{"paper":{"title":"Optimality of Operator-Like Wavelets for Representing Sparse AR(1) Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Michael Unser, Pedram Pad","submitted_at":"2013-12-04T13:10:47Z","abstract_excerpt":"It is known that the Karhunen-Lo\\`{e}ve transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes results in sinusoidal basis functions. The same sinusoidal bases come out of the independent-component analysis (ICA) and actually correspond to processes with completely independent samples. In this paper, we relax the Gaussian hypothesis and study how orthogonal transforms decouple symmetric-alpha-stable (S$\\alpha$S) AR(1) processes. The Gaussian case is not sparse and corresponds to $\\alpha=2$, while $0<\\alpha<2$ yields processes with sparse linear-prediction error. In the prese"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1147","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"}