Recovering Exponential Accuracy from Non-harmonic Fourier Data Through Spectral Reprojection

Spectral reprojection techniques make possible the recovery of exponential accuracy from the partial Fourier sum of a piecewise-analytic function, essentially conquering the Gibbs phenomenon for this class of functions. This paper extends this result to non-harmonic partial sums, proving that spectral reprojection can reduce the Gibbs phenomenon in nonharmonic reconstruction as well as remove reconstruction artifacts due to erratic sampling. We are particularly interested in the case where the Fourier samples form a frame. These techniques are motivated by a desire to improve the quality of images reconstructed from non-uniform Fourier data, such as magnetic resonance (MR) images.