Speaker

Prof. Anne Gelb

Title

"Edge detection: Reconstruction of piecewise smooth functions from their spectral data"

Abstract

Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a-priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurate results with high resolution near the discontinuities. Hence detection of the jump discontinuities is critical for all methods.

A new localized reconstruction method is formulated incorporating the detection of edges and a localized reconstruction technique. The method is robust and highly accurate, yielding spectral accuracy up to a small neighborhood of the jump discontinuities. Results are shown in one and two dimensions. Current investigation of a method yielding spectral accuracy up to the jump discontinuities are also discussed.