{"id":"https://openalex.org/W2761037628","doi":"https://doi.org/10.1109/tmi.2017.2760104","title":"A Direct Algorithm for Optimization Problems With the Huber Penalty","display_name":"A Direct Algorithm for Optimization Problems With the Huber Penalty","publication_year":2017,"publication_date":"2017-10-05","ids":{"openalex":"https://openalex.org/W2761037628","doi":"https://doi.org/10.1109/tmi.2017.2760104","mag":"2761037628","pmid":"https://pubmed.ncbi.nlm.nih.gov/28981412"},"language":"en","primary_location":{"id":"doi:10.1109/tmi.2017.2760104","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmi.2017.2760104","pdf_url":null,"source":{"id":"https://openalex.org/S58069681","display_name":"IEEE Transactions on Medical Imaging","issn_l":"0278-0062","issn":["0278-0062","1558-254X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Medical Imaging","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5779867","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060560582","display_name":"Jingyan Xu","orcid":"https://orcid.org/0000-0003-3047-8198"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jingyan Xu","raw_affiliation_strings":["Division of Medical Imaging Physics, Johns Hopkins University, Baltimore, MD, USA"],"raw_orcid":"https://orcid.org/0000-0003-3047-8198","affiliations":[{"raw_affiliation_string":"Division of Medical Imaging Physics, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014058139","display_name":"Fr\u00e9d\u00e9ric Noo","orcid":"https://orcid.org/0000-0002-5417-3439"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frederic Noo","raw_affiliation_strings":["Department of Radiology and Imaging Sciences, The University of Utah, Salt Lake City, UT, USA"],"raw_orcid":"https://orcid.org/0000-0002-5417-3439","affiliations":[{"raw_affiliation_string":"Department of Radiology and Imaging Sciences, The University of Utah, Salt Lake City, UT, USA","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034237477","display_name":"B.M.W. Tsui","orcid":"https://orcid.org/0000-0001-7928-5093"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin M. W. Tsui","raw_affiliation_strings":["Division of Medical Imaging Physics, Johns Hopkins University, Baltimore, MD, USA"],"raw_orcid":"https://orcid.org/0000-0001-7928-5093","affiliations":[{"raw_affiliation_string":"Division of Medical Imaging Physics, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4387,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.6744631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"162","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9998999834060669,"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/T12386","display_name":"Advanced X-ray and CT Imaging","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9966999888420105,"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/smoothing","display_name":"Smoothing","score":0.6498548984527588},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6254510879516602},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.623672604560852},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4932333827018738},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.492180734872818},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.489238977432251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4679478704929352},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.46636566519737244},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.45612066984176636},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.421896755695343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40295666456222534},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.12724894285202026},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.10092827677726746},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.07959243655204773}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6498548984527588},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6254510879516602},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.623672604560852},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4932333827018738},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.492180734872818},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.489238977432251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4679478704929352},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.46636566519737244},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.45612066984176636},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.421896755695343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40295666456222534},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.12724894285202026},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.10092827677726746},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.07959243655204773},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[{"descriptor_ui":"D000005","descriptor_name":"Abdomen","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D000005","descriptor_name":"Abdomen","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D000005","descriptor_name":"Abdomen","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019047","descriptor_name":"Phantoms, Imaging","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019047","descriptor_name":"Phantoms, Imaging","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019047","descriptor_name":"Phantoms, Imaging","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":4,"locations":[{"id":"doi:10.1109/tmi.2017.2760104","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmi.2017.2760104","pdf_url":null,"source":{"id":"https://openalex.org/S58069681","display_name":"IEEE Transactions on Medical Imaging","issn_l":"0278-0062","issn":["0278-0062","1558-254X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Medical Imaging","raw_type":"journal-article"},{"id":"pmid:28981412","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28981412","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on medical imaging","raw_type":null},{"id":"pmh:oai:europepmc.org:5283759","is_oa":false,"landing_page_url":"http://europepmc.org/pmc/articles/PMC5779867","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:5779867","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5779867","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Med Imaging","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:5779867","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5779867","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Med Imaging","raw_type":"Text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G8670718222","display_name":null,"funder_award_id":"R21CA211035","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"}],"funders":[{"id":"https://openalex.org/F4320310050","display_name":"University of Utah","ror":"https://ror.org/03r0ha626"},{"id":"https://openalex.org/F4320322923","display_name":"Siemens","ror":"https://ror.org/059mq0909"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337351","display_name":"National Cancer Institute","ror":"https://ror.org/040gcmg81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W192531571","https://openalex.org/W1494141862","https://openalex.org/W1980516134","https://openalex.org/W1987026656","https://openalex.org/W1997910206","https://openalex.org/W1999614991","https://openalex.org/W2000769684","https://openalex.org/W2008257035","https://openalex.org/W2013850411","https://openalex.org/W2014265988","https://openalex.org/W2024849317","https://openalex.org/W2025289780","https://openalex.org/W2041245290","https://openalex.org/W2050023599","https://openalex.org/W2052547439","https://openalex.org/W2070678378","https://openalex.org/W2075014097","https://openalex.org/W2082709304","https://openalex.org/W2092663520","https://openalex.org/W2098713549","https://openalex.org/W2100556411","https://openalex.org/W2108807480","https://openalex.org/W2131437840","https://openalex.org/W2138144773","https://openalex.org/W2162641328","https://openalex.org/W2167732364","https://openalex.org/W2327724807","https://openalex.org/W2913535645","https://openalex.org/W2936995161","https://openalex.org/W4210470138","https://openalex.org/W4244393449","https://openalex.org/W4249513058","https://openalex.org/W4250589301","https://openalex.org/W4253190278","https://openalex.org/W4300448178","https://openalex.org/W6663026575","https://openalex.org/W6676137660","https://openalex.org/W6679553865","https://openalex.org/W6761030284"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W1993992974","https://openalex.org/W1512294453","https://openalex.org/W2738234280","https://openalex.org/W2550734047","https://openalex.org/W2911841387","https://openalex.org/W2341571017","https://openalex.org/W2152043249"],"abstract_inverted_index":{"We":[0,274],"present":[1],"a":[2,50,75,222,252],"direct":[3,68,152,170,215,247],"(noniterative)":[4],"algorithm":[5,24,153,171,216,248],"for":[6,53,81,144,285],"1-D":[7,26,163,280],"quadratic":[8],"data":[9,41,88],"fitting":[10],"with":[11,174,228,267],"neighboring":[12],"intensity":[13],"differences":[14],"penalized":[15],"by":[16,100,221],"the":[17,67,85,93,101,109,115,121,151,160,166,169,178,201,204,207,214,229,232,246,278],"Huber":[18,233],"function.":[19,234],"Applications":[20],"of":[21,28,34,77,87,162,168,231,245,255],"such":[22,31],"an":[23,189],"include":[25],"processing":[27],"medical":[29],"signals,":[30],"as":[32,49,74],"smoothing":[33,140],"tissue":[35,137],"time":[36],"concentration":[37,138],"curves":[38],"in":[39,120,132,271],"kinetic":[40],"analysis":[42],"or":[43,55],"sinogram":[44,142,238],"preprocessing,":[45,239],"and":[46,59,127,141,154,188,243,258,261],"using":[47,123],"it":[48],"subproblem":[51],"solver":[52,281],"2-D":[54],"3-D":[56],"image":[57,145],"restoration":[58],"reconstruction.":[60],"dynamic":[61],"programming":[62],"was":[63,72],"used":[64,148,284],"to":[65,92,117,149,200,206],"develop":[66],"algorithm.":[69],"The":[70,90,194,210,235],"problem":[71,95,112,119],"reformulated":[73],"sequence":[76,122],"univariate":[78,94,110],"optimization":[79,111],"problems,":[80],",":[82,104],"where":[83],"is":[84,98,172],"number":[86],"points.":[89],"solution":[91,102,116],"at":[96,103,106,113],"index":[97],"parameterized":[99],"except":[105],".":[107],"Solving":[108],"yields":[114],"each":[118],"back-tracking.":[124],"Computational":[125],"issues":[126],"memory":[128],"cost":[129],"are":[130,147,249],"discussed":[131],"detail.":[133],"Two":[134],"numerical":[135],"studies,":[136],"curve":[139,164],"preprocessing":[143],"reconstruction,":[146],"validate":[150],"illustrate":[155],"its":[156],"practical":[157],"applications.":[158,287],"In":[159],"example":[161],"smoothing,":[165],"efficiency":[167],"compared":[173],"four":[175],"iterative":[176,179],"methods:":[177],"coordinate":[180],"descent,":[181],"Nesterov's":[182],"accelerated":[183],"gradient":[184],"descent":[185],"algorithm,":[186],"FISTA,":[187],"off-the-shelf":[190],"second":[191,236],"order":[192],"method.":[193],"first":[195],"two":[196],"methods":[197,220],"were":[198],"applied":[199],"primal":[202],"problem,":[203],"others":[205],"dual":[208],"problem.":[209],"comparisons":[211],"show":[212],"that":[213,241,259],"outperforms":[217],"all":[218],"other":[219],"significant":[223],"factor,":[224],"which":[225],"rapidly":[226],"grows":[227],"curvature":[230],"example,":[237],"showed":[240],"robustness":[242],"speed":[244],"maintained":[250],"over":[251],"wide":[253],"range":[254],"signal":[256],"variations,":[257],"noise":[260],"streaking":[262],"artifacts":[263],"could":[264],"be":[265,283],"reduced":[266],"almost":[268],"no":[269],"increase":[270],"computation":[272],"time.":[273],"also":[275],"outline":[276],"how":[277],"proposed":[279],"can":[282],"imaging":[286]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
