{"id":"https://openalex.org/W7214704750","doi":"https://doi.org/10.48550/arxiv.2609.33024","title":"Spherical ESPRIT by Paired Small Circles and Infinitesimal Rotations","display_name":"Spherical ESPRIT by Paired Small Circles and Infinitesimal Rotations","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214704750","doi":"https://doi.org/10.48550/arxiv.2609.33024"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33024","pdf_url":"https://arxiv.org/pdf/2609.33024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.33024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048863527","display_name":"Albert Fannjiang","orcid":"https://orcid.org/0000-0003-3150-7392","observed_orcids":["https://orcid.org/0000-0003-3150-7392"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fannjiang, Albert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048863527"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.6220999956130981,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.6220999956130981,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.13819999992847443,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.09679999947547913,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/infinitesimal-rotations","display_name":"infinitesimal rotations","score":0.7170000076293945},{"id":"https://openalex.org/keywords/angular-derivative","display_name":"angular derivative","score":0.7310000061988831},{"id":"https://openalex.org/keywords/identifiability","display_name":"identifiability","score":0.6840000152587891},{"id":"https://openalex.org/keywords/perturbation-bounds","display_name":"perturbation bounds","score":0.746999979019165},{"id":"https://openalex.org/keywords/bias-assessment","display_name":"bias assessment","score":0.38199999928474426},{"id":"https://openalex.org/keywords/spherical-signal-processing","display_name":"spherical signal processing","score":0.35100001096725464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7239999771118164},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6359999775886536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.588699996471405},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.41130000352859497},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.38420000672340393},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.3813999891281128},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.3472000062465668},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2597000002861023},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33024","pdf_url":"https://arxiv.org/pdf/2609.33024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.33024","doi":"https://doi.org/10.48550/arxiv.2609.33024","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.33024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33024","pdf_url":"https://arxiv.org/pdf/2609.33024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214704750.pdf","grobid_xml":"https://content.openalex.org/works/W7214704750.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7208838800","https://openalex.org/W4294643313","https://openalex.org/W2335004627","https://openalex.org/W3090899662","https://openalex.org/W7036812751","https://openalex.org/W2508934708","https://openalex.org/W3011667268","https://openalex.org/W2133954120","https://openalex.org/W2123933039","https://openalex.org/W2144095442"],"abstract_inverted_index":{"We":[0,62,102],"study":[1],"the":[2,34,40,45,65,83,90,112,125,135,144,162,187],"recovery":[3],"of":[4,111],"a":[5,17,58,105,116,131,168,196],"finite":[6,28,53,96],"three-dimensional":[7],"point":[8,74,181],"cloud":[9,75],"from":[10,57,155],"its":[11],"spherical":[12],"Fourier":[13],"signal":[14],"subspace":[15],"at":[16,172],"fixed":[18,173],"wavenumber.":[19],"Two":[20],"ESPRIT":[21],"constructions":[22,189],"are":[23],"analyzed.":[24],"The":[25,109],"first":[26],"uses":[27,36],"shifts":[29],"between":[30],"paired":[31],"small":[32],"circles;":[33],"second":[35],"angular":[37],"derivatives":[38],"on":[39,179],"whole":[41],"sphere.":[42],"Both":[43],"recover":[44,152],"same":[46],"commuting":[47],"coordinate":[48,113],"matrices,":[49],"either":[50],"through":[51],"their":[52,153,191],"exponentials":[54],"or":[55],"directly":[56],"coupled":[59],"linear":[60],"system.":[61],"prove":[63],"that":[64,77,124],"continuous":[66],"generator":[67,127,145],"system":[68],"is":[69,115,165,176],"injective":[70],"for":[71,167,195],"every":[72],"distinct":[73],"and":[76,151,190],"one":[78],"guard":[79],"harmonic":[80],"degree":[81],"preserves":[82],"retained":[84],"equations":[85],"exactly.":[86],"For":[87],"$s$":[88],"targets,":[89],"cutoff":[91],"$K\\ge":[92],"s$":[93],"gives":[94],"generic":[95],"identifiability,":[97],"but":[98],"not":[99],"uniform":[100],"conditioning.":[101],"also":[103],"derive":[104],"finite-cutoff":[106],"perturbation":[107,121],"bound.":[108],"accuracy":[110],"estimates":[114],"separate":[117,148],"issue.":[118],"A":[119],"one-target":[120],"calculation":[122],"shows":[123],"original":[126],"estimate":[128],"can":[129],"retain":[130],"nonzero":[132],"bias":[133],"as":[134,193],"wavenumber":[136],"increases.":[137],"To":[138],"address":[139],"this":[140],"bias,":[141],"we":[142],"use":[143,192],"eigenbasis":[146],"to":[147],"approximate":[149],"atoms":[150],"locations":[154],"amplitude-normalized":[156],"phases.":[157],"Under":[158],"pointwise":[159],"atom":[160],"dominance,":[161],"resulting":[163],"error":[164],"$O(\u03ba^{-1})$;":[166],"dominant":[169],"two-atom":[170],"mixture":[171],"separation,":[174],"it":[175],"$O(\u03ba^{-2})$.":[177],"Experiments":[178],"structured":[180],"clouds":[182],"with":[183],"smooth":[184],"perturbations":[185],"compare":[186],"two":[188],"initializers":[194],"common":[197],"MUSIC":[198],"refinement.":[199]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-30T00:00:00"}
