{"id":"https://openalex.org/W2112328859","doi":"https://doi.org/10.1109/icip.2007.4379951","title":"Hierarchical Tensor Approximation of Multidimensional Images","display_name":"Hierarchical Tensor Approximation of Multidimensional Images","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2112328859","doi":"https://doi.org/10.1109/icip.2007.4379951","mag":"2112328859"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2007.4379951","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2007.4379951","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Conference on Image Processing","raw_type":"proceedings-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/A5087152421","display_name":"Qing Wu","orcid":"https://orcid.org/0000-0002-9400-236X"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qing Wu","raw_affiliation_strings":["Department of Computer Science, University of Illinois, Urbana-Champaign, USA","Illinois Univ., Urbana"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois, Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Illinois Univ., Urbana","institution_ids":["https://openalex.org/I2801919071"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101603610","display_name":"Tian Xia","orcid":"https://orcid.org/0009-0001-2527-4257"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tian Xia","raw_affiliation_strings":["Department of Computer Science, University of Illinois, Urbana-Champaign, USA","Illinois Univ., Urbana"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois, Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Illinois Univ., Urbana","institution_ids":["https://openalex.org/I2801919071"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yizhou Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yizhou Yu","raw_affiliation_strings":["Department of Computer Science, University of Illinois, Urbana-Champaign, USA","Illinois Univ., Urbana"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois, Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Illinois Univ., Urbana","institution_ids":["https://openalex.org/I2801919071"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087152421"],"corresponding_institution_ids":["https://openalex.org/I157725225","https://openalex.org/I2801919071"],"apc_list":null,"apc_paid":null,"fwci":1.4843,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.80124224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"IV ","last_page":" 49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T12303","display_name":"Tensor decomposition and applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9984999895095825,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9977999925613403,"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/wavelet","display_name":"Wavelet","score":0.6923962831497192},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6289049983024597},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6242778301239014},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.591538667678833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.56742262840271},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.5126339793205261},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.483522891998291},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.48092886805534363},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.41925036907196045},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38053905963897705},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37553828954696655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3705625534057617},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13992154598236084}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6923962831497192},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6289049983024597},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6242778301239014},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.591538667678833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.56742262840271},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5126339793205261},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.483522891998291},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.48092886805534363},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.41925036907196045},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38053905963897705},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37553828954696655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3705625534057617},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13992154598236084},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/icip.2007.4379951","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2007.4379951","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Conference on Image Processing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.118.9763","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.118.9763","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-faculty.cs.uiuc.edu/~yyz/publication/htensor-icip07.pdf","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/151919","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/151919","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference_Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W33731299","https://openalex.org/W1485280399","https://openalex.org/W1760895834","https://openalex.org/W1991042426","https://openalex.org/W1994406579","https://openalex.org/W2000123870","https://openalex.org/W2002598080","https://openalex.org/W2018282388","https://openalex.org/W2053691921","https://openalex.org/W2132896093","https://openalex.org/W2148593155","https://openalex.org/W2157009172"],"related_works":["https://openalex.org/W4245508182","https://openalex.org/W4233511069","https://openalex.org/W2046633342","https://openalex.org/W2370050053","https://openalex.org/W2372936409","https://openalex.org/W53954450","https://openalex.org/W2365287829","https://openalex.org/W2389645710","https://openalex.org/W2379553594","https://openalex.org/W2351059076"],"abstract_inverted_index":{"Visual":[0],"data":[1,19],"comprises":[2],"of":[3,40,52,61],"multi-scale":[4,45],"and":[5,15,76,106],"inhomogeneous":[6,68],"signals.":[7],"In":[8,28],"this":[9,29],"paper,":[10],"we":[11],"exploit":[12],"these":[13],"characteristics":[14],"develop":[16],"an":[17,31],"adaptive":[18],"approximation":[20,82,98],"technique":[21,89],"based":[22],"on":[23],"a":[24,38,59,79],"hierarchical":[25],"tensor-based":[26],"transformation.":[27],"technique,":[30],"original":[32],"multi-dimensional":[33],"image":[34],"is":[35,55],"transformed":[36,75],"into":[37,58],"hierarchy":[39,54],"signals":[41],"to":[42,64],"expose":[43,65],"its":[44,66],"structures.":[46,69],"The":[47],"signal":[48],"at":[49],"each":[50],"level":[51],"the":[53],"further":[56,74],"divided":[57],"number":[60],"smaller":[62,71],"tensors":[63,72],"spatially":[67],"These":[70],"are":[73],"pruned":[77],"using":[78],"collective":[80],"tensor":[81,108],"technique.":[83],"Experimental":[84],"results":[85],"indicate":[86],"that":[87],"our":[88],"can":[90],"achieve":[91],"higher":[92],"compression":[93],"ratios":[94],"than":[95],"existing":[96],"functional":[97],"methods,":[99],"including":[100],"wavelet":[101,103],"transforms,":[102],"packet":[104],"transforms":[105],"single-level":[107],"approximation.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}