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Multigrid tomographic inversion with variable resolution data and image spaces.

Seungseok Oh1, Charles A Bouman, Kevin J Webb

  • 1Fujifilm Software (California), Inc., San Jose, CA 95110, USA. soh@fujifilmsoft.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 5, 2006
PubMed
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A novel multigrid inversion method improves computational efficiency for inverse problems by using variable resolutions in both data and image spaces. This approach accelerates convergence, especially in data-rich applications like medical imaging.

Area of Science:

  • Medical imaging
  • Computational science
  • Applied mathematics

Background:

  • Inverse problems in medical imaging, such as transmission and emission tomography, are computationally intensive.
  • Conventional multigrid methods offer computational savings but can be limited by fixed data resolution.
  • Data-rich applications present unique challenges due to varying data resolutions across scales.

Purpose of the Study:

  • To introduce a novel multigrid inversion approach with variable resolutions in both data and image spaces.
  • To enhance computational efficiency for inverse problems, particularly in data-rich scenarios.
  • To demonstrate the application and benefits of this approach in Bayesian reconstruction algorithms.

Main Methods:

  • Developed a multigrid inversion technique allowing independent variation of data and image space resolutions.

Related Experiment Videos

  • Applied the method to Bayesian reconstruction in transmission and emission tomography.
  • Utilized a generalized Gaussian Markov random field image prior with Poisson noise and quadratic data terms.
  • Main Results:

    • The proposed variable-resolution multigrid approach significantly improves convergence speed.
    • Demonstrated superior performance compared to fixed-grid iterative coordinate descent methods.
    • Outperformed multigrid methods that maintain fixed data resolution across scales.

    Conclusions:

    • The variable-resolution multigrid inversion method offers substantial computational advantages for inverse problems.
    • This approach is particularly beneficial for data-rich imaging applications, enhancing reconstruction speed.
    • The findings suggest a more efficient pathway for complex iterative reconstruction tasks in medical imaging.