{"paper":{"title":"Guarantees of Augmented Trace Norm Models in Tensor Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.IT"],"primary_cat":"cs.IT","authors_text":"Ji Li, Jiqing Han, Shiwen Deng, Tieran Zheng, Ziqiang Shi","submitted_at":"2012-07-23T08:59:58Z","abstract_excerpt":"This paper studies the recovery guarantees of the models of minimizing $\\|\\mathcal{X}\\|_*+\\frac{1}{2\\alpha}\\|\\mathcal{X}\\|_F^2$ where $\\mathcal{X}$ is a tensor and $\\|\\mathcal{X}\\|_*$ and $\\|\\mathcal{X}\\|_F$ are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing $\\|\\mathcal{X}\\|_*$ under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor $\\mathcal{X}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5326","kind":"arxiv","version":1},"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"}