{"paper":{"title":"Measure-Valued Variational Models with Applications to Diffusion-Weighted Imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jan Lellmann, Thomas Vogt","submitted_at":"2017-10-02T17:11:26Z","abstract_excerpt":"We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation seminorm for functions taking values in a Banach space. The seminorm penalizes jumps and is rotationally invariant under certain conditions. We prove existence of a minimizer for a class of variational problems based on this formulation of total variation, and provide an example where uniqueness fails to hold. Employing the Kan\\-torovich-Rubinstein transport norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00798","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}