{"paper":{"title":"Hierarchical restricted isometry property for Kronecker product measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"A. Flinth, G. Wunder, I. Roth, J. Eisert, R. Kueng","submitted_at":"2018-01-31T13:03:18Z","abstract_excerpt":"Hierarchically sparse signals and Kronecker product structured measurements arise naturally in a variety of applications. The simplest example of a hierarchical sparsity structure is two-level $(s,\\sigma)$-hierarchical sparsity which features $s$-block-sparse signals with $\\sigma$-sparse blocks. For a large class of algorithms recovery guarantees can be derived based on the restricted isometry property (RIP) of the measurement matrix and model-based variants thereof. We show that given two matrices $\\mathbf{A}$ and $\\mathbf{B}$ having the standard $s$-sparse and $\\sigma$-sparse RIP their Krone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10433","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"}