{"id":"https://openalex.org/W7153323565","doi":"https://doi.org/10.48550/arxiv.2604.08330","title":"Group-invariant moments under tomographic projections","display_name":"Group-invariant moments under tomographic projections","publication_year":2026,"publication_date":"2026-04-09","ids":{"openalex":"https://openalex.org/W7153323565","doi":"https://doi.org/10.48550/arxiv.2604.08330"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.08330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08330","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.08330","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133394895","display_name":"Amnon Balanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Balanov, Amnon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133329699","display_name":"Tamir Bendory","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bendory, Tamir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133316151","display_name":"Dan Edidin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edidin, Dan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.15889999270439148,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.15889999270439148,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.11490000039339066,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.11420000344514847,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.7023000121116638},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6028000116348267},{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.5634999871253967},{"id":"https://openalex.org/keywords/tomographic-reconstruction","display_name":"Tomographic reconstruction","score":0.5195000171661377},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.43810001015663147},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43779999017715454}],"concepts":[{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.7023000121116638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6593999862670898},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6028000116348267},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.5634999871253967},{"id":"https://openalex.org/C97742081","wikidata":"https://www.wikidata.org/wiki/Q7820109","display_name":"Tomographic reconstruction","level":3,"score":0.5195000171661377},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.42489999532699585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42260000109672546},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30809998512268066},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.2761000096797943}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.08330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08330","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.08330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08330","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"$f:\\mathbb{R}^n\\to\\mathbb{R}$":[1],"be":[2],"an":[3,38,76],"unknown":[4],"object,":[5],"and":[6,32,119],"suppose":[7],"the":[8,20,35,50,55,59,69,82,85,94,106,110,128,131,134,139,146],"observations":[9],"are":[10],"tomographic":[11,107],"projections":[12],"of":[13,17,19,54,65,68,133,145],"randomly":[14],"rotated":[15],"copies":[16],"$f$":[18],"form":[21],"$Y":[22],"=":[23],"P(R\\cdot":[24],"f)$,":[25],"where":[26],"$R$":[27],"is":[28,34],"Haar-uniform":[29],"in":[30,127],"$\\mathrm{SO}(n)$":[31],"$P$":[33],"projection":[36,136],"onto":[37],"$m$-dimensional":[39],"subspace,":[40],"so":[41],"that":[42],"$Y:\\mathbb{R}^m\\to\\mathbb{R}$.":[43],"We":[44,73],"prove":[45],"that,":[46],"whenever":[47],"$d\\le":[48],"m$,":[49],"$d$-th":[51,61,99],"order":[52,62,100,141],"moment":[53,64,102,112,144],"projected":[56],"data":[57],"determines":[58,138],"full":[60],"Haar-orbit":[63],"$f$,":[66],"independently":[67],"ambient":[70],"dimension":[71],"$n$.":[72],"further":[74],"provide":[75],"explicit":[77],"algorithmic":[78],"procedure":[79],"for":[80,93,116],"recovering":[81],"latter":[83],"from":[84],"former.":[86],"As":[87],"a":[88,124],"consequence,":[89],"any":[90],"identifiability":[91],"result":[92,122,126],"unprojected":[95],"model":[96],"based":[97],"on":[98],"group-invariant":[101],"extends":[103],"directly":[104],"to":[105],"setting":[108],"at":[109],"same":[111],"order.":[113],"In":[114],"particular,":[115],"$n=3$,":[117],"$m=2$,":[118],"$d=2$,":[120],"our":[121],"recovers":[123],"classical":[125],"cryo-EM":[129],"literature:":[130],"covariance":[132],"2D":[135],"images":[137],"second":[140],"rotationally":[142],"invariant":[143],"underlying":[147],"3D":[148],"object.":[149]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-11T00:00:00"}