High-resolution inversion of finite Fourier transform data through a localised polynomial approximation

Zhi Pei Liang, E. Mark Haacke, Cecil W. Thomas

Research output: Contribution to journalArticlepeer-review


The authors address the problem of high-resolution inversion of finite Fourier transform data, which is frequently encountered in tomographic image reconstruction. A new parametric modelling approach, which uses an adaptive localised polynomial approximation model of the object function, is proposed to overcome the Gibbs artifact and the limited-resolution problem associated with conventional FFT methods. An algorithm for finding the model parameters is given which makes use of linear prediction theory, singular-value decomposition and least-squares fitting methods. Reconstruction results from simulated and real magnetic resonance experimental data are also presented to demonstrate its capability for Gibbs ringing reduction and resolution enhancement.

Original languageEnglish (US)
Article number011
Pages (from-to)831-847
Number of pages17
JournalInverse Problems
Issue number5
StatePublished - 1989
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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