{"paper":{"title":"Error Bounds for Compressed Sensing Algorithms With Group Sparsity: A Unified Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"M. Eren Ahsen, M. Vidyasagar","submitted_at":"2015-12-29T13:10:25Z","abstract_excerpt":"In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\\ell_1$-norm minimization. Upper bounds for the $\\ell_2$- norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\\ell_1$-norm are given in [3]. When the unknown vector is not conventionally sparse but is \"group sparse\" instead, a variety of alternatives to the $\\ell_1$-norm have been proposed in the literature, including the group LASSO, sparse group LASSO, and group LASSO with tree structured o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08673","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"}