{"id":"https://openalex.org/W2150912629","doi":"https://doi.org/10.1109/tip.2013.2246175","title":"Analysis Operator Learning and its Application to Image Reconstruction","display_name":"Analysis Operator Learning and its Application to Image Reconstruction","publication_year":2013,"publication_date":"2013-02-11","ids":{"openalex":"https://openalex.org/W2150912629","doi":"https://doi.org/10.1109/tip.2013.2246175","mag":"2150912629","pmid":"https://pubmed.ncbi.nlm.nih.gov/23412611"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2013.2246175","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2013.2246175","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/1204.5309","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"S. Hawe","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S. Hawe","raw_affiliation_strings":["Department of Electrical Engineering, Technische Universit\u00e4t M\u00fcnchen, Munich 80290, Germany. simon.hawe@tum.de"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technische Universit\u00e4t M\u00fcnchen, Munich 80290, Germany. simon.hawe@tum.de","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":null,"display_name":"M. Kleinsteuber","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Kleinsteuber","raw_affiliation_strings":["Department of Electrical Engineering, Technische Universit\u00e4t M\u00fcnchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technische Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":null,"display_name":"K. Diepold","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"K. Diepold","raw_affiliation_strings":["Department of Electrical Engineering, Technische Universit\u00e4t M\u00fcnchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technische Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":19.8949,"has_fulltext":false,"cited_by_count":142,"citation_normalized_percentile":{"value":0.99691217,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"22","issue":"6","first_page":"2138","last_page":"2150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.5860000252723694,"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":0.5860000252723694,"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":0.11840000003576279,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.0982000008225441,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.6279000043869019},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5724999904632568},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5478000044822693},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5187000036239624},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4975999891757965},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4503999948501587},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.4498000144958496},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3853999972343445},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.3822000026702881}],"concepts":[{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.6279000043869019},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5724999904632568},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5478000044822693},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5187000036239624},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5095999836921692},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4975999891757965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4934000074863434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4927999973297119},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4503999948501587},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.4498000144958496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4325000047683716},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3709999918937683},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.3549000024795532},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C55020928","wikidata":"https://www.wikidata.org/wiki/Q3813865","display_name":"Image quality","level":3,"score":0.3359000086784363},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C182037307","wikidata":"https://www.wikidata.org/wiki/Q17039097","display_name":"Image gradient","level":5,"score":0.2687999904155731},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2013.2246175","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2013.2246175","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:23412611","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23412611","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:1204.5309","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.5309","pdf_url":"https://arxiv.org/pdf/1204.5309","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:1204.5309","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.5309","pdf_url":"https://arxiv.org/pdf/1204.5309","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1565013069","https://openalex.org/W1890834058","https://openalex.org/W1999174140","https://openalex.org/W2028737999","https://openalex.org/W2056370875","https://openalex.org/W2076223872","https://openalex.org/W2079354271","https://openalex.org/W2086962710","https://openalex.org/W2097074225","https://openalex.org/W2099321050","https://openalex.org/W2103559027","https://openalex.org/W2107844156","https://openalex.org/W2108560279","https://openalex.org/W2113945798","https://openalex.org/W2118297240","https://openalex.org/W2121058967","https://openalex.org/W2130184048","https://openalex.org/W2132680427","https://openalex.org/W2132984323","https://openalex.org/W2133665775","https://openalex.org/W2140514146","https://openalex.org/W2142940228","https://openalex.org/W2143731537","https://openalex.org/W2145096794","https://openalex.org/W2145263492","https://openalex.org/W2145534432","https://openalex.org/W2146738562","https://openalex.org/W2153663612","https://openalex.org/W2158874661","https://openalex.org/W2160547390","https://openalex.org/W2295936755","https://openalex.org/W4205293427","https://openalex.org/W6669934412","https://openalex.org/W6676727762","https://openalex.org/W6682009426"],"related_works":[],"abstract_inverted_index":{"Exploiting":[0],"a":[1,33,45],"priori":[2],"known":[3],"structural":[4],"information":[5],"lies":[6],"at":[7],"the":[8,50,60,64,73,101,105,131,143,152,156,190],"core":[9],"of":[10,36,40,52,90,104,133,155,180],"many":[11],"image":[12,53,167,172],"reconstruction":[13,54,91],"methods":[14,92,165],"that":[15,27],"can":[16,29],"be":[17,30,78],"stated":[18],"as":[19],"inverse":[20],"problems.":[21],"The":[22,88],"synthesis":[23],"model,":[24,62],"which":[25],"assumes":[26],"images":[28],"decomposed":[31],"into":[32],"linear":[34],"combination":[35],"very":[37],"few":[38],"atoms":[39],"some":[41],"dictionary,":[42],"is":[43,59,66,75,125],"now":[44],"well":[46],"established":[47],"tool":[48],"for":[49,115,166],"design":[51],"algorithms.":[55],"An":[56],"interesting":[57],"alternative":[58],"analysis":[61,70,96,118],"where":[63],"signal":[65],"multiplied":[67],"by":[68],"an":[69,95,113,117],"operator":[71,119],"and":[72,150,170],"outcome":[74],"assumed":[76],"to":[77,163,189],"sparse.":[79],"This":[80],"approach":[81,162,183],"has":[82],"only":[83],"recently":[84],"gained":[85],"increasing":[86],"interest.":[87],"quality":[89],"based":[93,126],"on":[94,100,127,130,148],"model":[97],"severely":[98],"depends":[99],"right":[102],"choice":[103],"suitable":[106],"operator.":[107],"In":[108],"this":[109],"paper,":[110],"we":[111,159],"present":[112],"algorithm":[114],"learning":[116],"from":[120],"training":[121],"images.":[122],"Our":[123,174],"method":[124,147],"l(p)-norm":[128],"minimization":[129],"set":[132],"full":[134],"rank":[135],"matrices":[136],"with":[137],"normalized":[138],"columns.":[139],"We":[140],"carefully":[141],"introduce":[142],"employed":[144],"conjugate":[145],"gradient":[146],"manifolds,":[149],"explain":[151],"underlying":[153],"geometry":[154],"constraints.":[157],"Moreover,":[158],"compare":[160],"our":[161,181],"state-of-the-art":[164,192],"denoising,":[168],"inpainting,":[169],"single":[171],"super-resolution.":[173],"numerical":[175],"results":[176],"show":[177],"competitive":[178],"performance":[179],"general":[182],"in":[184],"all":[185],"presented":[186],"applications":[187],"compared":[188],"specialized":[191],"techniques.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2016-06-24T00:00:00"}