50,550 research outputs found
Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation
We consider the problem of reconstruction of dielectrics from blind
backscattered experimental data. Experimental data were collected by a device,
which was built at University of North Carolina at Charlotte. This device sends
electrical pulses into the medium and collects the time resolved backscattered
data on a part of a plane. The spatially distributed dielectric constant
is the unknown
coefficient of a wave-like PDE. This coefficient is reconstructed from those
data in blind cases. To do this, a globally convergent numerical method is
used.Comment: 27 page
Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method
The problem to be studied in this work is within the context of coefficient
identification problems for the wave equation. More precisely, we consider the
problem of reconstruction of the refractive index (or equivalently, the
dielectric constant) of an inhomogeneous medium using one backscattering
boundary measurement. The goal of this paper is to analyze the performance of a
globally convergent algorithm of Beilina and Klibanov on experimental data
acquired in the Microwave Laboratory at University of North Carolina at
Charlotte. The main challenge working with experimental data is the the huge
misfit between these data and computationally simulated data. We present data
pre-processing steps to make the former somehow look similar to the latter.
Results of both non-blind and blind targets are shown indicating good
reconstructions even for high contrasts between the targets and the background
medium.Comment: 25 page
Computing Weakest Strategies for Safety Games of Imperfect Information
CEDAR (Counter Example Driven Antichain Refinement) is a new symbolic algorithm for computing weakest strategies for safety games of imperfect information. The algorithm computes a fixed point over the lattice of contravariant antichains. Here contravariant antichains are antichains over pairs consisting of an information set and an allow set representing the associated move. We demonstrate how the richer structure of contravariant antichains for representing antitone functions, as opposed to standard antichains for representing sets of downward closed sets, allows CEDAR to apply a significantly less complex controllable predecessor step than previous algorithms
Bayesian inference for inverse problems
Traditionally, the MaxEnt workshops start by a tutorial day. This paper
summarizes my talk during 2001'th workshop at John Hopkins University. The main
idea in this talk is to show how the Bayesian inference can naturally give us
all the necessary tools we need to solve real inverse problems: starting by
simple inversion where we assume to know exactly the forward model and all the
input model parameters up to more realistic advanced problems of myopic or
blind inversion where we may be uncertain about the forward model and we may
have noisy data. Starting by an introduction to inverse problems through a few
examples and explaining their ill posedness nature, I briefly presented the
main classical deterministic methods such as data matching and classical
regularization methods to show their limitations. I then presented the main
classical probabilistic methods based on likelihood, information theory and
maximum entropy and the Bayesian inference framework for such problems. I show
that the Bayesian framework, not only generalizes all these methods, but also
gives us natural tools, for example, for inferring the uncertainty of the
computed solutions, for the estimation of the hyperparameters or for handling
myopic or blind inversion problems. Finally, through a deconvolution problem
example, I presented a few state of the art methods based on Bayesian inference
particularly designed for some of the mass spectrometry data processing
problems.Comment: Presented at MaxEnt01. To appear in Bayesian Inference and Maximum
Entropy Methods, B. Fry (Ed.), AIP Proceedings. 20pages, 13 Postscript
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