{"id":"https://openalex.org/W2108586628","doi":"https://doi.org/10.1137/060671413","title":"Deblurring Methods Using Antireflective Boundary Conditions","display_name":"Deblurring Methods Using Antireflective Boundary Conditions","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2108586628","doi":"https://doi.org/10.1137/060671413","mag":"2108586628"},"language":"en","primary_location":{"id":"doi:10.1137/060671413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060671413","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5110755059","display_name":"Martin K. Christiansen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Christiansen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046248718","display_name":"Martin Hanke","orcid":"https://orcid.org/0000-0001-8620-452X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Hanke","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110755059"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8703,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.93294755,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"2","first_page":"855","last_page":"872"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/deblurring","display_name":"Deblurring","score":0.9620543718338013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7321230173110962},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7080968618392944},{"id":"https://openalex.org/keywords/anti-reflective-coating","display_name":"Anti-reflective coating","score":0.5406631231307983},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5146797299385071},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5121097564697266},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.501784086227417},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5006177425384521},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4299096465110779},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4139888286590576},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40751439332962036},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4038703441619873},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31264275312423706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2292909324169159},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.1265430748462677},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.123263418674469},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.10497879981994629},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.08080995082855225},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07481122016906738},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.05450788140296936}],"concepts":[{"id":"https://openalex.org/C2777693668","wikidata":"https://www.wikidata.org/wiki/Q25053743","display_name":"Deblurring","level":5,"score":0.9620543718338013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7321230173110962},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7080968618392944},{"id":"https://openalex.org/C108406538","wikidata":"https://www.wikidata.org/wiki/Q583040","display_name":"Anti-reflective coating","level":3,"score":0.5406631231307983},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5146797299385071},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5121097564697266},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.501784086227417},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5006177425384521},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4299096465110779},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4139888286590576},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40751439332962036},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4038703441619873},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31264275312423706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2292909324169159},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.1265430748462677},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.123263418674469},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.10497879981994629},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.08080995082855225},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07481122016906738},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.05450788140296936},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060671413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060671413","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.70.9837","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.9837","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://numerik.mathematik.uni-mainz.de/~hanke/christiansen.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":10,"referenced_works":["https://openalex.org/W1511121222","https://openalex.org/W1570089119","https://openalex.org/W1976865075","https://openalex.org/W1977149587","https://openalex.org/W1978157780","https://openalex.org/W2023706535","https://openalex.org/W2036513962","https://openalex.org/W2053189442","https://openalex.org/W2086600055","https://openalex.org/W2134572726"],"related_works":["https://openalex.org/W3200192952","https://openalex.org/W4308216825","https://openalex.org/W4312281738","https://openalex.org/W2062923025","https://openalex.org/W3009226622","https://openalex.org/W3015323103","https://openalex.org/W2786875726","https://openalex.org/W4226194415","https://openalex.org/W2008686286","https://openalex.org/W2066650801"],"abstract_inverted_index":{"In":[0],"this":[1,67],"paper":[2],"we":[3,57],"consider":[4],"the":[5,27,30,33,38,42,44,52,76,85,91,117],"numerical":[6,39],"solution":[7,28],"of":[8,26,32,66,120],"self-adjoint":[9],"deblurring":[10],"problems":[11,17],"on":[12],"bounded":[13],"intervals.":[14],"For":[15],"these":[16],"it":[18],"has":[19],"recently":[20],"been":[21],"shown":[22],"that":[23],"appropriate":[24],"modeling":[25],"near":[29],"boundary":[31,47,80],"interval":[34],"may":[35],"significantly":[36],"improve":[37],"reconstructions.":[40],"Among":[41],"alternatives":[43],"so-called":[45],"antireflective":[46],"condition":[48],"appears":[49],"to":[50,78,89,98,113],"be":[51],"best":[53],"known":[54],"choice.":[55],"Here":[56],"develop":[58],"an":[59],"appropriate,":[60],"i.e.,":[61],"stable":[62],"and":[63,82,111,122],"efficient":[64],"implementation":[65],"model":[68],"in":[69,101],"two":[70],"steps,":[71],"namely":[72],"by":[73],"(i)":[74],"transforming":[75],"problem":[77],"homogeneous":[79],"values,":[81],"(ii)":[83],"using":[84],"fast":[86],"sine":[87],"transform":[88],"solve":[90],"transformed":[92],"problem.":[93],"This":[94],"approach":[95],"allows":[96],"us":[97],"incorporate":[99],"regularization":[100],"a":[102],"very":[103],"straightforward":[104],"way.":[105],"Numerical":[106],"reconstructions":[107],"are":[108],"superior":[109],"qualitatively":[110],"quantitatively":[112],"those":[114],"obtained":[115],"with":[116],"reblurring":[118],"method":[119],"Donatelli":[121],"Serra-Capizzano.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"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":4},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}