{"id":"https://openalex.org/W1674362640","doi":null,"title":"Two-dimensional cubic convolution for image interpolation, restoration, and super-resolution","display_name":"Two-dimensional cubic convolution for image interpolation, restoration, and super-resolution","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1674362640","mag":"1674362640"},"language":"en","primary_location":{"id":"pmh:oai:digitalcommons.unl.edu:dissertations-10845","doi":null,"is_oa":false,"landing_page_url":"https://digitalcommons.unl.edu/dissertations/AAI3186881","pdf_url":null,"source":{"id":"https://openalex.org/S4306400577","display_name":"Lincoln (University of Nebraska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I114395901","host_organization_name":"University of Nebraska\u2013Lincoln","host_organization_lineage":["https://openalex.org/I114395901"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ETD collection for University of Nebraska-Lincoln","raw_type":"text"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"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/A5100841037","display_name":"Jiazheng Shi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiazheng Shi","raw_affiliation_strings":["The University of Nebraska-Lincoln"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Nebraska-Lincoln","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033419666","display_name":"Stephen E. Reichenbach","orcid":"https://orcid.org/0000-0001-8615-0795","observed_orcids":["https://orcid.org/0000-0001-8615-0795"]},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen E. Reichenbach","raw_affiliation_strings":["The University of Nebraska-Lincoln"],"raw_orcid":"https://orcid.org/0000-0001-8615-0795","affiliations":[{"raw_affiliation_string":"The University of Nebraska-Lincoln","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114395901"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9990000128746033,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9990000128746033,"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/T10688","display_name":"Image and Signal Denoising Methods","score":9.999999747378752e-05,"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/T11165","display_name":"Image and Video Quality Assessment","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cubic-convolution","display_name":"cubic convolution","score":0.7429999709129333},{"id":"https://openalex.org/keywords/image-interpolation","display_name":"image interpolation","score":0.7799999713897705},{"id":"https://openalex.org/keywords/image-restoration","display_name":"image restoration","score":0.7879999876022339},{"id":"https://openalex.org/keywords/image-super-resolution","display_name":"image super-resolution","score":0.8640000224113464},{"id":"https://openalex.org/keywords/power-spectrum","display_name":"power spectrum","score":0.9110000133514404},{"id":"https://openalex.org/keywords/markov-random-fields","display_name":"Markov random fields","score":0.8740000128746033},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"affine transformation","score":0.8389999866485596},{"id":"https://openalex.org/keywords/kernel-parameter-optimization","display_name":"kernel parameter optimization","score":0.6420000195503235},{"id":"https://openalex.org/keywords/aliasing","display_name":"aliasing","score":0.7289999723434448},{"id":"https://openalex.org/keywords/blurring","display_name":"blurring","score":0.7870000004768372},{"id":"https://openalex.org/keywords/image-reconstruction","display_name":"image reconstruction","score":0.5109999775886536}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7044044733047485},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5824409127235413},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5737810134887695},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.5640304684638977},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.48781493306159973},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.47050565481185913},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4357849955558777},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.33140408992767334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32314354181289673},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2822186350822449},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.26651108264923096},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2346896529197693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19107019901275635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15097251534461975},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08247354626655579},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:digitalcommons.unl.edu:dissertations-10845","doi":null,"is_oa":false,"landing_page_url":"https://digitalcommons.unl.edu/dissertations/AAI3186881","pdf_url":null,"source":{"id":"https://openalex.org/S4306400577","display_name":"Lincoln (University of Nebraska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I114395901","host_organization_name":"University of Nebraska\u2013Lincoln","host_organization_lineage":["https://openalex.org/I114395901"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ETD collection for University of Nebraska-Lincoln","raw_type":"text"},{"id":"mag:1674362640","doi":null,"is_oa":false,"landing_page_url":"https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=10845&context=dissertations","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7100901547","https://openalex.org/W2109613837","https://openalex.org/W1968503895","https://openalex.org/W2171958764","https://openalex.org/W1971023058","https://openalex.org/W2162284888","https://openalex.org/W2100703932","https://openalex.org/W2031722413","https://openalex.org/W2157494358","https://openalex.org/W2131745743"],"abstract_inverted_index":{"Cubic":[0,22,345],"convolution":[1,23,81,346],"has":[2,50],"been":[3,51],"used":[4],"for":[5,31,36,107,171,184,190,207,226,236,296,311],"image":[6,41,146,173,340,384,420],"interpolation":[7,20,142,147,158,288,309],"since":[8],"the":[9,47,92,124,131,157,163,186,218,234,271,293,306,323,396,401],"1970's":[10],"and":[11,19,27,59,113,175,192,206,217,232,265,276,282,302,342,355,361,380,394,410],"provides":[12],"a":[13,65,151,181,252,266],"good":[14],"compromise":[15],"between":[16],"computational":[17],"complexity":[18],"accuracy.":[21],"can":[24,144,284,333],"be":[25],"parameterized":[26],"then":[28],"optimized":[29],"either":[30],"general":[32,94],"performance":[33],"characteristics":[34],"or":[35,320,387],"optimal":[37,187,227],"fidelity":[38,274,310],"over":[39],"an":[40,369,382],"ensemble":[42],"with":[43,56,86,105,118,166,194,209,258,300,313,318,351,416],"specific":[44],"characteristics.":[45],"Traditionally,":[46],"cubic":[48,80],"kernel":[49],"derived":[52],"in":[53,64,374],"one":[54,57],"dimension":[55],"parameter":[58,188],"applied":[60],"to":[61,196,211,261,269,328,359,363],"two-dimensional":[62],"images":[63,69,135,312,317,412],"separable":[66],"fashion.":[67],"However,":[68],"typically":[70],"are":[71,348,357],"statistically":[72],"non-separable.":[73],"This":[74,177,249,391],"dissertation":[75,178,250,367,392],"develops":[76,180,251],"three":[77,87],"new":[78,141],"non-separable":[79],"kernels.":[82],"The":[83,115,140,223,240],"first":[84],"kernel,":[85,117,165],"parameters":[88,120,168],"(designated":[89,121,169],"2D-3PCC),":[90],"is":[91,229],"most":[93],"two-dimensional,":[95],"piecewise-cubic":[96],"interpolator":[97],"defined":[98],"on":[99,130,160,400],"[\u22122,":[100,103],"2]":[101,104],"\u00d7":[102],"constraints":[106],"biaxial":[108],"symmetry,":[109,111,128],"diagonal":[110,127],"continuity,":[112],"smoothness.":[114],"second":[116],"five":[119,167],"2D-5PCC),":[122],"relaxes":[123],"constraint":[125,159],"of":[126,154,198,246,292,372],"based":[129,399],"observation":[132],"that":[133,280,305,414],"many":[134],"have":[136],"rotationally":[137],"asymmetric":[138],"statistics.":[139],"kernels":[143,347],"improve":[145,308],"accuracy":[148],"by":[149,201],"incorporating":[150],"priori":[152],"knowledge":[153],"scenes.":[155],"Relaxing":[156],"2D-3PCC":[161,191,281],"yields":[162],"third":[164],"2D-5PCC-R),":[170],"one-pass":[172],"restoration":[174,341],"reconstruction.":[176],"also":[179],"closed-form":[182,241,267],"solution":[183,242,268],"determining":[185],"values":[189],"2D-5PCC":[193,283],"respect":[195,210],"ensembles":[197],"scenes":[199],"characterized":[200],"autocorrelation":[202,213,264],"(or":[203,214],"power":[204,215],"spectrum)":[205,216],"2D-5PCC-R":[208,332,373,417],"scene":[212,247,263],"continuous-discrete-continuous":[219],"(CDC)":[220],"imaging":[221,378,403],"system.":[222],"spatial-domain":[224],"formulation":[225],"parameterization":[228],"computationally":[230],"efficient":[231,362],"establishes":[233],"basis":[235],"locally":[237],"adaptive":[238],"filters.":[239],"supports":[243],"any":[244],"approximation":[245],"autocorrelation.":[248],"Markov":[253],"random":[254],"field":[255],"(MRF)":[256],"model":[257,262],"affine":[259],"transformation":[260],"fit":[270],"model.":[272,405],"Quantitative":[273],"analysis":[275,291],"visual":[277,421],"experiments":[278],"indicate":[279,413],"outperform":[285],"several":[286],"popular":[287,330],"methods.":[289,331,344],"An":[290],"error":[294,298],"budgets":[295],"reconstruction":[297,343],"associated":[299],"blurring":[301],"aliasing":[303],"illustrates":[304],"methods":[307,324],"aliased":[314],"components.":[315],"For":[316],"little":[319],"no":[321],"aliasing,":[322],"yield":[325],"results":[326,407],"similar":[327],"other":[329],"perform":[334],"as":[335,337],"well":[336],"traditional":[338],"two-pass":[339],"low-order":[349],"polynomials":[350],"small":[352],"spatial":[353],"support":[354],"so":[356],"easy":[358],"implement":[360],"apply.":[364],"Finally,":[365],"this":[366],"demonstrates":[368],"important":[370],"application":[371],"super-resolution":[375,397,415],"imaging.":[376],"Super-resolution":[377],"restores":[379],"reconstructs":[381],"enhanced":[383],"from":[385,408],"two":[386],"more":[388],"overlapping":[389],"images.":[390],"formulates":[393],"solves":[395],"problem":[398],"CDC":[402],"system":[404],"Experimental":[406],"simulation":[409],"real":[411],"significantly":[418],"improves":[419],"quality.":[422]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}
