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Convergent block-iterative algorithms for image reconstruction from inconsistent data.

C L Byrne1

  • 1Massachusetts Univ., Lowell, MA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1997
PubMed
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Rescaled block-iterative (BI) methods accelerate image reconstruction but fail in inconsistent cases, producing limit cycles (LCs). A novel feedback technique uses these LCs to construct approximate solutions, proving convergence.

Area of Science:

  • Medical Imaging
  • Computer Vision
  • Applied Mathematics

Background:

  • Iterative image reconstruction algorithms, including Cimmino-type, EMML, and SMART, are accelerated by rescaled block-iterative (BI) methods.
  • BI methods partition data into subsets, using one subset per iteration for faster convergence.
  • A key limitation of BI methods is their failure to converge in inconsistent data cases, resulting in limit cycles (LCs).

Purpose of the Study:

  • To investigate if limit cycles (LCs) generated by block-iterative (BI) methods contain sufficient information for constructing approximate solutions.
  • To develop and prove the convergence of a novel technique for addressing the inconsistent data problem in image reconstruction.

Main Methods:

  • A feedback technique was developed to utilize limit cycle (LC) vectors.

Related Experiment Videos

  • LC vectors were used to generate a new "data" vector, and the iterative algorithm was restarted.
  • Convergence of this nested iterative scheme to an approximate solution was mathematically proven.

    • Main Results:

    • The study demonstrates that limit cycles (LCs) retain sufficient information to construct approximate solutions.
    • A novel feedback method successfully overcomes the convergence failure of BI methods in inconsistent cases.
    • Preliminary findings suggest the feedback method's practical applicability in image reconstruction.

    Conclusions:

    • The proposed feedback technique effectively utilizes limit cycles (LCs) to achieve approximate solutions in image reconstruction, even with inconsistent data.
    • This method addresses a significant limitation of block-iterative (BI) algorithms.
    • The research opens avenues for more robust and practical image reconstruction techniques.