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Approximation errors and model reduction in optical tomography.
V Kolehmainen1, S R Arridge, J P Kaipio
1Dept. of Phys., Univ. Kuopio, Finland. Ville.Kolehmainen@uku.fi
Summary
Model reduction in optical diffusion tomography (ODT) is essential. Applying approximation error theory allows for sparser meshes, improving computational efficiency without sacrificing accuracy in ODT.
Area of Science:
- Biomedical Optics
- Computational Imaging
- Inverse Problems
Background:
- Model reduction is frequently necessary in optical diffusion tomography (ODT) due to computational constraints.
- Limited computation time or memory often necessitates the use of sparse meshes for the forward problem in ODT.
- Increasingly accurate measurements demand more precise forward problem solvers to fully utilize the data.
Purpose of the Study:
- To apply approximation error theory to optical diffusion tomography (ODT).
- To investigate the impact of estimating and employing approximation errors on mesh density in ODT.
- To determine if ODT can utilize mesh densities previously considered unacceptable.
Main Methods:
- Application of approximation error theory to the ODT model.
- Analysis of the relationship between measurement accuracy and forward problem solver requirements.
- Evaluation of mesh densities under varying approximation error conditions.
Main Results:
- Demonstration that estimating and employing approximation errors is feasible in ODT.
- Identification of conditions where sparser meshes are acceptable.
- Quantification of the benefits of approximation error estimation for computational efficiency.
Conclusions:
- Approximation error theory provides a framework for optimizing mesh density in ODT.
- The findings suggest a potential for improved computational efficiency in ODT without compromising data integrity.
- This approach enables the use of less dense meshes, making ODT more accessible with limited computational resources.
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