Convergence of level sets in fractional Laplacian regularization

Abstract The use of the fractional Laplacian in image denoising and regularization inverse problems has enjoyed a recent surge popularity, since for discontinuous functions it can behave less aggressively than methods based on H 1 norms, while being linear computable with fast spectral numerical methods. In this work, we examine regularized vanishing noise parameter regime. clean data is assumed piecewise constant first case, continuous satisfying source condition second. these settings, prove results convergence level set boundaries respect to Hausdorff distance, additionally rates case indicatrix data. main technical tool purpose family barriers constructed by Savin Valdinoci studying Allen–Cahn equation. To help put context, comparisons total variation classical are provided throughout.