{"id":"https://openalex.org/W2049893860","doi":"https://doi.org/10.1109/tip.2014.2299065","title":"Insights Into Analysis Operator Learning: From Patch-Based Sparse Models to Higher Order MRFs","display_name":"Insights Into Analysis Operator Learning: From Patch-Based Sparse Models to Higher Order MRFs","publication_year":2014,"publication_date":"2014-01-31","ids":{"openalex":"https://openalex.org/W2049893860","doi":"https://doi.org/10.1109/tip.2014.2299065","mag":"2049893860","pmid":"https://pubmed.ncbi.nlm.nih.gov/24474375"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2014.2299065","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2014.2299065","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/1401.2804","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077938164","display_name":"Yunjin Chen","orcid":"https://orcid.org/0000-0002-4428-2797"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Yunjin Chen","raw_affiliation_strings":["Graz University of Technology, Institute for Computer Graphics and Vision, Graz, Austria","[Inst. for Comput. Graphics & Vision, Graz Univ. of Technol., Graz, Austria]"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, Institute for Computer Graphics and Vision, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"[Inst. for Comput. Graphics & Vision, Graz Univ. of Technol., Graz, Austria]","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076203786","display_name":"Ren\u00e9 Ranftl","orcid":"https://orcid.org/0000-0003-4158-2759"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Rene Ranftl","raw_affiliation_strings":["Graz University of Technology, Institute for Computer Graphics and Vision, Graz, Austria","[Inst. for Comput. Graphics & Vision, Graz Univ. of Technol., Graz, Austria]"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, Institute for Computer Graphics and Vision, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"[Inst. for Comput. Graphics & Vision, Graz Univ. of Technol., Graz, Austria]","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032205387","display_name":"Thomas Pock","orcid":"https://orcid.org/0000-0001-6120-1058"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Thomas Pock","raw_affiliation_strings":["Graz University of Technology, Institute for Computer Graphics and Vision, Graz, Austria","[Inst. for Comput. Graphics & Vision, Graz Univ. of Technol., Graz, Austria]"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, Institute for Computer Graphics and Vision, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"[Inst. for Comput. Graphics & Vision, Graz Univ. of Technol., Graz, Austria]","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077938164"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":null,"apc_paid":null,"fwci":16.4308,"has_fulltext":false,"cited_by_count":116,"citation_normalized_percentile":{"value":0.99608118,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"23","issue":"3","first_page":"1060","last_page":"1072"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998999834060669,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9976999759674072,"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/operator","display_name":"Operator (biology)","score":0.6791387796401978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6516090631484985},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5535743236541748},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4945478141307831},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.43615877628326416},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4266567826271057},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.42465895414352417},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.4116244614124298},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3594752550125122},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35776516795158386},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32295936346054077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.258239209651947},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.13898682594299316}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6791387796401978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6516090631484985},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5535743236541748},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4945478141307831},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.43615877628326416},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4266567826271057},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.42465895414352417},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4116244614124298},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3594752550125122},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35776516795158386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32295936346054077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.258239209651947},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.13898682594299316},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[{"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":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","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":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2014.2299065","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2014.2299065","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:24474375","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24474375","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:1401.2804","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.2804","pdf_url":"https://arxiv.org/pdf/1401.2804","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:1401.2804","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.2804","pdf_url":"https://arxiv.org/pdf/1401.2804","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":0.4399999976158142,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W1588663000","https://openalex.org/W1802356529","https://openalex.org/W1840913791","https://openalex.org/W1970163214","https://openalex.org/W1989975849","https://openalex.org/W1994281301","https://openalex.org/W2005876975","https://openalex.org/W2051434435","https://openalex.org/W2056370875","https://openalex.org/W2075674485","https://openalex.org/W2079182758","https://openalex.org/W2092663520","https://openalex.org/W2097323375","https://openalex.org/W2107844156","https://openalex.org/W2107861471","https://openalex.org/W2108454251","https://openalex.org/W2110158442","https://openalex.org/W2113606819","https://openalex.org/W2114122776","https://openalex.org/W2115374334","https://openalex.org/W2119290843","https://openalex.org/W2124659975","https://openalex.org/W2130184048","https://openalex.org/W2130248603","https://openalex.org/W2138448681","https://openalex.org/W2139643804","https://openalex.org/W2146738562","https://openalex.org/W2148056225","https://openalex.org/W2149974988","https://openalex.org/W2150912629","https://openalex.org/W2153663612","https://openalex.org/W2158449358","https://openalex.org/W2158874661","https://openalex.org/W2158915909","https://openalex.org/W2160547390","https://openalex.org/W2161259395","https://openalex.org/W2171650716","https://openalex.org/W2172275395","https://openalex.org/W2187061624","https://openalex.org/W2257784670","https://openalex.org/W2536599074","https://openalex.org/W2963811803","https://openalex.org/W3100455090","https://openalex.org/W4240554544","https://openalex.org/W6635100096","https://openalex.org/W6638840822","https://openalex.org/W6670322988","https://openalex.org/W6677143480","https://openalex.org/W6680389264","https://openalex.org/W6680414531","https://openalex.org/W6681524908","https://openalex.org/W6682009426","https://openalex.org/W6686960354","https://openalex.org/W7057979703"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W2387058352","https://openalex.org/W2004814108","https://openalex.org/W2130187411","https://openalex.org/W2890544631","https://openalex.org/W2511090434","https://openalex.org/W4224009465","https://openalex.org/W1981453930","https://openalex.org/W2930504574","https://openalex.org/W2985373316"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"a":[3,46,157],"new":[4,17],"learning":[5,61,143],"algorithm":[6],"for":[7],"the":[8,20,33,53,67,76,81,87,94,103,108,114],"recently":[9],"introduced":[10],"co-sparse":[11,21,88],"analysis":[12,22,54,59,77,89,141],"model.":[13,109],"First,":[14],"we":[15,44,120],"give":[16],"insights":[18],"into":[19],"model":[23,37,90],"by":[24],"establishing":[25],"connections":[26],"to":[27,51,75,112,125,162,166],"filter-based":[28],"MRF":[29],"models,":[30],"such":[31],"as":[32],"field":[34],"of":[35,38,83,86,116],"experts":[36],"Roth":[39],"and":[40,91,145,164],"Black.":[41],"For":[42],"training,":[43],"introduce":[45],"technique":[47],"called":[48,99],"bi-level":[49],"optimization":[50],"learn":[52],"operators.":[55],"Compared":[56],"with":[57,73,149],"existing":[58,140],"operator":[60,142],"approaches,":[62],"our":[63,117,122,135],"training":[64,118],"procedure":[65],"has":[66],"advantage":[68],"that":[69,93,134,159],"it":[70],"is":[71,102,160],"unconstrained":[72],"respect":[74],"operator.":[78],"We":[79],"investigate":[80],"effect":[82],"different":[84],"aspects":[85],"show":[92,133],"sparsity":[95],"promoting":[96],"function":[97],"(also":[98],"penalty":[100],"function)":[101],"most":[104],"important":[105],"factor":[106],"in":[107],"In":[110],"order":[111],"demonstrate":[113],"effectiveness":[115],"approach,":[119],"apply":[121],"trained":[123,136],"models":[124,137],"various":[126],"classical":[127],"image":[128,151],"restoration":[129],"problems.":[130],"Numerical":[131],"experiments":[132],"clearly":[138],"outperform":[139],"approaches":[144],"are":[146],"on":[147],"par":[148],"state-of-the-art":[150],"denoising":[152],"algorithms.":[153],"Our":[154],"approach":[155],"develops":[156],"framework":[158],"intuitive":[161],"understand":[163],"easy":[165],"implement.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":6}],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2025-10-10T00:00:00"}
