{"paper":{"title":"Enhanced image approximation using shifted rank-1 reconstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Florian Bo{\\ss}mann, Jianwei Ma","submitted_at":"2018-10-03T10:42:28Z","abstract_excerpt":"Low rank approximation has been extensively studied in the past. It is most suitable to reproduce rectangular like structures in the data. In this work we introduce a generalization using shifted rank-1 matrices to approximate $A\\in\\mathbb{C}^{M\\times N}$. These matrices are of the form $S_{\\lambda}(uv^*)$ where $u\\in\\mathbb{C}^M$, $v\\in\\mathbb{C}^N$ and $\\lambda\\in\\mathbb{Z}^N$.The operator $S_{\\lambda}$ circularly shifts the k-th column of $uv^*$ by $\\lambda_k$. These kind of shifts naturally appear in applications, where an object $u$ is observed in $N$ measurements at different positions i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01681","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"}