February Fourier Talks 2007

Detecting jump discontinuities given Fourier data

In a few important applications, sensor data are collected in the form of Fourier coefficients and it is desirable to determine the locations of discontinuities in the corresponding temporal or spatial signal. This presentation will begin with a summary of an approach developed by Gelb and Tadmor in a deterministic setting. Then, a statistical characterization of this approach will be introduced that leads to a detector with quantifiable performance in the presence of noise.