Edge Detection from Two-Dimensional Fourier Data using Gaussian Mollifiers

This paper discusses the detection of edges from two-dimensional truncated Fourier spectral data. Compared to edge detection from pixel data, this is a more challenging problem since we seek accurate local information from a small number of often noisy global measurements. We propose a highly effective algorithm using a specific class of spectral mollifiers which converges uniformly to sharp peaks along the singular support of the function. We provide theoretical guarantees and numerical simulations to show that the resulting edge map is free of spurious edges and oscillations.