{"paper":{"title":"Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Canyi Lu, Jiashi Feng, Shuicheng Yan, Wei Liu, Yudong Chen, Zhouchen Lin","submitted_at":"2017-08-14T15:42:05Z","abstract_excerpt":"This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin 2011) and its induced tensor tubal rank and tensor nuclear norm. Consider that we have a 3-way tensor ${\\mathcal{X}}\\in\\mathbb{R}^{n_1\\times n_2\\times n_3}$ such that ${\\mathcal{X}}={\\mathcal{L}}_0+{\\mathcal{E}}_0$, where ${\\mathcal{L}}_0$ has low tubal rank and ${\\mathcal{E}}_0$ is sparse. Is that possible to recover both components? In this work, we prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04181","kind":"arxiv","version":3},"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"}