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On the direct Fourier method for computer tomography.

D Gottlieb1, B Gustafsson, P Forssén

  • 1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. dig@cfm.brown.edu

IEEE Transactions on Medical Imaging
|June 30, 2000
PubMed
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This study analyzes errors in direct Fourier methods (DFM) for X-ray image reconstruction. It proposes an alternative interpolation technique and a method to mitigate the Gibbs phenomenon, improving image quality.

Area of Science:

  • Medical Imaging
  • Computational Science
  • Image Reconstruction

Background:

  • Direct Fourier Methods (DFM) are used for image reconstruction from X-ray projections.
  • Image quality degradation is often caused by the Gibbs phenomenon.
  • Accurate error estimation is crucial for reliable image reconstruction.

Purpose of the Study:

  • To estimate errors in direct Fourier methods using numerical analysis.
  • To propose an alternative interpolation method for DFM.
  • To address and overcome the Gibbs phenomenon in image reconstruction.

Main Methods:

  • Application of numerical analysis concepts for error estimation.
  • Development of an alternative interpolation strategy for DFM.
  • Implementation of a novel technique to counteract the Gibbs phenomenon.

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Main Results:

  • Quantification of errors inherent in DFM.
  • Estimation of the number of terms required for the alternative interpolation.
  • Demonstration of the efficacy of the proposed method in reducing the Gibbs phenomenon.

Conclusions:

  • The proposed numerical analysis approach provides error estimates for DFM.
  • The alternative interpolation and Gibbs phenomenon mitigation enhance reconstruction quality.
  • This research offers improvements for X-ray image reconstruction techniques.