{"doi":"10.1093/imaiai/iaab003","title":"Super-resolution multi-reference alignment","abstract":"Abstract We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled and noisy observations. We focus on the low SNR regime, and show that a signal in ${\\mathbb{R}}^M$ is uniquely determined when the number $L$ of samples per observation is of the order of the square root of the signal’s length ($L=O(\\sqrt{M})$). Phrased more informally, one can square the resolution. This result holds if the number of observations is proportional to $1/\\textrm{SNR}^3$. In contrast, with fewer observations recovery is impossible even when the observations are not down-sampled ($L=M$). The analysis combines tools from statistical signal processing and invariant theory. We design an expectation-maximization algorithm and demonstrate that it can super-resolve the signal in challenging SNR regimes.","journal":"Information and Inference A Journal of the IMA","year":2021,"id":207184,"datarank":0.24141568686511508,"base_score":1.6094379124341003,"endowment":1.6094379124341003,"self_citation_contribution":0.24141568686511508,"citation_network_contribution":0.0,"self_endowment_contribution":0.24141568686511508,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":4,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.96,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":461170,"name":"Ariel Jaffe","orcid":"0000-0001-7637-7128","position":1,"is_corresponding":false},{"id":792269,"name":"William Leeb","orcid":"0000-0002-8617-3548","position":2,"is_corresponding":false},{"id":792270,"name":"Nir Sharon","orcid":"0000-0001-6329-3857","position":3,"is_corresponding":false},{"id":285325,"name":"Amit Singer","orcid":"0000-0002-6975-7955","position":4,"is_corresponding":false},{"id":792268,"name":"Tamir Bendory","orcid":"0000-0003-2373-9388","position":0,"is_corresponding":true}],"reference_count":75,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-07-18T23:51:45.688025Z","pmid":"35966813","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}