{"id":"https://openalex.org/W2572258776","doi":"https://doi.org/10.1109/tgrs.2016.2637882","title":"An Optimal Nonnegative Eigenvalue Decomposition for the Freeman and Durden Three-Component Scattering Model","display_name":"An Optimal Nonnegative Eigenvalue Decomposition for the Freeman and Durden Three-Component Scattering Model","publication_year":2017,"publication_date":"2017-01-19","ids":{"openalex":"https://openalex.org/W2572258776","doi":"https://doi.org/10.1109/tgrs.2016.2637882","mag":"2572258776"},"language":"en","primary_location":{"id":"doi:10.1109/tgrs.2016.2637882","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2016.2637882","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"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 Geoscience and Remote Sensing","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/A5030966271","display_name":"Yu Xian Lim","orcid":"https://orcid.org/0000-0002-3777-7986"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu Xian Lim","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-3777-7986","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007230271","display_name":"Mariko Burgin","orcid":"https://orcid.org/0000-0002-2410-9727"},"institutions":[{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mariko S. Burgin","raw_affiliation_strings":["Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-2410-9727","affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066893692","display_name":"J.J. van Zyl","orcid":null},"institutions":[{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jakob J. van Zyl","raw_affiliation_strings":["Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":35.088,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.99247706,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"55","issue":"4","first_page":"2167","last_page":"2176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10801","display_name":"Synthetic Aperture Radar (SAR) Applications and Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T10801","display_name":"Synthetic Aperture Radar (SAR) Applications and Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11038","display_name":"Advanced SAR Imaging Techniques","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6424813270568848},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5711014270782471},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5377296209335327},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.5012636184692383},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4468404948711395},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.44622179865837097},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.44365033507347107},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.44207024574279785},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.4387011229991913},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.418770968914032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3910529613494873},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38981667160987854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.383117139339447},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21945348381996155},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18352913856506348},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.11130079627037048},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08617019653320312}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6424813270568848},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5711014270782471},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5377296209335327},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.5012636184692383},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4468404948711395},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.44622179865837097},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.44365033507347107},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.44207024574279785},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.4387011229991913},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.418770968914032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3910529613494873},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38981667160987854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.383117139339447},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21945348381996155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18352913856506348},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.11130079627037048},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08617019653320312},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tgrs.2016.2637882","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2016.2637882","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"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 Geoscience and Remote Sensing","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:73833","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/73833/","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":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332375","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W348255556","https://openalex.org/W1965782635","https://openalex.org/W1974024703","https://openalex.org/W2016995863","https://openalex.org/W2026203301","https://openalex.org/W2036627634","https://openalex.org/W2044781968","https://openalex.org/W2047008513","https://openalex.org/W2060463330","https://openalex.org/W2078985447","https://openalex.org/W2096893798","https://openalex.org/W2097272115","https://openalex.org/W2121039887","https://openalex.org/W2131035246","https://openalex.org/W2139824394","https://openalex.org/W2141424348","https://openalex.org/W2145253696","https://openalex.org/W2150059023","https://openalex.org/W2170481611","https://openalex.org/W2171056811","https://openalex.org/W3023911918"],"related_works":["https://openalex.org/W1972373683","https://openalex.org/W2000169474","https://openalex.org/W2289858865","https://openalex.org/W2112519774","https://openalex.org/W2470850800","https://openalex.org/W2110126483","https://openalex.org/W2150953077","https://openalex.org/W2548342391","https://openalex.org/W4287208482","https://openalex.org/W3155045649"],"abstract_inverted_index":{"Model-based":[0],"decomposition":[1,18,135],"allows":[2],"the":[3,42,46,60,64,68,71,84,87,95,99,108,113,126,132,155,160,164],"physical":[4],"interpretation":[5],"of":[6,12,70,115],"polarimetric":[7],"radar":[8],"scattering":[9,14,157],"in":[10,38,90,98,107],"terms":[11,44],"various":[13],"mechanisms.":[15],"A":[16],"three-component":[17],"proposed":[19,137],"by":[20,123,138],"Freeman":[21],"and":[22,45],"Durden":[23],"has":[24],"been":[25,31],"popular,":[26],"though":[27],"significant":[28],"shortcomings":[29],"have":[30],"identified.":[32],"In":[33,57,76],"particular,":[34],"it":[35],"can":[36],"result":[37],"negative":[39],"eigenvalues":[40],"for":[41,53,63,86],"component":[43,106],"remainder":[47,100],"matrix,":[48],"hence":[49],"violating":[50],"fundamental":[51],"requirements":[52],"physically":[54],"meaningful":[55],"decompositions.":[56],"addition,":[58],"since":[59],"algorithm":[61,149],"solves":[62],"canopy":[65,72],"term":[66],"first,":[67],"contribution":[69],"is":[73],"often":[74],"over-estimated.":[75],"this":[77,147],"paper,":[78],"we":[79],"show":[80,145],"how":[81],"to":[82,154],"determine":[83],"parameters":[85],"Freeman-Durden":[88,127,162],"model":[89],"a":[91],"way":[92],"that":[93,146],"minimizes":[94],"total":[96],"power":[97,153],"matrix":[101],"without":[102],"favoring":[103],"any":[104],"individual":[105],"model,":[109],"while":[110],"simultaneously":[111],"satisfying":[112],"constraints":[114],"nonnegative":[116,133],"eigenvalues.":[117],"We":[118],"illustrate":[119],"our":[120],"analytical":[121],"solution":[122],"comparison":[124],"with":[125],"algorithm,":[128],"as":[129,131],"well":[130],"eigenvalue":[134],"(NNED)":[136],"van":[139],"Zyl":[140],"et":[141],"al.":[142],"The":[143],"results":[144],"optimum":[148],"generally":[150],"assigns":[151],"less":[152],"volume":[156],"than":[158],"either":[159],"original":[161],"or":[163],"NNED":[165],"algorithms.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":8},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}