Journal ArticleDOI
Characterizing inclusions in optical tomography
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In this paper, the authors investigate the possibility of characterizing inhomogeneities in the framework of the diffusion approximation of the radiative transfer equation using the factorization method, for purely scattering inclusions, or if the scattering and absorption coefficients interplay in a correct way, if and only if the point source lies inside one of the inclusions.Abstract:
In optical tomography, one tries to determine the spatial absorption and scattering distributions inside a body by using measured pairs of inward and outward fluxes of near-infrared light on the object boundary. In many practically important situations, the scatter and the absorption inside the object are smooth apart from inclusions where at least one of the two optical parameters jumps to a higher or lower value. In this work, we investigate the possibility of characterizing these inhomogeneities in the framework of the diffusion approximation of the radiative transfer equation using the factorization method: for purely scattering inclusions, or if the scattering and absorption coefficients interplay in a correct way, the outcoming flux corresponding to a point source belongs to the range of an operator, determined through boundary measurements, if and only if the point source lies inside one of the inclusions.read more
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Handbook of mathematical methods in imaging
TL;DR: In this article, the Mumford and Shah Model and its applications in total variation image restoration are discussed. But the authors focus on the reconstruction of 3D information, rather than the analysis of the image.
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Factorization method and irregular inclusions in electrical impedance tomography
Bastian Gebauer,Nuutti Hyvönen +1 more
TL;DR: In this paper, it was shown that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite.
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The Factorization Method for Real Elliptic Problems
TL;DR: In this article, the authors developed a general framework for the Factorization Method by considering sym-metric and coercive operators between abstract Hilbert spaces and showed that the important range characterization holds if the difference between the inclusions and the background medium satisfies a coerciveness condition which can immediately be translated into a condition on the coefficients of a given realelliptic problem.
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Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography
TL;DR: In this article, the Kirsch factorization method is translated to the framework of the complete electrode model of electrical impedance tomography and its functionality is demonstrated through two-dimensional numerical experiments.
References
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Journal ArticleDOI
Optical tomography in medical imaging
TL;DR: A review of methods for the forward and inverse problems in optical tomography can be found in this paper, where the authors focus on the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction.
Journal ArticleDOI
Mathematical Analysis and Numerical Methods for Science and Technology
TL;DR: These six volumes as mentioned in this paper compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers.
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The boundary value problems of mathematical physics
TL;DR: In this paper, the method of finite differences is used to compare Equations of Elliptic Type, Parabolic Type, Hyperbolic Type, and Equation of Parabolical Type.
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Partial Differential Equations I: Basic Theory
TL;DR: In this article, the Laplace Equation and Wave Equation on a Riemannian manifold and the wave equation on a product manifold and energy conservation were studied. But the authors focus on the divergence of a vector field.