18 August 1997 New imaging algorithm in diffusion tomography
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Proceedings Volume 2979, Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II; (1997); doi: 10.1117/12.280254
Event: BiOS '97, Part of Photonics West, 1997, San Jose, CA, United States
Abstract
A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.
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Michael V. Klibanov, Thomas R. Lucas, Robert M. Frank, "New imaging algorithm in diffusion tomography", Proc. SPIE 2979, Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, (18 August 1997); doi: 10.1117/12.280254; https://doi.org/10.1117/12.280254
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KEYWORDS
Electronic support measures

Diffusion

Tomography

Inverse problems

Chemical elements

Matrices

Numerical analysis

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