{"id":"https://openalex.org/W4363672235","doi":"https://doi.org/10.1142/s0219691323500212","title":"The null space property of the weighted \u2113r \u2212 \u21131 minimization","display_name":"The null space property of the weighted \u2113r \u2212 \u21131 minimization","publication_year":2023,"publication_date":"2023-04-11","ids":{"openalex":"https://openalex.org/W4363672235","doi":"https://doi.org/10.1142/s0219691323500212"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691323500212","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691323500212","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052836808","display_name":"Jianwen Huang","orcid":"https://orcid.org/0000-0003-3792-1383"},"institutions":[{"id":"https://openalex.org/I126924076","display_name":"Chongqing Normal University","ror":"https://ror.org/01dcw5w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I126924076"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianwen Huang","raw_affiliation_strings":["School of Mathematics, Chongqing Normal University, Chongqing 400047, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Chongqing Normal University, Chongqing 400047, P. R. China","institution_ids":["https://openalex.org/I126924076"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103261875","display_name":"Xinling Liu","orcid":"https://orcid.org/0000-0003-0007-0781"},"institutions":[{"id":"https://openalex.org/I16351329","display_name":"China West Normal University","ror":"https://ror.org/04s99y476","country_code":"CN","type":"education","lineage":["https://openalex.org/I16351329"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinling Liu","raw_affiliation_strings":["College of Mathematics and Information, China West Normal University, Nanchong 637009, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information, China West Normal University, Nanchong 637009, P. R. China","institution_ids":["https://openalex.org/I16351329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100781892","display_name":"Jinping Jia","orcid":"https://orcid.org/0000-0003-2409-338X"},"institutions":[{"id":"https://openalex.org/I4210163834","display_name":"Tianshui Normal University","ror":"https://ror.org/05kc6dc21","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163834"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinping Jia","raw_affiliation_strings":["School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P. R. China","institution_ids":["https://openalex.org/I4210163834"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3672,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.5007533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"06","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.6857309937477112},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.6572529673576355},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6456725001335144},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6383816599845886},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6383001804351807},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5556848049163818},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5329651832580566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3796234130859375},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3503352105617523},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32543033361434937},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26660168170928955},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.19933250546455383},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08354693651199341},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.05313459038734436}],"concepts":[{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.6857309937477112},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.6572529673576355},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6456725001335144},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6383816599845886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6383001804351807},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5556848049163818},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5329651832580566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3796234130859375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3503352105617523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32543033361434937},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26660168170928955},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.19933250546455383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08354693651199341},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.05313459038734436},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691323500212","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691323500212","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1794668820","display_name":null,"funder_award_id":"21JR1RE292","funder_id":"https://openalex.org/F4320322880","funder_display_name":"Natural Science Foundation of Gansu Province"},{"id":"https://openalex.org/G3476095843","display_name":null,"funder_award_id":"62063031","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5531621529","display_name":null,"funder_award_id":"12101454","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7959659299","display_name":null,"funder_award_id":"20B001","funder_id":"https://openalex.org/F4320335881","funder_display_name":"Fundamental Research Funds of China West Normal University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322880","display_name":"Natural Science Foundation of Gansu Province","ror":null},{"id":"https://openalex.org/F4320335881","display_name":"Fundamental Research Funds of China West Normal University","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W1824175539","https://openalex.org/W2000150201","https://openalex.org/W2012961725","https://openalex.org/W2015418199","https://openalex.org/W2020390700","https://openalex.org/W2025666718","https://openalex.org/W2033585806","https://openalex.org/W2075506710","https://openalex.org/W2134074206","https://openalex.org/W2147846067","https://openalex.org/W2315788538","https://openalex.org/W2346302321","https://openalex.org/W2601883894","https://openalex.org/W2766178683","https://openalex.org/W2886722903","https://openalex.org/W2921133280","https://openalex.org/W2963459904","https://openalex.org/W3084383934","https://openalex.org/W3111631795","https://openalex.org/W3166814550","https://openalex.org/W3196184468","https://openalex.org/W3207522052","https://openalex.org/W4320005289"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W1595179898","https://openalex.org/W2167853904","https://openalex.org/W627651491","https://openalex.org/W1189950277","https://openalex.org/W2020174565","https://openalex.org/W3159222891","https://openalex.org/W2613636631","https://openalex.org/W2963109107","https://openalex.org/W4363672235"],"abstract_inverted_index":{"The":[0],"null":[1,10],"space":[2,11],"property":[3,138],"(NSP),":[4],"which":[5],"relies":[6],"merely":[7],"on":[8],"the":[9,13,31,45,52,58,65,73,92,104,110,125,135,141],"of":[12,30,42,44,106,150],"sensing":[14],"matrix":[15],"column":[16],"space,":[17],"has":[18],"drawn":[19],"numerous":[20],"interests":[21],"in":[22],"sparse":[23],"signal":[24],"recovery.":[25],"This":[26],"paper":[27],"studies":[28],"NSP":[29,43,71,82,131],"weighted":[32,46,53,59,66,77,111,126],"[Formula:":[33,47,54,60,67,74,78,84,112,127],"see":[34,37,48,55,61,68,75,79,85,113,128],"text]":[35,49,56,62,69,76,80,114,129],"([Formula:":[36],"text])":[38],"minimization.":[39],"Several":[40],"versions":[41],"minimization":[50,115],"including":[51],"NSP,":[57,64],"stable":[63,130],"robust":[70,81],"and":[72],"for":[83,103],"text],":[86],"are":[87,96,116],"proposed,":[88],"as":[89,91],"well":[90],"associating":[93],"considerable":[94],"results":[95],"derived.":[97],"Under":[98],"these":[99],"NSPs,":[100],"sufficient":[101],"conditions":[102],"recovery":[105],"(sparse)":[107],"signals":[108],"with":[109],"established.":[117],"Furthermore,":[118],"we":[119,144],"show":[120],"that":[121,149],"to":[122],"some":[123],"extent,":[124],"is":[132,146],"weaker":[133],"than":[134,148],"restricted":[136],"isometric":[137],"(RIP).":[139],"And":[140],"RIP":[142],"condition":[143],"obtained":[145],"better":[147],"Zhou":[151],"(2022).":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}