&lt;title&gt;NIR imaging in random media using time domain data&lt;/title&gt;

Model, Regine; Huenlich, Rolf; Orlt, Matthias; Walzel, Monika

doi:10.1117/12.260829

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Inverse Problem Under Consideration and Its Applications1

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1997

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“…for a suitable function f (x), cf Model et al [26]. In any case, the point is that if (2.5) holds, then the measurement of one of the functions ϕ or ψ leads to the values of the second one.…”

Section: Inverse Problem Under Consideration and Its Applicationsmentioning

confidence: 99%

A fast and accurate imaging algorithm in optical/diffusion tomography

1997

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An n-dimensional (n = 2, 3) inverse problem for the parabolic/diffusion equationThe problem consists of determining the function a(x) inside of a bounded domain ⊂ R n given the values of the solution u(x, t) for a single source location x 0 ∈ ∂ on a set of detectors {x i } m i=1 ⊂ ∂ , where ∂ is the boundary of . A novel numerical method is derived and tested. Numerical tests are conducted for n = 2 and for ranges of parameters which are realistic for applications to early breast cancer diagnosis and the search for mines in murky shallow water using ultrafast laser pulses. The main innovation of this method lies in a new approach for a novel linearized problem (LP). Such a LP is derived and reduced to a well-posed boundary-value problem for a coupled system of elliptic partial differential equations. A principal advantage of this technique is in its speed and accuracy, since it leads to the factorization of well conditioned, sparse matrices with non-zero entries clustered in a narrow band near the diagonal. The authors call this approach the elliptic systems method (ESM). The ESM can be extended to other imaging modalities.

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Section: Inverse Problem Under Consideration and Its Applicationsmentioning

confidence: 99%