{"id":"https://openalex.org/W1990851110","doi":"https://doi.org/10.1090/s0025-5718-2012-02599-3","title":"An adaptive inverse scale space method for compressed sensing","display_name":"An adaptive inverse scale space method for compressed sensing","publication_year":2012,"publication_date":"2012-06-07","ids":{"openalex":"https://openalex.org/W1990851110","doi":"https://doi.org/10.1090/s0025-5718-2012-02599-3","mag":"1990851110"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02599-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02599-3","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02599-3/S0025-5718-2012-02599-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02599-3/S0025-5718-2012-02599-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069220813","display_name":"Martin Burger","orcid":"https://orcid.org/0000-0003-2619-2912"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]},{"id":"https://openalex.org/I4210167157","display_name":"Institut f\u00fcr Technische und Angewandte Physik (Germany)","ror":"https://ror.org/05vt21141","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210167157"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Burger","raw_affiliation_strings":["Westf\u00c3\u00a4lische Wilhelms-Universit\u00c3\u00a4t M\u00c3\u00bcnster, Institut f\u00c3\u00bcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00c3\u00bcnster, Germany","Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Institut f\u00fcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00fcnster, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westf\u00c3\u00a4lische Wilhelms-Universit\u00c3\u00a4t M\u00c3\u00bcnster, Institut f\u00c3\u00bcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00c3\u00bcnster, Germany","institution_ids":["https://openalex.org/I4210167157"]},{"raw_affiliation_string":"Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Institut f\u00fcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110285333","display_name":"Michael M\u00f6ller","orcid":null},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael M\u00f6ller","raw_affiliation_strings":["Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Institut f\u00fcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00fcnster, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Institut f\u00fcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008341403","display_name":"Martin Benning","orcid":"https://orcid.org/0000-0002-6203-1350"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]},{"id":"https://openalex.org/I4210167157","display_name":"Institut f\u00fcr Technische und Angewandte Physik (Germany)","ror":"https://ror.org/05vt21141","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210167157"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Benning","raw_affiliation_strings":["Westf\u00c3\u00a4lische Wilhelms-Universit\u00c3\u00a4t M\u00c3\u00bcnster, Institut f\u00c3\u00bcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00c3\u00bcnster, Germany","Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Institut f\u00fcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00fcnster, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Westf\u00c3\u00a4lische Wilhelms-Universit\u00c3\u00a4t M\u00c3\u00bcnster, Institut f\u00c3\u00bcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00c3\u00bcnster, Germany","institution_ids":["https://openalex.org/I4210167157"]},{"raw_affiliation_string":"Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Institut f\u00fcr Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112756955","display_name":"Stanley Osher","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stanley Osher","raw_affiliation_strings":["Department of Mathematics, University of California Los Angeles. Portola Plaza, Los Angeles, California 90095","Department of Mathematics, University of California Los Angeles, Portola Plaza, Los Angeles, California 90095"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California Los Angeles. Portola Plaza, Los Angeles, California 90095","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, University of California Los Angeles, Portola Plaza, Los Angeles, California 90095","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.105,"has_fulltext":true,"cited_by_count":91,"citation_normalized_percentile":{"value":0.9543088,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"82","issue":"281","first_page":"269","last_page":"299"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9969000220298767,"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/mathematics","display_name":"Mathematics","score":0.7458856105804443},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6757069230079651},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6455158591270447},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5907549858093262},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.5810865163803101},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5754337906837463},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5617318749427795},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5368647575378418},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48053035140037537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4696093499660492},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4629111886024475},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43088996410369873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22448018193244934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1582239866256714},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08991670608520508}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7458856105804443},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6757069230079651},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6455158591270447},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5907549858093262},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.5810865163803101},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5754337906837463},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5617318749427795},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5368647575378418},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48053035140037537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4696093499660492},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4629111886024475},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43088996410369873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22448018193244934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1582239866256714},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08991670608520508},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02599-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02599-3","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02599-3/S0025-5718-2012-02599-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.385.3872","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.385.3872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwmath.uni-muenster.de/num/publications/2013/BMBO13/cam11-08.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02599-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02599-3","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02599-3/S0025-5718-2012-02599-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1568214398","display_name":"Algorithms for Threat Detection (ATD): adaptive sensing and sensor fusion for real time chemical and biological threats","funder_award_id":"0914856","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4289685286","display_name":null,"funder_award_id":"DMS-0835863","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5990242347","display_name":null,"funder_award_id":"DMS-0914856","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7235448541","display_name":"CDI Type I. Mixing the Data to Knowledge direction: Computational Thinking for Faint Feature Detection by Feedback Control and Sensitivity/Resolution Enhancement of Matrix Images","funder_award_id":"0835863","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8241154039","display_name":"Collaborative Research: ATD (Algorithms for Threat Detection): Inverse Problems Methods in Chemical Threat Detection","funder_award_id":"0914561","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1990851110.pdf","grobid_xml":"https://content.openalex.org/works/W1990851110.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W207373900","https://openalex.org/W1653619892","https://openalex.org/W1815093352","https://openalex.org/W1984553293","https://openalex.org/W1984856013","https://openalex.org/W1996287810","https://openalex.org/W2005082281","https://openalex.org/W2006630289","https://openalex.org/W2008457246","https://openalex.org/W2011181254","https://openalex.org/W2023206259","https://openalex.org/W2033468335","https://openalex.org/W2043683510","https://openalex.org/W2048834141","https://openalex.org/W2061315188","https://openalex.org/W2072378378","https://openalex.org/W2075506710","https://openalex.org/W2079275676","https://openalex.org/W2079516848","https://openalex.org/W2080385522","https://openalex.org/W2095978736","https://openalex.org/W2103559027","https://openalex.org/W2115706991","https://openalex.org/W2127271355","https://openalex.org/W2128659236","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2147656689","https://openalex.org/W2151693816","https://openalex.org/W2154332973","https://openalex.org/W2158252006","https://openalex.org/W2289917018","https://openalex.org/W2296616510","https://openalex.org/W2532205281","https://openalex.org/W2547617174","https://openalex.org/W2798817241","https://openalex.org/W2953000435","https://openalex.org/W2963322354","https://openalex.org/W3099047247","https://openalex.org/W4285719527","https://openalex.org/W4301021743"],"related_works":["https://openalex.org/W2158224665","https://openalex.org/W2379589510","https://openalex.org/W2810730439","https://openalex.org/W4300044672","https://openalex.org/W1881631164","https://openalex.org/W2208932071","https://openalex.org/W2082465502","https://openalex.org/W3155039083","https://openalex.org/W1543136835","https://openalex.org/W4210375670"],"abstract_inverted_index":{"In":[0,85],"this":[1],"paper":[2],"we":[3,87],"introduce":[4],"a":[5,60,69,74],"novel":[6],"adaptive":[7],"approach":[8],"for":[9],"solving":[10,59],"<inline-formula":[11],"content-type=\"math/mathml\">":[12],"<mml:math":[13],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14],"alttext=\"script":[15],"l":[16],"Superscript":[17],"1\">":[18],"<mml:semantics>":[19],"<mml:msup>":[20],"<mml:mi>":[21],"\u2113":[22],"</mml:mi>":[23],"<mml:mn>1</mml:mn>":[24],"</mml:msup>":[25],"<mml:annotation":[26],"encoding=\"application/x-tex\">\\ell":[27],"^1</mml:annotation>":[28],"</mml:semantics>":[29],"</mml:math>":[30],"</inline-formula>":[31],"-minimization":[32],"problems":[33],"as":[34,77,79],"frequently":[35],"arising":[36],"in":[37,73,91],"compressed":[38],"sensing,":[39],"which":[40],"is":[41],"based":[42],"on":[43],"the":[44],"recently":[45],"introduced":[46],"inverse":[47],"scale":[48],"space":[49],"method.":[50],"The":[51],"scheme":[52],"allows":[53],"to":[54],"efficiently":[55],"compute":[56],"minimizers":[57],"by":[58],"sequence":[61],"of":[62],"low-dimensional":[63],"nonnegative":[64],"least-squares":[65],"problems.":[66],"We":[67],"provide":[68],"detailed":[70],"convergence":[71],"analysis":[72],"general":[75],"setup":[76],"well":[78],"refined":[80],"results":[81],"under":[82],"special":[83],"conditions.":[84],"addition,":[86],"discuss":[88],"experimental":[89],"observations":[90],"several":[92],"numerical":[93],"examples.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":46},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}