{"id":"https://openalex.org/W2017392482","doi":"https://doi.org/10.1142/s0219691315500137","title":"Rank-deficient spectral factorization and wavelets completion problem","display_name":"Rank-deficient spectral factorization and wavelets completion problem","publication_year":2015,"publication_date":"2015-03-23","ids":{"openalex":"https://openalex.org/W2017392482","doi":"https://doi.org/10.1142/s0219691315500137","mag":"2017392482"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691315500137","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691315500137","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/A5055776599","display_name":"Lasha Ephremidze","orcid":"https://orcid.org/0000-0002-1000-3841"},"institutions":[{"id":"https://openalex.org/I120250893","display_name":"New York University Abu Dhabi","ror":"https://ror.org/00e5k0821","country_code":"AE","type":"education","lineage":["https://openalex.org/I120250893","https://openalex.org/I57206974"]}],"countries":["AE"],"is_corresponding":true,"raw_author_name":"L. Ephremidze","raw_affiliation_strings":["Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates","institution_ids":["https://openalex.org/I120250893"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060512518","display_name":"Ilya M. Spitkovsky","orcid":"https://orcid.org/0000-0002-1411-3036"},"institutions":[{"id":"https://openalex.org/I120250893","display_name":"New York University Abu Dhabi","ror":"https://ror.org/00e5k0821","country_code":"AE","type":"education","lineage":["https://openalex.org/I120250893","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I16285277","display_name":"William & Mary","ror":"https://ror.org/03hsf0573","country_code":"US","type":"education","lineage":["https://openalex.org/I16285277"]},{"id":"https://openalex.org/I267592682","display_name":"Williams (United States)","ror":"https://ror.org/007zhvp17","country_code":"US","type":"company","lineage":["https://openalex.org/I267592682"]}],"countries":["AE","US"],"is_corresponding":false,"raw_author_name":"I. Spitkovsky","raw_affiliation_strings":["Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA","Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA","institution_ids":["https://openalex.org/I16285277","https://openalex.org/I267592682"]},{"raw_affiliation_string":"Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates","institution_ids":["https://openalex.org/I120250893"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089856883","display_name":"Edem Lagvilava","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"E. Lagvilava","raw_affiliation_strings":["A. Razmadze Mathematical Institute, I. Javakhishvili State University, Tbilisi 0177, Georgia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"A. Razmadze Mathematical Institute, I. Javakhishvili State University, Tbilisi 0177, Georgia","institution_ids":["https://openalex.org/I102808428"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055776599"],"corresponding_institution_ids":["https://openalex.org/I120250893"],"apc_list":null,"apc_paid":null,"fwci":0.1872,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57798316,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"03","first_page":"1550013","last_page":"1550013"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9993000030517578,"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":0.9934999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6829833388328552},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.645660936832428},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6300851702690125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5248191952705383},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32543325424194336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31478118896484375},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28947192430496216},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19607225060462952}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6829833388328552},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.645660936832428},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6300851702690125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5248191952705383},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32543325424194336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31478118896484375},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28947192430496216},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19607225060462952}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691315500137","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691315500137","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":[{"score":0.41999998688697815,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W23086234","https://openalex.org/W194894291","https://openalex.org/W1481646516","https://openalex.org/W1483072194","https://openalex.org/W1523857737","https://openalex.org/W1586699705","https://openalex.org/W1594152515","https://openalex.org/W1953948525","https://openalex.org/W1969030037","https://openalex.org/W1975540652","https://openalex.org/W1993904566","https://openalex.org/W1996204837","https://openalex.org/W2020117202","https://openalex.org/W2023723226","https://openalex.org/W2030381152","https://openalex.org/W2032355054","https://openalex.org/W2052497621","https://openalex.org/W2062024414","https://openalex.org/W2076870022","https://openalex.org/W2079186636","https://openalex.org/W2087081164","https://openalex.org/W2101789093","https://openalex.org/W2115755118","https://openalex.org/W2163101083","https://openalex.org/W2165783715","https://openalex.org/W2316727981","https://openalex.org/W2963622596","https://openalex.org/W3000113561","https://openalex.org/W4237966721","https://openalex.org/W4240770664","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"simple":[1],"constructive":[2],"proof":[3],"of":[4],"polynomial":[5],"matrix":[6],"spectral":[7],"factorization":[8],"theorem":[9],"is":[10,17],"presented":[11],"in":[12],"the":[13,26],"rank-deficient":[14],"case.":[15],"It":[16],"then":[18],"used":[19],"to":[20,25],"provide":[21],"an":[22],"elementary":[23],"solution":[24],"wavelets":[27],"completion":[28],"problem.":[29]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
