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A general framework for nonlinear multigrid inversion.

Seungseok Oh1, Adam B Milstein, Charles A Bouman

  • 1School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-2035, USA. ohs@ecn.purdue.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 14, 2005
PubMed
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This study introduces a novel nonlinear multigrid inversion framework for complex imaging problems like optical diffusion tomography. The method significantly reduces computational cost by using coarser discretizations at lower resolutions, enabling efficient image reconstruction.

Area of Science:

  • Computational imaging
  • Applied mathematics
  • Image reconstruction

Background:

  • Advanced imaging modalities like optical diffusion tomography rely on solving complex inverse problems.
  • These problems are often nonlinear and computationally intensive, posing significant challenges for image reconstruction.
  • Existing methods struggle with the computational demands of high-resolution, accurate image reconstruction.

Purpose of the Study:

  • To develop a general and efficient framework for nonlinear inverse problems.
  • To significantly reduce the computational cost associated with image reconstruction in demanding applications.
  • To provide a robust method applicable to various inverse problems, including those in optical diffusion tomography.

Main Methods:

  • A novel nonlinear multigrid inversion algorithm is proposed, leveraging recursive multigrid techniques.

Related Experiment Videos

  • The method dynamically adjusts cost functionals across different scales to align with the finest scale objective.
  • Forward and inverse problems are coarsely discretized at lower resolutions to minimize computation.

    • Main Results:

    • The proposed multigrid inversion algorithm demonstrates potential for substantial computational savings.
    • Application to Bayesian optical diffusion tomography with a specific prior model showed significant efficiency gains.
    • Numerical results indicate robust convergence even for nonconvex optimization problems with varied initializations.

    Conclusions:

    • The nonlinear multigrid inversion framework offers an efficient solution for computationally expensive inverse problems in imaging.
    • This approach enables significant reductions in computation time, making advanced imaging techniques more feasible.
    • The method's robustness and applicability to challenging optimization problems highlight its potential impact on scientific imaging.