{"ID":2893654,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13480","arxiv_id":"2507.13480","title":"Multiresolution local smoothness detection in non-uniformly sampled multivariate signals","abstract":"Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity within the framework of microlocal spaces introduced by Jaffard. The central tool in our analysis is the fast samplet transform, a distributional wavelet transform tailored to scattered data. We establish a connection between the decay of samplet coefficients and the pointwise regularity of multivariate signals. As a by product, we derive decay estimates for functions belonging to classical Hölder spaces and Sobolev-Slobodeckij spaces. While traditional wavelets are effective for regularity detection in low-dimensional structured data, samplets demonstrate robust performance even for higher dimensional and scattered data. To illustrate our theoretical findings, we present extensive numerical studies detecting local regularity of one-, two- and three-dimensional signals, ranging from non-uniformly sampled time series over image segmentation to edge detection in point clouds.","short_abstract":"Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity within the framework of microlocal spaces introduced by Jaffard. The central to...","url_abs":"https://arxiv.org/abs/2507.13480","url_pdf":"https://arxiv.org/pdf/2507.13480v1","authors":"[\"Sara Avesani\",\"Gianluca Giacchi\",\"Michael Multerer\"]","published":"2025-07-17T18:46:01Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.CV\",\"cs.LG\"]","methods":"[]","has_code":false}