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Tomographic reconstruction and estimation based on multiscale natural-pixel bases.

M Bhatia1, W C Karl, A S Willsky

  • 1J.P. Morgan and Co. Inc., New York, NY.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1997
PubMed
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This study introduces a novel multiscale reconstruction technique for tomographic imaging using nearly orthonormal basis functions. This method effectively handles incomplete and noisy projection data, enabling object reconstruction at multiple resolutions.

Area of Science:

  • Image reconstruction
  • Computational imaging
  • Applied mathematics

Background:

  • Tomographic imaging often faces challenges with incomplete, irregular, and noisy projection data.
  • Existing reconstruction methods struggle with ill-conditioning arising from imaging system geometry.
  • Multiscale representations are crucial for handling complex data and achieving robust reconstructions.

Purpose of the Study:

  • To develop a multiscale reconstruction technique for tomographic imaging from incomplete data.
  • To address ill-conditioning and noise in projection data for improved object reconstruction.
  • To enable object reconstruction at multiple scales or resolutions.

Main Methods:

  • Utilizing a natural pixel-type representation to construct nearly orthonormal multiscale basis functions.

Related Experiment Videos

  • Exploiting the sparsity of the system matrix for efficient reconstruction.
  • Developing a multiscale reconstruction procedure by partitioning the system matrix by scales.
  • Extending the technique for noisy data using maximum a posteriori probability (MAP) estimation with a self-similar prior.

    • Main Results:

    • Achieved extremely sparse system matrices due to nearly orthonormal basis functions.
    • Successfully addressed ill-conditioning by isolating it in the coarsest scale elements.
    • Developed a reconstruction procedure involving inversion of only well-conditioned, sparse matrices.
    • Demonstrated the capability to reconstruct objects at multiple scales from incomplete and noisy data.

    Conclusions:

    • The proposed multiscale reconstruction framework offers a robust solution for incomplete and noisy tomographic data.
    • The technique effectively regularizes imaging problems and facilitates object feature recognition directly from projection data.
    • This approach enhances the applicability of tomography in various scientific and engineering domains requiring high-resolution imaging.