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Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: part I.

Murat Guven1, Laurel Reilly-Raska, Lu Zhou

  • 1Intel Corporation, Santa Clara, CA 95054 USA. guven@rpi.edu

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|February 5, 2010
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Summary
This summary is machine-generated.

Discretization significantly impacts fluorescence diffuse optical tomography accuracy. This study analyzes errors from numerical methods in forward and inverse problems, offering theorems to guide adaptive algorithm design for better imaging.

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Area of Science:

  • Biomedical Imaging
  • Computational Science

Background:

  • Numerical solutions for inverse and forward problems are crucial in imaging.
  • Discretization is a key factor affecting imaging accuracy.

Purpose of the Study:

  • Analyze the impact of discretization on fluorescence diffuse optical tomography (FDOT) accuracy.
  • Identify factors contributing to high reconstruction errors in FDOT.
  • Develop adaptive discretization algorithms for improved FDOT.

Main Methods:

  • Modeled the forward problem using diffusion equations and finite element discretization.
  • Employed an optimization framework with Tikhonov regularization for the inverse problem.
  • Discretized the inverse problem using variational formulation and Galerkin projection.

Main Results:

  • Presented two theorems detailing error sources in FDOT reconstruction.
  • Highlighted mutual dependence of forward/inverse problems, source/detector configurations, and inverse problem formulation as key error factors.
  • Demonstrated error analysis implications through numerical experiments.

Conclusions:

  • Discretization error analysis is vital for accurate FDOT.
  • Theorems provide insights into optimizing FDOT parameters and algorithms.
  • Results inform the design of novel adaptive discretization strategies for enhanced imaging performance.