{"paper":{"title":"Convergence of the Generalized Alternating Projection Algorithm for Compressive Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","stat.AP"],"primary_cat":"cs.IT","authors_text":"Hong Jiang, Paul Wilford, Xin Yuan","submitted_at":"2015-09-04T21:15:44Z","abstract_excerpt":"The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem $\\yv = \\Amat \\xv + \\epsilonv$. By assuming that $\\Amat\\Amat\\ts$ is invertible, we prove that GAP converges linearly within a certain range of step-size when the sensing matrix $\\Amat$ satisfies restricted isometry property (RIP) condition of $\\delta_{2K}$, where $K$ is the sparsity of $\\xv$. The theoretical analysis is extended to the adaptively iterative thresholding (AIT) algorithms, for which the convergence rate is also derived based on $\\delta_{2K}$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06253","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"}