{"id":"https://openalex.org/W3199147857","doi":"https://doi.org/10.1109/lsp.2021.3112105","title":"Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators","display_name":"Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3199147857","doi":"https://doi.org/10.1109/lsp.2021.3112105","mag":"3199147857"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2021.3112105","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2021.3112105","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mpra.ub.uni-muenchen.de/81731/1/MPRA_paper_81731.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042992454","display_name":"Pradip Sasmal","orcid":"https://orcid.org/0000-0003-0111-2509"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pradip Sasmal","raw_affiliation_strings":["ECE, Indian Institute of Science, 29120 Bangalore, India, 560012 (e-mail: pradipsasmal@iisc.ac.in)","Deptartment of ECE, Indian Institute of Science, Bangalore, India"],"raw_orcid":"https://orcid.org/0000-0003-0111-2509","affiliations":[{"raw_affiliation_string":"ECE, Indian Institute of Science, 29120 Bangalore, India, 560012 (e-mail: pradipsasmal@iisc.ac.in)","institution_ids":["https://openalex.org/I59270414"]},{"raw_affiliation_string":"Deptartment of ECE, Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041107486","display_name":"Prasad Theeda","orcid":"https://orcid.org/0000-0003-0449-3749"},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prasad Theeda","raw_affiliation_strings":["Mathematics, Vellore Institute of Technology (VIT) University, Vellore, Tamilnadu, India, (e-mail: prasad.theeda@vit.ac.in)","[Vellore Institute of Technology (VIT University), Vellore, Tamilnadu, India]"],"raw_orcid":"https://orcid.org/0000-0003-0449-3749","affiliations":[{"raw_affiliation_string":"Mathematics, Vellore Institute of Technology (VIT) University, Vellore, Tamilnadu, India, (e-mail: prasad.theeda@vit.ac.in)","institution_ids":["https://openalex.org/I876193797"]},{"raw_affiliation_string":"[Vellore Institute of Technology (VIT University), Vellore, Tamilnadu, India]","institution_ids":["https://openalex.org/I876193797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023233176","display_name":"Phanindra Jampana","orcid":"https://orcid.org/0000-0002-9678-5249"},"institutions":[{"id":"https://openalex.org/I55664587","display_name":"Indian Institute of Chemical Technology","ror":"https://ror.org/040dky007","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I4210134808","https://openalex.org/I55664587","https://openalex.org/I66760702"]},{"id":"https://openalex.org/I65181880","display_name":"Indian Institute of Technology Hyderabad","ror":"https://ror.org/01j4v3x97","country_code":"IN","type":"education","lineage":["https://openalex.org/I65181880"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Phanindra Varma Jampana","raw_affiliation_strings":["Chemical Engineering, IIT-Hyderabad, Hyderabad, Telangana, India, 502205 (e-mail: pjampana@iith.ac.in)","[Indian Institute of Technology, Hyderabad, Telangana, India]"],"raw_orcid":"https://orcid.org/0000-0002-9678-5249","affiliations":[{"raw_affiliation_string":"Chemical Engineering, IIT-Hyderabad, Hyderabad, Telangana, India, 502205 (e-mail: pjampana@iith.ac.in)","institution_ids":["https://openalex.org/I55664587"]},{"raw_affiliation_string":"[Indian Institute of Technology, Hyderabad, Telangana, India]","institution_ids":["https://openalex.org/I65181880"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048867062","display_name":"C. S. Sastry","orcid":"https://orcid.org/0000-0002-8706-1767"},"institutions":[{"id":"https://openalex.org/I55664587","display_name":"Indian Institute of Chemical Technology","ror":"https://ror.org/040dky007","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I4210134808","https://openalex.org/I55664587","https://openalex.org/I66760702"]},{"id":"https://openalex.org/I65181880","display_name":"Indian Institute of Technology Hyderabad","ror":"https://ror.org/01j4v3x97","country_code":"IN","type":"education","lineage":["https://openalex.org/I65181880"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Challa S. Sastry","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Hyderabad, Hyderabad, India, 502001 (e-mail: csastry@iith.ac.in)","[Indian Institute of Technology, Hyderabad, Telangana, India]"],"raw_orcid":"https://orcid.org/0000-0002-8706-1767","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Hyderabad, Hyderabad, India, 502001 (e-mail: csastry@iith.ac.in)","institution_ids":["https://openalex.org/I55664587","https://openalex.org/I65181880"]},{"raw_affiliation_string":"[Indian Institute of Technology, Hyderabad, Telangana, India]","institution_ids":["https://openalex.org/I65181880"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.6423,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64410985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":null,"first_page":"1928","last_page":"1932"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9986000061035156,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980000257492065,"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":0.9937999844551086,"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":0.7358724474906921},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6540424227714539},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.5328880548477173},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45493704080581665},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.44269272685050964},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.4274361729621887},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2627210021018982},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21631741523742676}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7358724474906921},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6540424227714539},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.5328880548477173},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45493704080581665},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.44269272685050964},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.4274361729621887},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2627210021018982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21631741523742676},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2021.3112105","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2021.3112105","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai::81731","is_oa":true,"landing_page_url":"https://eprints.iisc.ac.in/81731/1/IEEE_sig_pro_let_28_1928-1932_2021.pdf","pdf_url":"https://mpra.ub.uni-muenchen.de/81731/1/MPRA_paper_81731.pdf","source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai::81731","is_oa":true,"landing_page_url":"https://eprints.iisc.ac.in/81731/1/IEEE_sig_pro_let_28_1928-1932_2021.pdf","pdf_url":"https://mpra.ub.uni-muenchen.de/81731/1/MPRA_paper_81731.pdf","source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3199147857.pdf","grobid_xml":"https://content.openalex.org/works/W3199147857.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1516260093","https://openalex.org/W1591116419","https://openalex.org/W2020503492","https://openalex.org/W2030034184","https://openalex.org/W2057206714","https://openalex.org/W2072704718","https://openalex.org/W2086869478","https://openalex.org/W2097323375","https://openalex.org/W2102129292","https://openalex.org/W2118297240","https://openalex.org/W2119337797","https://openalex.org/W2134033146","https://openalex.org/W2760478169","https://openalex.org/W2791086216","https://openalex.org/W2912522929","https://openalex.org/W2921957994","https://openalex.org/W4235713725","https://openalex.org/W4292170079"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W4289867043","https://openalex.org/W2784467519","https://openalex.org/W2366459771","https://openalex.org/W1973736094","https://openalex.org/W2963453621","https://openalex.org/W2350707375","https://openalex.org/W2377881809","https://openalex.org/W2355516922","https://openalex.org/W1959408986"],"abstract_inverted_index":{"Frames":[0],"with":[1,116,141],"a":[2,20,68,120,160],"large":[3],"minimum":[4,32],"angle":[5,34,91,146],"between":[6],"any":[7],"two":[8],"distinct":[9],"frame":[10,33,90,115,134,140,145,167],"vectors":[11],"are":[12,42],"desirable":[13],"in":[14],"many":[15],"present":[16,100,176],"day":[17],"applications.":[18],"For":[19],"unit":[21,132],"norm":[22,133],"frame,":[23],"the":[24,28,31,50,65,73,88,96,99,105,130,149,156,165,177],"absolute":[25],"value":[26],"of":[27,30,55,67,72,129,159],"cosine":[29],"is":[35],"also":[36,175],"known":[37],"as":[38],"coherence.":[39],"Two":[40],"frames":[41],"equivalent":[43,114,139,172],"if":[44],"one":[45],"can":[46,62,136,168],"be":[47],"obtained":[48,163],"from":[49,164],"other":[51,93],"via":[52],"left":[53],"action":[54,66],"an":[56,82,113,138,171],"invertible":[57],"linear":[58,69,84],"operator.":[59,70],"Frame":[60],"angles":[61],"change":[63],"under":[64],"Most":[71],"existing":[74],"works":[75],"solve":[76],"different":[77],"optimization":[78],"problems":[79],"to":[80,111,148],"find":[81,112],"optimal":[83],"operator":[85],"that":[86,135,155,180],"maximizes":[87],"minimal":[89,144],"(in":[92],"words,":[94],"minimizes":[95],"coherence).":[97],"In":[98,123],"work,":[101],"nevertheless,":[102],"we":[103,126],"consider":[104],"question:":[106],"Is":[107],"it":[108],"always":[109],"possible":[110],"smaller":[117],"coherence":[118],"for":[119],"given":[121],"frame.":[122,173],"this":[124],"paper,":[125],"derive":[127],"properties":[128],"initial":[131,150,166],"ensure":[137],"strictly":[142],"larger":[143],"compared":[147],"one.":[151],"It":[152],"turns":[153],"out":[154],"nullspace":[157],"property":[158],"certain":[161],"matrix":[162],"guarantee":[169],"such":[170],"We":[174],"numerical":[178],"results":[179],"support":[181],"our":[182],"theoretical":[183],"claims.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
