{"id":"https://openalex.org/W1965782635","doi":"https://doi.org/10.1109/lgrs.2013.2270033","title":"Four-Component Scattering Power Decomposition of Remainder Coherency Matrices Constrained for Nonnegative Eigenvalues","display_name":"Four-Component Scattering Power Decomposition of Remainder Coherency Matrices Constrained for Nonnegative Eigenvalues","publication_year":2013,"publication_date":"2013-07-22","ids":{"openalex":"https://openalex.org/W1965782635","doi":"https://doi.org/10.1109/lgrs.2013.2270033","mag":"1965782635"},"language":"en","primary_location":{"id":"doi:10.1109/lgrs.2013.2270033","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lgrs.2013.2270033","pdf_url":null,"source":{"id":"https://openalex.org/S126920919","display_name":"IEEE Geoscience and Remote Sensing Letters","issn_l":"1545-598X","issn":["1545-598X","1558-0571"],"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 Geoscience and Remote Sensing Letters","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/A5101561115","display_name":"Gaofeng Liu","orcid":"https://orcid.org/0000-0002-9340-9029"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gaofeng Liu","raw_affiliation_strings":["National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China","Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100662583","display_name":"Ming Li","orcid":"https://orcid.org/0000-0002-4706-5173"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Li","raw_affiliation_strings":["National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China","Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100454900","display_name":"Yajun Wang","orcid":"https://orcid.org/0000-0003-1936-4747"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yajun Wang","raw_affiliation_strings":["National Key Laboratory of Radar Signal Processing, Xidian University , Xi'an, China","Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Radar Signal Processing, Xidian University , Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088683171","display_name":"Peng Zhang","orcid":"https://orcid.org/0000-0002-8065-0948"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Zhang","raw_affiliation_strings":["National Key Laboratory of Radar Signal Processing, Xidian University , Xi'an, China","Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Radar Signal Processing, Xidian University , Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103006322","display_name":"Yan Wu","orcid":"https://orcid.org/0000-0001-6464-1630"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Wu","raw_affiliation_strings":["Remote Sensing Image Processing and Computation Group, School of Electronic Engineering, Xidian University, Xi'an, China","Remote Sensing Image Process. & Comput. Group, Xidian Univ., Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Remote Sensing Image Processing and Computation Group, School of Electronic Engineering, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Remote Sensing Image Process. & Comput. Group, Xidian Univ., Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100411968","display_name":"Hongwei Liu","orcid":"https://orcid.org/0000-0003-4046-163X"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Liu","raw_affiliation_strings":["National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China","Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Nat. key Lab. of Radar Signal Process., Xidian Univ., Xi'an, , China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5101561115"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":13.6797,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9817393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"494","last_page":"498"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11312","display_name":"Soil Moisture and Remote Sensing","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10644","display_name":"Cryospheric studies and observations","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.9749070405960083},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.691771924495697},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.5304046869277954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5222725868225098},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5215094685554504},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.5203142166137695},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.44839560985565186},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.41455650329589844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3859020471572876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34953275322914124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21700790524482727},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1530408263206482},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13920533657073975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12474027276039124}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.9749070405960083},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.691771924495697},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.5304046869277954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5222725868225098},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5215094685554504},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.5203142166137695},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.44839560985565186},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.41455650329589844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3859020471572876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34953275322914124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21700790524482727},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1530408263206482},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13920533657073975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12474027276039124},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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":1,"locations":[{"id":"doi:10.1109/lgrs.2013.2270033","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lgrs.2013.2270033","pdf_url":null,"source":{"id":"https://openalex.org/S126920919","display_name":"IEEE Geoscience and Remote Sensing Letters","issn_l":"1545-598X","issn":["1545-598X","1558-0571"],"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 Geoscience and Remote Sensing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8399999737739563,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W2054102563","https://openalex.org/W2086501003","https://openalex.org/W2091079473","https://openalex.org/W2097272115","https://openalex.org/W2130762895","https://openalex.org/W2131035246","https://openalex.org/W2134053010","https://openalex.org/W2141424348","https://openalex.org/W2141502803","https://openalex.org/W2150059023","https://openalex.org/W2156759776","https://openalex.org/W2170481611","https://openalex.org/W2488646725"],"related_works":["https://openalex.org/W4315487898","https://openalex.org/W2289858865","https://openalex.org/W2470850800","https://openalex.org/W2150953077","https://openalex.org/W2110126483","https://openalex.org/W2112519774","https://openalex.org/W2548342391","https://openalex.org/W4287208482","https://openalex.org/W3155045649","https://openalex.org/W2148026948"],"abstract_inverted_index":{"The":[0,207],"motivation":[1],"of":[2,14,56,148,158,172],"this":[3],"letter":[4],"is":[5,19,24,75,111,165,184,200],"to":[6,94,97,167,186,197,202],"resolve":[7,187],"the":[8,22,33,36,48,57,62,78,81,95,99,106,109,124,130,139,145,149,156,176,180,188,195,204,214],"nonnegative":[9,82],"eigenvalue":[10,83],"constraint":[11],"(NNEC)":[12],"problem":[13,50,147],"four-component":[15],"decomposition":[16,84,88],"(FCD).":[17],"It":[18],"analyzed":[20,76],"that":[21,51,77,122,144,213],"NNEC":[23,49,100,146,189],"an":[25],"essential":[26],"requirement":[27],"for":[28,86,108,226],"remainder":[29,53,126,134,151,182],"coherency":[30,54,127,135,152],"matrices":[31,55,67,136,153],"in":[32],"FCD,":[34],"however":[35],"measured":[37,208],"polarimetric":[38],"synthetic":[39],"aperture":[40],"radar":[41],"(POLSAR)":[42],"data":[43,210],"experiment":[44,211],"shows":[45,212],"there":[46],"exits":[47],"some":[52],"FCD":[58,96,110,216],"do":[59],"not":[60,69],"satisfy":[61,138],"NNEC,":[63,131],"which":[64,199],"means":[65],"these":[66],"are":[68],"positive":[70],"semi-definite.":[71],"In":[72],"addition,":[73],"it":[74],"scheme":[79,104],"using":[80,105],"(NNED)":[85],"three-component":[87],"(TCD)":[89],"cannot":[90],"be":[91],"directly":[92],"extended":[93],"overcome":[98],"problem,":[101],"so":[102],"a":[103,120,162],"NNED":[107],"proposed":[112,215],"as":[113],"follow.":[114],"From":[115],"matrix":[116,128],"theory,":[117],"we":[118,141,192],"draw":[119],"conclusion":[121],"if":[123],"last":[125,150],"satisfies":[129],"then":[132],"all":[133,169],"also":[137],"NNEC;":[140],"successively":[142],"analyze":[143],"results":[154],"from":[155],"overestimation":[157,177],"scattering":[159,173,221,225],"powers.":[160],"Then":[161],"shrinkage":[163,205],"coefficient":[164],"used":[166,201],"depress":[168,223],"possible":[170],"overestimations":[171],"powers,":[174],"and":[175,222],"case":[178],"with":[179],"minimum":[181],"power":[183],"chosen":[185],"problem.":[190],"Moreover,":[191],"have":[193],"simplified":[194],"solution":[196],"NNED,":[198],"calculate":[203],"coefficient.":[206],"POLSAR":[209],"can":[217],"further":[218],"enhance":[219],"double-bounce":[220],"volume":[224],"urban":[227],"areas.":[228]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}