Search results for "Inverse problem"
showing 10 items of 163 documents
An inverse problem for the fractional Schrödinger equation in a magnetic field
2020
This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrodinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely many measurements of solutions taken in arbitrary open subsets of the exterior. The proof is based on Alessandrini's identity and the Runge approximation property, thus generalizing some previous works on the fractional Laplacian. Moreover, we show with a simple model that the FMSE relates to a long jump random walk with weights.
An augmented MFS approach for brain activity reconstruction
2017
Abstract Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving rise to electric and magnetic fields, which can be modeled by the quasi-stationary approximation of Maxwell’s equations. Electroencephalography (EEG) and magnetoencephalography (MEG) techniques allow for reconstructing the cerebral electrical currents and thus investigating the neuronal activity in the human brain in a non-invasive way. This is a typical electromagnetic inverse problem which can be addressed in two stages. In the first one a physical and geometrical representation of the head is used to find the relation between a given source mo…
Eddy current flaw detection with neural network applications
2005
Abstract Eddy current inspection is a fast and effective method for detecting and sizing most of the flaws in conducting materials. The inverse problem solution, i.e., inferencing about possible defect, based on the measurement signal from the eddy current probe, is a difficult task. In this paper an implementation of artificial neural networks for multi-frequency eddy current testing on conducting layers (aluminum, copper) and ferrous tubes has been presented.
Intensive wave power and steel quenching 3-D model for cylindrical sample. Time direct and reverse formulations and solutions
2017
In this paper we develop mathematical models for three dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. As additional conditions the temperature and heat flux at the end time are given. In some cases we give expression of wave energy. In some cases we give expression of wave energy. Some solutions of time inverse problems are obtained in the form of first kind Fredholm integral equation, but others has been obtained in closed analytical form as series. We viewed both direct and inverse problems at the time. For the time inverse pr…
Desychronization of one-parameter families of stable vector fields
2005
Given a one-parameter family of vector fields on , Fλ(x), , such that for each λ, Fλ has a global asymptotically stable equilibrium point xλ, we construct a vector field on of the form G(λ, x) = (g(λ, x), Fλ(x)) which exhibits chaotic behaviour. This result is an incursion in the inverse problem of master–slave synchronization.This paper discusses self-disorganization of parameter dependent stable vector fields. Motivations are found in applications to drug design: one way to lead an unfriendly organism to death is to destabilize its metabolism. In this paper we envisage the mathematical aspect of the question. We show that for a very stable system (one globally attracting equilibrium state…
A simple inverse procedure to determine heat flux on the tool in orthogonal cutting
2006
The applications of numerical simulation to machining processes have been more and more increasing in the last decade: today, a quite effective predictive capability has been reached, at least as far as global cutting variables (for instance cutting forces) are concerned. On the other hand, the capability to predict local cutting variables (i.e. stresses acting on the tool, temperature distribution, residual stresses in the machined surface) has to be furtherly improved, as well as effective experimental procedures to validate numerical results have to be developed. The aim of this paper is the proposition of an innovative approach, based on an simple inverse procedure, in order to identify…
Deep Non-Line-of-Sight Reconstruction
2020
The recent years have seen a surge of interest in methods for imaging beyond the direct line of sight. The most prominent techniques rely on time-resolved optical impulse responses, obtained by illuminating a diffuse wall with an ultrashort light pulse and observing multi-bounce indirect reflections with an ultrafast time-resolved imager. Reconstruction of geometry from such data, however, is a complex non-linear inverse problem that comes with substantial computational demands. In this paper, we employ convolutional feed-forward networks for solving the reconstruction problem efficiently while maintaining good reconstruction quality. Specifically, we devise a tailored autoencoder architect…
Joint Gaussian Processes for Biophysical Parameter Retrieval
2017
Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding problem, and for this reason, often the application of a nonlinear statistical regression is preferred. In general, regression models predict the biophysical parameter of interest from the corresponding received radiance. However, this approach does not employ the physical information encoded in the RTMs. An alternative strategy, which attempts to include the physical knowledge, co…
CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
2017
International audience; In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a ``twicing'' flavor a…
Thresholding projection estimators in functional linear models
2008
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.