some discrete gradient approximation as penalty term. We show that this procedure yields local volatilities which appear to be qualitatively correct.
A numerical method for imaging of biological microstructures by VHF waves
2014
Imaging techniques give a fundamental support to medical diagnostics during the pathology discovery as well as for the characterization of bio-medical structures. The imaging methods involve electromagnetic waves in a frequency range that spans from some Hz to GHz and over. Most of these methods involve ionizing waves and scanning of a large human body area even if only a focused inspection is needed. In this paper, a numerical method to evaluate the shape of microstructures for application in the medical field, with a very low invasiveness for the human body, is proposed. In particular, the tooth’s root canal is considered. In fact, this is one of the hot topics in the endodontic procedure…
Adjoint-based sampling methods for electromagnetic scattering
2010
In this paper we investigate the efficient realization of sampling methods based on solutions of certain adjoint problems. This adjoint approach does not require the explicit knowledge of the Green's function for the background medium, and allows us to sample for all points and all dipole directions simultaneously; thus, several limitations of standard sampling methods are relieved. A detailed derivation of the adjoint approach is presented for two electromagnetic model problems, but the framework can be applied to a much wider class of problems. We also discuss a relation of the adjoint sampling method to standard backprojection algorithms, and present numerical tests that illustrate the e…