Search results for " inverse problems"
showing 7 items of 7 documents
Jacobian of solutions to the conductivity equation in limited view
2022
Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…
A New Procedure for the Evaluation of Non-Uniform Residual Stresses by the Hole Drilling Method Based on the Newton-Raphson Technique
2010
The hole drilling method is one of the most used semi-destructive techniques for the analysis of residual stresses in mechanical components. The non-uniform stresses are evaluated by solving an integral equation in which the strains relieved by drilling a hole are introduced. In this paper a new calculation procedure, based on the Newton-Raphson method for the determination of zeroes of functions, is presented. This technique allows the user to introduce complex and effective forms of stress functions for the solution of the problem. All the relationships needed for the evaluation of the stresses are obtained in explicit form, eliminating the need to use additional mathematical tools. The t…
Learning, regularization and ill-posed inverse problems
2005
Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we provide a positive answer to both questions. Indeed, considering the square loss, we translate the learning problem in the language of regularization theory and show that consistency results and optimal regularization parameter choice can be derived by the discretization of the corresponding inverse prob…
Learning from examples as an inverse problem
2005
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 continuo…
Numerical modelling of electromagnetic sources by integral formulation
2012
Analysis of electromagnetic (EM) transients can be carried out by employing a eld approach in frequency domain, based on an appropriate integral equation. This approach is a powerful method for the analysis of EM antennas and scatterers. Recent work by the authors in modeling electromagnetic scattering in frequency domain are summarized. Thin-wire electric eld integral equation has been handled and possible application in obtaining sources localization information are discussed. Moments method (MoM) is used and time domain analysis is also carried out by discrete Fourier transform. Di erent approaches have been considered by using direct MoM formulation. Simulation results obtained both via…
A meshfree approach for brain activity source modeling
2015
Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving raise to electric and magnetic fields, which are representable by means of quasi-stationary approximation of the Maxwell’s equations. Measurements of electric scalar potential differences at the scalp and magnetic fields near the head constitute the input data for, respectively, electroencephalography (EEG) and magnetoencepharography (MEG), which 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 erectromagnetic inverse problem, since measuremen…
Some Features of Modeling Ultrasound Propagation in Non-Destructive Control of Metal Structures Based on the Magnetostrictive Effect
2023
A method and mathematical models of direct and inverse problems of ultrasonic testing and diagnostics of complex metal structures for defects were developed and tested. A prototype of a system for magnetostrictive control of elements of the objects under study was manufactured and experimentally tested. Mathematical simulation of ultrasonic testing processes using MATLAB and the COMSOL Multiphysics software environment was carried out. The adequacy of the mathematical models was verified by the results of their comparison with real physical experiments. Information support and a methodology that implements it was developed, which ensure the functioning of the control facilities for these ob…