{"corpus_id":206687235,"paper_sha":"25f7a27a2c8bb01df6937952645844ccc4dff89e","doi":"10.1109/TGRS.2003.819189","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2165755981,"dblp_id":"journals/tgrs/ChangD04","acl_id":null,"title":"Estimation of number of spectrally distinct signal sources in hyperspectral imagery","year":2004,"publication_date":"2004-03-15","venue":"IEEE Transactions on Geoscience and Remote Sensing","journal":{"name":"IEEE Transactions on Geoscience and Remote Sensing","pages":"608-619","volume":"42"},"journal_issn":null,"journal_title":null,"publication_types":["JournalArticle"],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Computer Science","Engineering","Environmental Science"],"reference_count":27,"citation_count":1003,"influential_citation_count":81,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"With very high spectral resolution, hyperspectral sensors can now uncover many unknown signal sources which cannot be identified by visual inspection or a priori. In order to account for such unknown signal sources, we introduce a new definition, referred to as virtual dimensionality (VD) in this paper. It is defined as the minimum number of spectrally distinct signal sources that characterize the hyperspectral data from the perspective view of target detection and classification. It is different from the commonly used intrinsic dimensionality (ID) in the sense that the signal sources are determined by the proposed VD based only on their distinct spectral properties. These signal sources may include unknown interfering sources, which cannot be identified by prior knowledge. With this new definition, three Neyman-Pearson detection theory-based thresholding methods are developed to determine the VD of hyperspectral imagery, where eigenvalues are used to measure signal energies in a detection model. In order to evaluate the performance of the proposed methods, two information criteria, an information criterion (AIC) and minimum description length (MDL), and the factor analysis-based method proposed by Malinowski, are considered for comparative analysis. As demonstrated in computer simulations, all the methods and criteria studied in this paper may work effectively when noise is independent identically distributed. This is, unfortunately, not true when some of them are applied to real image data. Experiments show that all the three eigenthresholding based methods (i.e., the Harsanyi-Farrand-Chang (HFC), the noise-whitened HFC (NWHFC), and the noise subspace projection (NSP) methods) produce more reliable estimates of VD compared to the AIC, MDL, and Malinowski's empirical indicator function, which generally overestimate VD significantly. In summary, three contributions are made in this paper, 1) an introduction of the new definition of VD, 2) three Neyman-Pearson detection theory-based thresholding methods, HFC, NWHFC, and NSP derived for VD estimation, and 3) experiments that show the AIC and MDL commonly used in passive array processing and the second-order statistic-based Malinowski's method are not effective measures in VD estimation.","claims":[{"public_id":"cl_7332c2b0f9d035ef053536e808a0a95e","status":"active","text":"Experiments show that the three eigenthresholding-based methods (HFC, NWHFC, NSP) produce more reliable estimates of VD compared to AIC, MDL, and Malinowski's empirical indicator function, which generally overestimate VD significantly.","confidence":0.9,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_7332c2b0f9d035ef053536e808a0a95e"},{"public_id":"cl_c24d6cb0adddbe379a9ccaf34500c0ec","status":"active","text":"Three Neyman-Pearson detection theory-based thresholding methods—Harsanyi-Farrand-Chang (HFC), noise-whitened HFC (NWHFC), and noise subspace projection (NSP)—are developed for VD estimation.","confidence":0.95,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_c24d6cb0adddbe379a9ccaf34500c0ec"},{"public_id":"cl_4bb011e1b0b0402d80c83fea41afd1ec","status":"active","text":"Virtual dimensionality (VD) is defined as the minimum number of spectrally distinct signal sources that characterize hyperspectral data from the perspective of target detection and classification.","confidence":0.95,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_4bb011e1b0b0402d80c83fea41afd1ec"}],"concepts":[{"public_id":"co_032fea31e01aee4f2a77d70e932deec5","status":"active","name":"virtual dimensionality","description":"The minimum number of spectrally distinct signal sources that characterize hyperspectral data from the perspective of target detection and classification.","types":["definition"],"aliases":["VD"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_032fea31e01aee4f2a77d70e932deec5"},{"public_id":"co_0d1f9ed087acb16b89ff24c102ba902e","status":"active","name":"eigenthresholding-based methods","description":"Methods that use eigenvalues to measure signal energies in a detection model for VD estimation, including HFC, NWHFC, and NSP.","types":["method category"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_0d1f9ed087acb16b89ff24c102ba902e"},{"public_id":"co_691443f810cbffa6d1d946711241c0c8","status":"active","name":"noise subspace projection (NSP) method","description":"A Neyman-Pearson detection theory-based method that uses noise subspace projection for VD estimation.","types":["method"],"aliases":["NSP"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_691443f810cbffa6d1d946711241c0c8"},{"public_id":"co_7815c46b894f5a679e9ad22a1b97b359","status":"active","name":"spectrally distinct signal sources","description":"Signal sources in hyperspectral imagery that are distinguished solely by their spectral properties, possibly including unknown interfering sources.","types":["entity"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_7815c46b894f5a679e9ad22a1b97b359"},{"public_id":"co_7d1f1f035b784358c3fc683d9e2f22eb","status":"active","name":"Malinowski's empirical indicator function","description":"A factor analysis-based method proposed by Malinowski for estimating dimensionality, found to overestimate VD significantly on real image data.","types":["method"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_7d1f1f035b784358c3fc683d9e2f22eb"},{"public_id":"co_9484bf5f406d914a5bb45053ea3a2353","status":"active","name":"Harsanyi-Farrand-Chang (HFC) method","description":"A Neyman-Pearson detection theory-based eigenthresholding method for estimating virtual dimensionality.","types":["method"],"aliases":["HFC"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_9484bf5f406d914a5bb45053ea3a2353"},{"public_id":"co_c52f9353eb09369916b1b22f18c41fc7","status":"active","name":"noise-whitened HFC (NWHFC) method","description":"A variant of the HFC method that applies noise whitening before thresholding for VD estimation.","types":["method"],"aliases":["NWHFC"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_c52f9353eb09369916b1b22f18c41fc7"},{"public_id":"co_cc51ac2f0534af4b9ce3113c65e7875c","status":"active","name":"Neyman-Pearson detection theory","description":"A statistical detection framework used to derive thresholding methods for determining virtual dimensionality.","types":["theory"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_cc51ac2f0534af4b9ce3113c65e7875c"},{"public_id":"co_d95a05f74b6d9dbc8d7e899a039f259d","status":"active","name":"MDL","description":"A minimum description length criterion used for comparative analysis in VD estimation, found to overestimate VD significantly on real image data.","types":["method"],"aliases":["minimum description length"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_d95a05f74b6d9dbc8d7e899a039f259d"},{"public_id":"co_f7c23253c7f614be4086789a968b7550","status":"active","name":"AIC","description":"An information criterion used for comparative analysis in VD estimation, found to overestimate VD significantly on real image data.","types":["method"],"aliases":["Akaike information criterion"],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_f7c23253c7f614be4086789a968b7550"}],"external_ids":{"DOI":"10.1109/TGRS.2003.819189","ArXiv":null,"PubMed":null,"PubMedCentral":null,"MAG":2165755981,"DBLP":"journals/tgrs/ChangD04","ACL":null},"open_access":{"is_open_access":false,"pdf_url":null,"landing_url":"https://sah.borca.ai/papers/206687235","source":null,"pdf_url_source":null,"license":null,"reason":"pdf_url_not_indexed"},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":false,"full_text_source":null,"count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":635786,"paper_uid":"d48acfd6-9dab-4710-8c33-aee2fb4c8e90","canonical_identity":{"paper_id":635786,"paper_uid":"d48acfd6-9dab-4710-8c33-aee2fb4c8e90","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/206687235"}