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O(N(2)log(2)N) filtered backprojection reconstruction algorithm for tomography.

S Basu1, Y Bresler

  • 1Gen. Electr. Corp. Res. and Dev. Center, Niskayuna, NY 12309, USA. basu@crd.ge.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 12, 2008
PubMed
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A novel hierarchical algorithm accelerates parallel beam tomography reconstruction, significantly reducing computational cost while maintaining image quality. This fast filtered backprojection (FBP) method offers substantial speedups over existing techniques.

Area of Science:

  • Medical Imaging
  • Computational Science

Background:

  • Filtered backprojection (FBP) is a standard algorithm for parallel beam tomography reconstruction.
  • Existing accelerated algorithms offer reduced computational cost but may compromise image fidelity.

Purpose of the Study:

  • To introduce a new, accelerated filtered backprojection (FBP) algorithm for parallel beam tomography.
  • To enhance the computational efficiency of tomographic reconstruction while preserving accuracy.

Main Methods:

  • Developed a hierarchical decomposition of the backprojection operation.
  • Reduced computational complexity from O(N^3) to O(N^2 log^2 N).
  • Performed numerical studies to analyze parameter choices and cost-distortion trade-offs.

Main Results:

Related Experiment Videos

  • The hierarchical algorithm achieves a computational cost of O(N^2 log^2 N).
  • Demonstrated superior cost-distortion performance compared to Fourier and multilevel inversion algorithms.
  • Achieved RMS reconstruction errors comparable to standard FBP with significant speedup (over 40-fold in an example).

Conclusions:

  • The proposed hierarchical scheme provides a favorable balance between computational cost and reconstruction accuracy.
  • This accelerated FBP algorithm offers a practical solution for faster, high-quality tomographic image reconstruction.