{"id":"https://openalex.org/W2561409850","doi":"https://doi.org/10.1109/tit.2018.2861887","title":"Comments on \u201cImproving Compressed Sensing With the Diamond Norm\u201d\u2013Saturation of the Norm Inequalities Between Diamond and Nuclear Norm","display_name":"Comments on \u201cImproving Compressed Sensing With the Diamond Norm\u201d\u2013Saturation of the Norm Inequalities Between Diamond and Nuclear Norm","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2561409850","doi":"https://doi.org/10.1109/tit.2018.2861887","mag":"2561409850"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2861887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2861887","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.07931","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ulrich Michel","orcid":"https://orcid.org/0000-0002-5284-9407"},"institutions":[{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich Michel","raw_affiliation_strings":["Institute for Theoretical Physics, University of Cologne, Cologne, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5284-9407","affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, University of Cologne, Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Martin Kliesch","orcid":"https://orcid.org/0000-0002-8009-0549"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Martin Kliesch","raw_affiliation_strings":["Institute of Theoretical Physics and Astrophysics, University of Gda\u0144sk, Gda\u0144sk, Poland"],"raw_orcid":"https://orcid.org/0000-0002-8009-0549","affiliations":[{"raw_affiliation_string":"Institute of Theoretical Physics and Astrophysics, University of Gda\u0144sk, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Richard Kueng","orcid":null},"institutions":[{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Richard Kueng","raw_affiliation_strings":["Institute for Theoretical Physics, University of Cologne, Cologne, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, University of Cologne, Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]}]},{"author_position":"last","author":{"id":null,"display_name":"David Gross","orcid":"https://orcid.org/0000-0001-8888-3028"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I4210129739","display_name":"ARC Centre of Excellence for Engineered Quantum Systems","ror":"https://ror.org/03rtykw43","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210129739","https://openalex.org/I4210132349"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David Gross","raw_affiliation_strings":["Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW, Australia"],"raw_orcid":"https://orcid.org/0000-0001-8888-3028","affiliations":[{"raw_affiliation_string":"Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602","https://openalex.org/I4210129739"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5339,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57026587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"64","issue":"11","first_page":"7443","last_page":"7445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.8241999745368958,"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":0.8241999745368958,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.026799999177455902,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.020500000566244125,"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/matrix-norm","display_name":"Matrix norm","score":0.715499997138977},{"id":"https://openalex.org/keywords/diamond","display_name":"Diamond","score":0.6692000031471252},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6452999711036682},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.5479000210762024},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.39500001072883606},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.388700008392334}],"concepts":[{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.715499997138977},{"id":"https://openalex.org/C2776921476","wikidata":"https://www.wikidata.org/wiki/Q5283","display_name":"Diamond","level":2,"score":0.6692000031471252},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6452999711036682},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.5479000210762024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5199999809265137},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.36160001158714294},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36000001430511475},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.30390000343322754},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2581000030040741},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25290000438690186}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2018.2861887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2861887","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.07931","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.07931","pdf_url":"https://arxiv.org/pdf/1612.07931","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:90748","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20181108-092816240","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.07931","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.07931","pdf_url":"https://arxiv.org/pdf/1612.07931","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"publishedVersion","is_accepted":true,"is_published":true,"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":4,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W2015775929","https://openalex.org/W2116102644","https://openalex.org/W2260322515"],"related_works":[],"abstract_inverted_index":{"The":[0,26],"diamond":[1,32],"norm":[2,27,33,39],"plays":[3],"an":[4],"important":[5],"role":[6],"in":[7,34],"quantum":[8],"information":[9],"and":[10,60],"operator":[11],"theory.":[12],"Recently,":[13],"it":[14],"has":[15],"also":[16],"been":[17],"proposed":[18],"as":[19,42],"a":[20,51],"regularizer":[21],"for":[22],"low-rank":[23],"matrix":[24],"recovery.":[25],"constants":[28],"that":[29],"bound":[30],"the":[31,37,58],"terms":[35],"of":[36,54],"nuclear":[38],"(also":[40],"known":[41],"trace":[43],"norm)":[44],"are":[45],"explicitly":[46],"known.":[47],"This":[48],"paper":[49],"provides":[50],"simple":[52],"characterization":[53],"all":[55],"operators":[56],"saturating":[57],"upper":[59],"lower":[61],"bounds.":[62]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2017-01-06T00:00:00"}
