# Optical tomography as a PDE-constrained optimization problem

@article{Abdoulaev2005OpticalTA, title={Optical tomography as a PDE-constrained optimization problem}, author={Gassan Abdoulaev and Kui Ren and Andreas H. Hielscher}, journal={Inverse Problems}, year={2005}, volume={21}, pages={1507 - 1530} }

We report on the implementation of an augmented Lagrangian approach for solving the inverse problems in diffuse optical tomography (DOT). The forward model of light propagation is the radiative transport equation (RTE). The inverse problem is formulated as a minimization problem with the RTE being considered as an equality constraint on the set of ‘optical properties—radiance’ pairs. This approach allows the incorporation of the recently developed technique of PDE-constrained optimization…

## 74 Citations

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- 2008

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### Diffuse optical tomographic imaging of biological media by time-dependent parabolic SP(N) equations: a two-dimensional study.

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- 2012

The results suggest the DOT algorithm based on the TD-pSPN model outperforms the DE, and accurately reconstructs optical parameter distributions of biological media both spatially and quantitatively.

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Novel methods of Calculus of Variations in L∞ are utilised to lay the mathematical foundations of FOT, which is posed as a PDE-constrained minimisation problem in Lp and L ∞.

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