{"id":"https://openalex.org/W1580244397","doi":"https://doi.org/10.1007/11408031_52","title":"A Four-Pixel Scheme for Singular Differential Equations","display_name":"A Four-Pixel Scheme for Singular Differential Equations","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1580244397","doi":"https://doi.org/10.1007/11408031_52","mag":"1580244397"},"language":"en","primary_location":{"id":"doi:10.1007/11408031_52","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11408031_52","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5055314620","display_name":"Martin Welk","orcid":"https://orcid.org/0000-0002-6268-7050"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Welk","raw_affiliation_strings":["Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, 66041, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, 66041, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007086183","display_name":"Joachim Weickert","orcid":"https://orcid.org/0000-0002-8494-0045"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Joachim Weickert","raw_affiliation_strings":["Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, 66041, Saarbr\u00fccken, Germany","Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E1.1, 66041, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, 66041, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]},{"raw_affiliation_string":"Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E1.1, 66041, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008755474","display_name":"Gabriele Steidl","orcid":"https://orcid.org/0000-0003-4638-9245"},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gabriele Steidl","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of Mannheim, D7, 27, 68131, Mannheim, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of Mannheim, D7, 27, 68131, Mannheim, Germany","institution_ids":["https://openalex.org/I177802217"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055314620"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":5.811,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.97561537,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"610","last_page":"621"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9944000244140625,"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":0.9944000244140625,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9771000146865845,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7129893898963928},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.64378821849823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6268733143806458},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5606346726417542},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5012984275817871},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.4957481324672699},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47984883189201355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4563160836696625},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.455163836479187},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45242488384246826},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.44370588660240173},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43829748034477234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35397911071777344},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2726561725139618},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.20161068439483643},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1477571725845337},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.07098445296287537}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7129893898963928},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.64378821849823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6268733143806458},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5606346726417542},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5012984275817871},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4957481324672699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47984883189201355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4563160836696625},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.455163836479187},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45242488384246826},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.44370588660240173},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43829748034477234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35397911071777344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2726561725139618},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.20161068439483643},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1477571725845337},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.07098445296287537},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/11408031_52","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11408031_52","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.569.1026","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.569.1026","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.uni-kl.de/uploads/tx_sibibtex/www_ss05-spr.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1480546554","https://openalex.org/W1536341104","https://openalex.org/W1602798041","https://openalex.org/W1967110495","https://openalex.org/W1976342262","https://openalex.org/W1992276332","https://openalex.org/W2005089986","https://openalex.org/W2020198739","https://openalex.org/W2021528463","https://openalex.org/W2022088322","https://openalex.org/W2028421615","https://openalex.org/W2042280704","https://openalex.org/W2055841222","https://openalex.org/W2065164181","https://openalex.org/W2089231054","https://openalex.org/W2103559027","https://openalex.org/W2122890444","https://openalex.org/W2130136085","https://openalex.org/W2144275666","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2156575092","https://openalex.org/W2161836297","https://openalex.org/W2164822588","https://openalex.org/W2167373005","https://openalex.org/W2481865072","https://openalex.org/W3011612142","https://openalex.org/W4254409917"],"related_works":["https://openalex.org/W3204175910","https://openalex.org/W2072006507","https://openalex.org/W2049021870","https://openalex.org/W2145337406","https://openalex.org/W4300332839","https://openalex.org/W2017040016","https://openalex.org/W2084575444","https://openalex.org/W1976975662","https://openalex.org/W1647166283","https://openalex.org/W4360615000"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}