{"paper":{"title":"Bilinear Recovery using Adaptive Vector-AMP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alyson K. Fletcher, Philip Schniter, Subrata Sarkar, Sundeep Rangan","submitted_at":"2018-08-31T18:54:21Z","abstract_excerpt":"We consider the problem of jointly recovering the vector $\\boldsymbol{b}$ and the matrix $\\boldsymbol{C}$ from noisy measurements $\\boldsymbol{Y} = \\boldsymbol{A}(\\boldsymbol{b})\\boldsymbol{C} + \\boldsymbol{W}$, where $\\boldsymbol{A}(\\cdot)$ is a known affine linear function of $\\boldsymbol{b}$ (i.e., $\\boldsymbol{A}(\\boldsymbol{b})=\\boldsymbol{A}_0+\\sum_{i=1}^Q b_i \\boldsymbol{A}_i$ with known matrices $\\boldsymbol{A}_i$). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00024","kind":"arxiv","version":2},"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"}