{"id":"https://openalex.org/W3011389392","doi":"https://doi.org/10.1137/20m1326246","title":"Sparsity Promoting Hybrid Solvers for Hierarchical Bayesian Inverse Problems","display_name":"Sparsity Promoting Hybrid Solvers for Hierarchical Bayesian Inverse Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3011389392","doi":"https://doi.org/10.1137/20m1326246","mag":"3011389392"},"language":"en","primary_location":{"id":"doi:10.1137/20m1326246","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1326246","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.06532","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090411877","display_name":"Daniela Calvetti","orcid":"https://orcid.org/0000-0001-5696-718X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniela Calvetti","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5696-718X","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003447883","display_name":"Monica Pragliola","orcid":"https://orcid.org/0000-0002-3074-1550"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Monica Pragliola","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062429950","display_name":"Erkki Somersalo","orcid":"https://orcid.org/0000-0001-5099-3512"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erkki Somersalo","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5099-3512","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1801,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.43980974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"42","issue":"6","first_page":"A3761","last_page":"A3784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9979000091552734,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.5952427983283997},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.5947946906089783},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5366854667663574},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.524029552936554},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.521623969078064},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4558809995651245},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4543856382369995},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.4401557445526123},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4364883303642273},{"id":"https://openalex.org/keywords/gibbs-sampling","display_name":"Gibbs sampling","score":0.43586987257003784},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37717029452323914},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35124170780181885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5952427983283997},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5947946906089783},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5366854667663574},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.524029552936554},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.521623969078064},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4558809995651245},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4543856382369995},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.4401557445526123},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4364883303642273},{"id":"https://openalex.org/C158424031","wikidata":"https://www.wikidata.org/wiki/Q1191905","display_name":"Gibbs sampling","level":3,"score":0.43586987257003784},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37717029452323914},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35124170780181885},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1326246","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1326246","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.06532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.06532","pdf_url":"https://arxiv.org/pdf/2003.06532","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3011389392","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.06532.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.06532","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.06532","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":"pmh:oai:arXiv.org:2003.06532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.06532","pdf_url":"https://arxiv.org/pdf/2003.06532","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.8799999952316284,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G3985315924","display_name":null,"funder_award_id":"DMS-1522334","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4599484382","display_name":null,"funder_award_id":"DMS-1714617","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W572586305","https://openalex.org/W1531455566","https://openalex.org/W1976709621","https://openalex.org/W1999092643","https://openalex.org/W2000384178","https://openalex.org/W2000688949","https://openalex.org/W2005876975","https://openalex.org/W2050834445","https://openalex.org/W2097323375","https://openalex.org/W2119883478","https://openalex.org/W2122315118","https://openalex.org/W2129131372","https://openalex.org/W2142940228","https://openalex.org/W2164278908","https://openalex.org/W2164289056","https://openalex.org/W2164452299","https://openalex.org/W2166087152","https://openalex.org/W2291795049","https://openalex.org/W2332990274","https://openalex.org/W2560042709","https://openalex.org/W2767142010","https://openalex.org/W2789408438","https://openalex.org/W2799274016","https://openalex.org/W2910526316","https://openalex.org/W2980939245","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W2910526316","https://openalex.org/W2574317185","https://openalex.org/W2962794632","https://openalex.org/W2899782288","https://openalex.org/W2125448670","https://openalex.org/W2950038553","https://openalex.org/W2952653535","https://openalex.org/W2414029883","https://openalex.org/W3214073196","https://openalex.org/W1543618960","https://openalex.org/W2233806934","https://openalex.org/W3123458303","https://openalex.org/W2954428299","https://openalex.org/W2313588640","https://openalex.org/W2792925054","https://openalex.org/W2766880757","https://openalex.org/W2999664547","https://openalex.org/W3037347970","https://openalex.org/W3012247396","https://openalex.org/W14625021"],"abstract_inverted_index":{"The":[0,69,159,226],"recovery":[1],"of":[2,23,31,39,89,118,177,210,228],"sparse":[3],"generative":[4],"models":[5,61,126],"from":[6],"few":[7],"noisy":[8],"measurements":[9],"is":[10,74,82,174,232],"an":[11],"important":[12],"and":[13,35,53,66,78,109,214],"challenging":[14],"problem.":[15],"Many":[16],"deterministic":[17],"algorithms":[18,194,231],"rely":[19],"on":[20],"some":[21,145],"form":[22],"$\\ell_1$-$\\ell_2$":[24],"minimization":[25],"to":[26,127,205],"combine":[27],"the":[28,32,36,40,47,83,90,97,119,148,164,175,182,198,211,229],"computational":[29,54],"convenience":[30],"$\\ell_2$":[33],"penalty":[34],"sparsity":[37,51,123,173,223],"promotion":[38,52],"$\\ell_1$.":[41],"It":[42],"was":[43],"recently":[44],"shown":[45],"within":[46],"Bayesian":[48],"framework":[49],"that":[50,170,195,221],"efficiency":[55],"can":[56,92,140],"be":[57,93],"attained":[58],"with":[59,62,96,202,234],"hierarchical":[60,125],"conditionally":[63],"Gaussian":[64],"priors":[65],"gamma":[67,130,203,219],"hyperpriors.":[68],"related":[70],"Gibbs":[71,136],"energy":[72,137],"function":[73],"a":[75,85,128,186,208,217],"convex":[76,135],"functional,":[77],"its":[79],"minimizer,":[80,189],"which":[81],"maximum":[84],"posteriori":[86],"(MAP)":[87],"estimate":[88],"posterior,":[91],"computed":[94,235],"efficiently":[95],"globally":[98,134],"convergent":[99],"Iterated":[100],"Alternating":[101],"Sequential":[102],"(IAS)":[103],"algorithm":[104],"[D.":[105,150],"Calvetti,":[106],"E.":[107],"Somersalo,":[108],"A.":[110],"Strang,":[111],"Inverse":[112,154],"Problems,":[113,155],"35":[114],"(2019),":[115],"035003].":[116],"Generalization":[117],"hyperpriors":[120,169,204],"for":[121,144,147,167],"these":[122],"promoting":[124],"generalized":[129,218],"family":[131],"either":[132],"yield":[133],"functionals":[138],"or":[139],"exhibit":[141],"local":[142,178,188],"convexity":[143],"choices":[146],"hyperparameters":[149],"Calvetti":[151],"et":[152],"al.,":[153],"36":[156],"(2020),":[157],"025010].":[158],"main":[160],"problem":[161],"in":[162,207],"computing":[163],"MAP":[165],"solution":[166],"greedy":[168],"strongly":[171],"promote":[172],"presence":[176],"minima.":[179],"To":[180],"overcome":[181],"premature":[183],"stopping":[184],"at":[185],"spurious":[187],"we":[190],"propose":[191],"two":[192,230],"hybrid":[193],"first":[196],"exploit":[197],"global":[199],"convergence":[200],"associated":[201],"arrive":[206],"neighborhood":[209],"unique":[212],"minimizer":[213],"then":[215],"adopt":[216],"hyperprior":[220],"promotes":[222],"more":[224],"strongly.":[225],"performance":[227],"illustrated":[233],"examples.":[236]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}