Characterizing inclusions in optical tomography

@article{Hyvnen2004CharacterizingII,
  title={Characterizing inclusions in optical tomography},
  author={Nuutti Hyv{\"o}nen},
  journal={Inverse Problems},
  year={2004},
  volume={20},
  pages={737-751}
}
  • N. Hyvönen
  • Published 19 March 2004
  • Mathematics
  • Inverse Problems
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… 
Locating small inclusions in diffuse optical tomography by a direct imaging method
Optical tomography is a typical non-invasive medical imaging technique, which aims to reconstruct geometric and physical properties of tissues by passing near infrared light through tissues for
Determining the absorption in anisotropic media
Abstract. The problem in Optical Tomography of determining the spatially dependent absorption coefficient in an anisotropic medium with a-priori known strong scattering is considered. The problem is
Reconstructions in impedance and optical tomography with singular interfaces
Singular layers modelled by a tangential diffusion process supported on an embedded closed surface (of co-dimension 1) have found applications in tomography problems. In optical tomography they may
Time-harmonic diffuse optical tomography: H\"older stability of the derivatives of the optical properties of a medium at the boundary
We study the inverse problem in Optical Tomography of determining the optical properties of a medium Ω ⊂ R, with n ≥ 3, under the so-called diffusion approximation. We consider the time-harmonic case
Lipschitz stability at the boundary for time-harmonic diffuse optical tomography
ABSTRACT We study the inverse problem in Optical Tomography of determining the optical properties of a medium , with , under the so-called diffusion approximation. We consider the time-harmonic case
Application of a weaker formulation of the factorization method to the characterization of absorbing inclusions in optical tomography
In the framework of diffuse tomography, i.e. optical tomography and electrical impedance tomography, the factorization method of Andreas Kirsch provides a tool for locating inhomogeneities inside an
Stable determination at the boundary of the optical properties of a medium: the static case
The problem of the stable determination of the coefficients of second order elliptic partial differential equations arising in inverse problems is considered. Results of uniqueness and stability at
...
...

References

SHOWING 1-10 OF 19 REFERENCES
Diffusion tomography in dense media
Explicit Characterization of Inclusions in Electrical Impedance Tomography
TLDR
It is shown that this procedure is conceptually similar to a recent method proposed by Kirsch in inverse scattering theory and holds true if and only if the dipole singularity lies inside the inhomogeneity.
Estimation of optical absorption in anisotropic background
In this paper we present a model for anisotropic light propagation and reconstructions of optical absorption coefficient in the presence of anisotropies. To model the anisotropies, we derive the
Complete Electrode Model of Electrical Impedance Tomography: Approximation Properties and Characterization of Inclusions
TLDR
It is demonstrated how inclusions with strictly higher or lower conductivities can be characterized by the limit behavior of the range of a boundary operator, determined through electrode measurements, when the electrodes get infinitely small and cover all...
Partial Differential Equations I: Basic Theory
TLDR
Existence and regularity of solutions to the Dirichlet problem and the weak and strong maximum principles are studied.
The Boundary Value Problems of Mathematical Physics
I Preliminary Considerations.- II Equations of Elliptic Type.- III Equations of Parabolic Type.- IV Equations of Hyperbolic Type.- V Some Generalizations.- VI The Method of Finite Differences.
Partial Differential Equations I (New York: Springer
  • 1996
ANALYSIS OF OPTICAL TOMOGRAPHY WITH NON-SCATTERING REGIONS
  • N. Hyvönen
  • Mathematics, Physics
    Proceedings of the Edinburgh Mathematical Society
  • 2002
Abstract This paper provides mathematical analysis of optical tomography in a situation when the examined object, for example the human brain, is strongly scattering with non-scattering inclusions.
Mathematical Analysis and Numerical Methods for Science and Technology
These six volumes - the result of a ten year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge
...
...