{"paper":{"title":"A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Martin Vetterli, Robin Scheibler, Saeid Haghighatshoar","submitted_at":"2013-10-07T14:46:51Z","abstract_excerpt":"A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^\\alpha)$, scales sub-linearly in $N$ for some $0 < \\alpha < 1$. Assuming a random support model for the non-zero transform domain components, the algorithm reconstructs the WHT of the signal with a sample complexity $O(K \\log_2(\\frac{N}{K}))$, a computational complexity $O(K\\log_2(K)\\log_2(\\frac{N}{K}))$ and with a very high probability asymptotically tending to 1.\n  The approach is based on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1803","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"}