{"id":"https://openalex.org/W2062943478","doi":"https://doi.org/10.1137/11085760x","title":"MCMC-Based Image Reconstruction with Uncertainty Quantification","display_name":"MCMC-Based Image Reconstruction with Uncertainty Quantification","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2062943478","doi":"https://doi.org/10.1137/11085760x","mag":"2062943478"},"language":"en","primary_location":{"id":"doi:10.1137/11085760x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11085760x","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010944499","display_name":"Johnathan M. Bardsley","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Johnathan M. Bardsley","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010944499"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.05,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.93859311,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"34","issue":"3","first_page":"A1316","last_page":"A1332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9921000003814697,"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":0.9921000003814697,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9873999953269958,"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/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.7203425168991089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7139042019844055},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.6565556526184082},{"id":"https://openalex.org/keywords/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.5158335566520691},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.49291086196899414},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.46726030111312866},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46677345037460327},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4367888569831848},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.4261452853679657},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3935502767562866},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.39007097482681274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3865513205528259},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.31053900718688965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22411876916885376},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21047568321228027},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10670667886734009}],"concepts":[{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.7203425168991089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7139042019844055},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.6565556526184082},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.5158335566520691},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.49291086196899414},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.46726030111312866},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46677345037460327},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4367888569831848},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.4261452853679657},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3935502767562866},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.39007097482681274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3865513205528259},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31053900718688965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22411876916885376},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21047568321228027},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10670667886734009},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/11085760x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11085760x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1963643305","https://openalex.org/W1976484026","https://openalex.org/W1988848921","https://openalex.org/W2037277678","https://openalex.org/W2041717489","https://openalex.org/W2049882758","https://openalex.org/W2070051828","https://openalex.org/W2071706611","https://openalex.org/W2081774672","https://openalex.org/W2085346773","https://openalex.org/W2114220616","https://openalex.org/W2114424556","https://openalex.org/W2121402967","https://openalex.org/W2140054106","https://openalex.org/W2143909904","https://openalex.org/W2149498546","https://openalex.org/W2165715950","https://openalex.org/W2170164530","https://openalex.org/W2963777151","https://openalex.org/W4230320149"],"related_works":["https://openalex.org/W1839961359","https://openalex.org/W2749105521","https://openalex.org/W2360343897","https://openalex.org/W140737605","https://openalex.org/W2075146114","https://openalex.org/W2564453433","https://openalex.org/W3188213007","https://openalex.org/W2374214022","https://openalex.org/W1947575127","https://openalex.org/W2029137001"],"abstract_inverted_index":{"The":[0],"connection":[1],"between":[2],"Bayesian":[3,158],"statistics":[4,159],"and":[5,62,123,165,172,211,229,234,256,259,268],"the":[6,40,45,48,52,57,60,63,68,71,77,84,95,103,119,132,137,157,176,184,203,209,236,264],"technique":[7],"of":[8,34,47,59,70,83,94,105,110,124,134,169,208],"regularization":[9,32,41,218],"for":[10,30,107,175],"inverse":[11,120],"problems":[12,121],"has":[13,100,153],"been":[14],"given":[15],"significant":[16],"attention":[17],"in":[18,87,97,118,128,156,193,273],"recent":[19],"years.":[20],"For":[21,244],"example,":[22],"Bayes'":[23],"law":[24],"is":[25,90,131,161,266],"frequently":[26],"used":[27],"as":[28,76],"motivation":[29],"variational":[31],"methods":[33,197],"Tikhonov":[35],"type.":[36],"In":[37],"this":[38,98,129],"setting,":[39],"function":[42,54],"corresponds":[43,55,66],"to":[44,56,67,126,163,182,189],"negative-log":[46,58],"prior":[49,212,237],"probability":[50],"density;":[51],"fit-to-data":[53],"likelihood;":[61],"regularized":[64,114],"solution":[65],"maximizer":[69],"posterior":[72,138],"density":[73],"function,":[74],"known":[75],"maximum":[78],"a":[79,145,167,239],"posteriori":[80],"(MAP)":[81],"estimator":[82],"unknown,":[85],"which":[86,152,216],"our":[88,245,260],"case":[89],"an":[91],"image.":[92],"Much":[93],"work":[96],"direction":[99],"focused":[101],"on":[102,224],"development":[104],"techniques":[106],"efficient":[108],"computation":[109],"MAP":[111],"estimators":[112],"(or":[113],"solutions).":[115],"Less":[116],"explored":[117],"community,":[122],"interest":[125],"us":[127],"paper,":[130],"problem":[133],"sampling":[135],"from":[136,252],"density.":[139],"To":[140],"do":[141],"this,":[142],"we":[143,179,248],"use":[144,183],"Markov":[146,241],"chain":[147],"Monte":[148],"Carlo":[149],"(MCMC)":[150],"method,":[151],"previously":[154],"appeared":[155],"literature,":[160],"straightforward":[162],"implement,":[164],"provides":[166,206],"means":[168],"both":[170,253],"estimation":[171],"uncertainty":[173],"quantification":[174],"unknown.":[177],"Additionally,":[178],"show":[180,262],"how":[181],"preconditioned":[185],"conjugate":[186],"gradient":[187],"method":[188,205],"compute":[190],"image":[191,254],"samples":[192,207],"cases":[194,251],"where":[195],"direct":[196],"are":[198],"not":[199],"feasible.":[200],"And":[201],"finally,":[202],"MCMC":[204],"noise":[210,233],"precision":[213],"(inverse-variance)":[214],"parameters,":[215],"makes":[217],"parameter":[219],"selection":[220],"unnecessary.":[221],"We":[222],"focus":[223],"linear":[225],"models":[226],"with":[227],"independent":[228],"identically":[230],"distributed":[231],"Gaussian":[232,240],"define":[235],"using":[238],"random":[242],"field.":[243],"numerical":[246],"experiments,":[247],"consider":[249],"test":[250],"deconvolution":[255],"computed":[257],"tomography,":[258],"results":[261],"that":[263],"approach":[265],"effective":[267],"surprisingly":[269],"computationally":[270],"efficient,":[271],"even":[272],"large-scale":[274],"cases.":[275]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}