Enhanced Detection of Edges in Spectral

Abstract. We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where [f ](x) := f(x+)− f(x−) 6= 0. Our approach is based on two main aspects—localization using appropriate concentration kernels and separation of scales by nonlinear enhancement. To detect such edges, one employs concentration kernels, Kǫ(·), depending on the small scale ǫ. It is shown that odd kernels, properly scaled, and admissible (in the sense of having small W−1,∞moments of order O(ǫ)) satisfy Kǫ ∗ f(x) = [f ](x) + O(ǫ), thus recovering both the location and amplitudes of all edges. As an example we consider general concentration kernels of the formKσ N (t) = ∑