{"id":"https://openalex.org/W2123031198","doi":"https://doi.org/10.1109/tip.2010.2076294","title":"An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems","display_name":"An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems","publication_year":2010,"publication_date":"2010-09-15","ids":{"openalex":"https://openalex.org/W2123031198","doi":"https://doi.org/10.1109/tip.2010.2076294","mag":"2123031198","pmid":"https://pubmed.ncbi.nlm.nih.gov/20840899"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2010.2076294","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2010.2076294","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0912.3481","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"M V Afonso","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120471","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210120471"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"M V Afonso","raw_affiliation_strings":["Instituto de Telecomunica\u00e7\u00f5es and Department of Electrical and Computer Engineering, Instituto Superior T\u00e9cnico, 1049-001 Lisboa, Portugal. mafonso@lx.it.pt"],"affiliations":[{"raw_affiliation_string":"Instituto de Telecomunica\u00e7\u00f5es and Department of Electrical and Computer Engineering, Instituto Superior T\u00e9cnico, 1049-001 Lisboa, Portugal. mafonso@lx.it.pt","institution_ids":["https://openalex.org/I4210120471"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jos\u00e9 M Bioucas-Dias","orcid":null},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":null,"type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]},{"id":"https://openalex.org/I4210120471","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210120471"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 M Bioucas-Dias","raw_affiliation_strings":["Instituto de Telecomunica\u00e7\u00f5es and the Department of Electrical and Computer Engineering, Instituto Superior T\u00e9cnico, Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Instituto de Telecomunica\u00e7\u00f5es and the Department of Electrical and Computer Engineering, Instituto Superior T\u00e9cnico, Lisboa, Portugal","institution_ids":["https://openalex.org/I4210120471","https://openalex.org/I4387152517"]}]},{"author_position":"last","author":{"id":null,"display_name":"M\u00e1rio A T Figueiredo","orcid":null},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":null,"type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]},{"id":"https://openalex.org/I4210120471","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210120471"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"M\u00e1rio A T Figueiredo","raw_affiliation_strings":["Instituto de Telecomunica\u00e7\u00f5es and the Department of Electrical and Computer Engineering, Instituto Superior T\u00e9cnico, Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Instituto de Telecomunica\u00e7\u00f5es and the Department of Electrical and Computer Engineering, Instituto Superior T\u00e9cnico, Lisboa, Portugal","institution_ids":["https://openalex.org/I4210120471","https://openalex.org/I4387152517"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210120471"],"apc_list":null,"apc_paid":null,"fwci":34.2391,"has_fulltext":false,"cited_by_count":904,"citation_normalized_percentile":{"value":0.99866206,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"20","issue":"3","first_page":"681","last_page":"695"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.8065999746322632,"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":0.8065999746322632,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.04230000078678131,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.03400000184774399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8300999999046326},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5728999972343445},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5547000169754028},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.5127999782562256},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5066999793052673},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.5022000074386597},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5016000270843506},{"id":"https://openalex.org/keywords/deconvolution","display_name":"Deconvolution","score":0.48989999294281006},{"id":"https://openalex.org/keywords/constrained-optimization-problem","display_name":"Constrained optimization problem","score":0.4740000069141388}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8300999999046326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6114000082015991},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5728999972343445},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5547000169754028},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5066999793052673},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.5022000074386597},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.48989999294281006},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.4740000069141388},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46209999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4544000029563904},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44040000438690186},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.40639999508857727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4041000008583069},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.35749998688697815},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3361000120639801},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.31290000677108765},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.2533000111579895},{"id":"https://openalex.org/C30044814","wikidata":"https://www.wikidata.org/wiki/Q11334452","display_name":"Blind deconvolution","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2010.2076294","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2010.2076294","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:20840899","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20840899","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 image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:arXiv.org:0912.3481","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0912.3481","pdf_url":"https://arxiv.org/pdf/0912.3481","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0912.3481","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0912.3481","pdf_url":"https://arxiv.org/pdf/0912.3481","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1514248469","https://openalex.org/W1850000976","https://openalex.org/W1975377467","https://openalex.org/W1978333359","https://openalex.org/W1986931325","https://openalex.org/W1996287810","https://openalex.org/W2001200209","https://openalex.org/W2005089986","https://openalex.org/W2005909187","https://openalex.org/W2006262045","https://openalex.org/W2016859302","https://openalex.org/W2022905067","https://openalex.org/W2023722580","https://openalex.org/W2028349405","https://openalex.org/W2045079045","https://openalex.org/W2057624533","https://openalex.org/W2058532290","https://openalex.org/W2077237786","https://openalex.org/W2083042020","https://openalex.org/W2086670019","https://openalex.org/W2100556411","https://openalex.org/W2100705753","https://openalex.org/W2101675075","https://openalex.org/W2103559027","https://openalex.org/W2105536051","https://openalex.org/W2107844156","https://openalex.org/W2109449402","https://openalex.org/W2110505738","https://openalex.org/W2115528090","https://openalex.org/W2115706991","https://openalex.org/W2118064110","https://openalex.org/W2123664929","https://openalex.org/W2125935528","https://openalex.org/W2126607811","https://openalex.org/W2129276048","https://openalex.org/W2142280715","https://openalex.org/W2145534432","https://openalex.org/W2148791483","https://openalex.org/W2159262137","https://openalex.org/W2164452299","https://openalex.org/W2167732364","https://openalex.org/W3022380717","https://openalex.org/W4249667877","https://openalex.org/W4250955649"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1,73],"a":[2,20,64,74,114,173,188],"new":[3,75],"fast":[4],"algorithm":[5,77,141,186],"for":[6,153,191],"solving":[7],"one":[8,80],"of":[9,48,57,67,82,104,116,145,151,175],"the":[10,27,30,33,38,55,102,146,168,184,192],"standard":[11],"approaches":[12],"to":[13,78,92,101,111],"ill-posed":[14],"linear":[15],"inverse":[16],"problems":[17,50,84,181],"(IPLIP),":[18],"where":[19],"(possibly":[21],"nonsmooth)":[22],"regularizer":[23,39],"is":[24,142,187],"minimized":[25],"under":[26],"constraint":[28,41],"that":[29,162,183],"solution":[31],"explains":[32],"observations":[34,125],"sufficiently":[35],"well.":[36],"Although":[37],"and":[40,61,121,178],"are":[42,158,165],"usually":[43],"convex,":[44],"several":[45],"particular":[46],"features":[47],"these":[49,163],"(huge":[51],"dimensionality,":[52],"nonsmoothness)":[53],"preclude":[54],"use":[56],"off-the-shelf":[58],"optimization":[59],"tools":[60],"have":[62],"stimulated":[63],"considerable":[65],"amount":[66],"research.":[68],"In":[69],"this":[70],"paper,":[71],"we":[72,160],"efficient":[76],"handle":[79],"class":[81],"constrained":[83],"(often":[85],"known":[86],"as":[87,127],"basis":[88],"pursuit":[89],"denoising)":[90],"tailored":[91],"image":[93,176],"recovery":[94],"applications.":[95],"The":[96,139],"proposed":[97,140,169,185],"algorithm,":[98],"which":[99,154],"belongs":[100],"family":[103],"augmented":[105],"Lagrangian":[106],"methods,":[107],"can":[108],"be":[109],"used":[110],"deal":[112],"with":[113],"variety":[115],"imaging":[117],"IPLIP,":[118],"including":[119],"deconvolution":[120],"reconstruction":[122,179],"from":[123],"compressive":[124],"(such":[126],"MRI),":[128],"using":[129],"either":[130],"total-variation":[131],"or":[132],"wavelet-based":[133],"(or,":[134],"more":[135],"generally,":[136],"frame-based)":[137],"regularization.":[138],"an":[143],"instance":[144],"so-called":[147],"alternating":[148],"direction":[149],"method":[150],"multipliers,":[152],"convergence":[155],"sufficient":[156],"conditions":[157,164],"known;":[159],"show":[161,182],"satisfied":[166],"by":[167],"algorithm.":[170],"Experiments":[171],"on":[172],"set":[174],"restoration":[177],"benchmark":[180],"strong":[189],"contender":[190],"state-of-the-art.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":36},{"year":2024,"cited_by_count":40},{"year":2023,"cited_by_count":65},{"year":2022,"cited_by_count":68},{"year":2021,"cited_by_count":56},{"year":2020,"cited_by_count":72},{"year":2019,"cited_by_count":66},{"year":2018,"cited_by_count":88},{"year":2017,"cited_by_count":98},{"year":2016,"cited_by_count":73},{"year":2015,"cited_by_count":77},{"year":2014,"cited_by_count":61},{"year":2013,"cited_by_count":46},{"year":2012,"cited_by_count":31}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}