Iterative spectral mollification and conjugation for successive edge detection

Abstract

Fourier concentration method is a well-established method for finding edges given a set of truncated Fourier data. However, it is hard to distinguish weak jumps from the Gibbs oscillations with the method unless the concentration is highly refined locally. In this note, we show that it is possible to find all edges whether strong or weak by using the method iteratively. The iterative method first finds strong edges followed by an iterative procedure in which previously found edges are smoothed by local adaptive mollifier. The iterative method is advantageous when the ratio of the largest to smallest jump magnitudes is significantly large.