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Image reconstruction from limited Fourier data.

Hsin M Shieh1, Charles L Byrne

  • 1Department of Electrical Engineering, Feng Chia University, Seatwen, Taichung, Taiwan 40724. hmshieh@fcu.edu.tw

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|October 19, 2006
PubMed
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This study reconstructs functions with bounded support using Fourier transform data. The method models the function as sigma-band-limited, with sigma impacting the reconstruction resolution.

Area of Science:

  • Signal Processing
  • Applied Mathematics
  • Fourier Analysis

Background:

  • Reconstructing functions with bounded support from limited Fourier data is challenging.
  • Functions with bounded support are not band-limited, requiring alternative modeling approaches.

Purpose of the Study:

  • To develop a method for reconstructing functions with bounded support using Fourier transform information.
  • To investigate the influence of sigma-band-limited modeling on reconstruction resolution.

Main Methods:

  • Modeling the target function as a sigma-band-limited function.
  • Utilizing finitely many values of the function's Fourier transform for reconstruction.
  • Analyzing the impact of the parameter sigma on the reconstruction fidelity.

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Main Results:

  • A novel reconstruction method is presented for bounded support functions.
  • The choice of sigma directly affects the achievable resolution in the reconstruction.
  • Demonstrated the feasibility of reconstructing functions from partial Fourier data.

Conclusions:

  • The sigma-band-limited model provides a viable approach for function reconstruction.
  • Optimizing sigma is crucial for balancing data limitations and desired resolution.
  • This method offers potential for applications where signal support is known but band-limitation is not.