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Autoregression and Structured Low-Rank Modeling of Sinogram Neighborhoods.

Rodrigo A Lobos1, Muhammad Usman Ghani2, W Clem Karl2

  • 1Signal and Image Processing Institute, Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA 90089 USA.

IEEE Transactions on Computational Imaging
|January 21, 2022
PubMed
Summary

This study reveals novel autoregressive relationships in sinograms, enabling linear prediction of missing data. Structured low-rank matrix recovery offers a new method for sinogram restoration with comparable performance to deep learning.

Keywords:
AutoregressionSinogram restorationStructured low-rank matrix recoveryTomographic imaging

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Area of Science:

  • Medical Imaging
  • Signal Processing
  • Applied Mathematics

Background:

  • Sinograms are fundamental to tomographic imaging but contain inherent data redundancy.
  • Existing methods have not fully exploited the complex redundancies present in sinogram data.

Purpose of the Study:

  • To introduce novel theory on sinogram data-dependent autoregressive relationships.
  • To develop a structured low-rank matrix recovery approach for sinogram restoration.

Main Methods:

  • Derivation of data-dependent autoregressive relationships in sinograms.
  • Formulation of sinogram restoration as a structured low-rank matrix recovery problem.
  • Linear prediction of missing/degraded sinogram samples using neighboring data.

Main Results:

  • Demonstrated that sinograms often satisfy multiple autoregressive relationships.
  • Showcased the effectiveness of structured low-rank matrix recovery on real and simulated X-ray datasets.
  • Achieved performance comparable to state-of-the-art deep learning methods for sinogram recovery.

Conclusions:

  • Autoregressive constraints provide a powerful, complementary approach to existing sinogram restoration techniques.
  • Structured low-rank matrix recovery is a viable and effective method for enhancing tomographic imaging data.
  • Potential for synergistic integration of autoregressive methods with current deep learning approaches.