{"id":"https://openalex.org/W7160289038","doi":"https://doi.org/10.48550/arxiv.2605.02327","title":"Denoising data using convex relaxations","display_name":"Denoising data using convex relaxations","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160289038","doi":"https://doi.org/10.48550/arxiv.2605.02327"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02327","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02327","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02327","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135323632","display_name":"Charles Fefferman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fefferman, Charles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135294292","display_name":"Aalok Gangopadhyay","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gangopadhyay, Aalok","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135387002","display_name":"Matti Lassas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lassas, Matti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113151502","display_name":"Jonathan Marty","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marty, Jonathan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135327285","display_name":"Hariharan Narayanan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Narayanan, Hariharan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10136","display_name":"Statistical Methods and Inference","score":0.27149999141693115,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.27149999141693115,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.09969999641180038,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.04170000180602074,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/convex-hull","display_name":"Convex hull","score":0.5738000273704529},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5005999803543091},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.48919999599456787},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.4864000082015991},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.4828999936580658},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4821999967098236},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43320000171661377},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4242999851703644},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41370001435279846},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4002000093460083}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7373999953269958},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5738000273704529},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4864000082015991},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43320000171661377},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4194999933242798},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4002000093460083},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3398999869823456},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.33649998903274536},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C27931671","wikidata":"https://www.wikidata.org/wiki/Q7634497","display_name":"Sufficient dimension reduction","level":3,"score":0.33059999346733093},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3264999985694885},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.32019999623298645},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31630000472068787},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.31520000100135803},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2768999934196472},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.2637999951839447},{"id":"https://openalex.org/C194531419","wikidata":"https://www.wikidata.org/wiki/Q17104825","display_name":"Nuisance parameter","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02327","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02327","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02327","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02327","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"We":[0,29,56,115],"study":[1],"the":[2,9,22,45,48,52,72,80,88,95,118,121,138],"problem":[3],"of":[4,51,71,120],"denoising":[5],"observations":[6,46],"\\(Y_i=X_i+Z_i\\),":[7],"where":[8],"latent":[10,54,81],"variables":[11,24],"\\(X_i\\)":[12],"are":[13,26],"sampled":[14],"from":[15,66],"a":[16,31,58,76,124],"low-dimensional":[17],"manifold":[18],"in":[19],"\\(\\mathbb{R}^n\\)":[20],"and":[21,42,90,134,142],"noise":[23],"\\(Z_i\\)":[25],"isotropic":[27],"Gaussian.":[28],"propose":[30],"convex-relaxation":[32],"estimator":[33],"that":[34,61],"first":[35],"reduces":[36],"dimension":[37],"by":[38,129],"principal":[39],"component":[40],"analysis":[41,99],"then":[43],"projects":[44],"onto":[47],"convex":[49,107,113],"hull":[50],"projected":[53],"manifold.":[55],"construct":[57],"statistical":[59],"oracle":[60,89],"estimates":[62,136],"its":[63],"supporting":[64],"hyperplanes":[65],"empirical":[67],"Gaussian":[68],"tail":[69],"probabilities":[70],"noisy":[73],"sample.":[74],"Under":[75],"lower-mass":[77],"condition":[78],"on":[79],"distribution,":[82],"we":[83],"prove":[84],"finite-sample":[85],"guarantees":[86],"for":[87,94,103,112,123,137],"derive":[91],"error":[92],"bounds":[93,102,111],"resulting":[96],"denoiser.":[97],"The":[98],"combines":[100],"risk":[101],"least-squares":[104],"projection":[105],"under":[106],"constraints":[108],"with":[109],"entropy":[110],"hulls.":[114],"also":[116],"verify":[117],"assumptions":[119],"framework":[122],"Cryo-Electron":[125],"Microscopy":[126],"observation":[127],"model":[128],"establishing":[130],"suitable":[131],"covering":[132],"number":[133],"Lipschitz":[135],"associated":[139],"group":[140],"action":[141],"imaging":[143],"operators.":[144]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-06T00:00:00"}
