Adityavikram Viswanathan

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  Incorporating Edge Information in Fourier Reconstruction Schemes with Application to Magnetic Resonance Imaging
  Adityavikram Viswanathan

  Fourier reconstruction of piecewise-smooth functions suffers from the familiar Gibbs phenomenon. In Fourier imaging modalities such as magnetic resonance imaging (MRI), this manifests as a loss of detail in the neighborhood of tissue boundaries (due to the Gibbs ringing artifact) as well as long scan times necessitated by the collection of a large number of spectral coefficients (due to the poor convergence properties of the reconstruction method). We present a framework for incorporating edge information - for example, the locations and values of jump discontinuities of a function - in the reconstruction. We show that a simple relationship exists between global Fourier data and local edge information. Knowledge of such edges, either a priori or estimated, enables the synthesis of high-mode spectral coefficients beyond those collected by the MR scanner. Incorporating these synthesized coefficients in an augmented Fourier partial sum reconstruction allows for the generation of scans with significantly improved effective resolution. Further use of spectral re-projection schemes can result in the elimination of all Gibbs artifacts. Numerical results showing accelerated convergence and improved reconstruction quality will be presented.