{"id":"https://openalex.org/W613352991","doi":"https://doi.org/10.1137/1.9781611972344","title":"Linear and Nonlinear Inverse Problems with Practical Applications","display_name":"Linear and Nonlinear Inverse Problems with Practical Applications","publication_year":2012,"publication_date":"2012-10-31","ids":{"openalex":"https://openalex.org/W613352991","doi":"https://doi.org/10.1137/1.9781611972344","mag":"613352991"},"language":"en","primary_location":{"id":"doi:10.1137/1.9781611972344","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611972344","pdf_url":null,"source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"monograph"},"type":"book","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/A5014028993","display_name":"Jennifer L. Mueller","orcid":"https://orcid.org/0000-0002-2583-5771"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jennifer L. Mueller","raw_affiliation_strings":["COLORADO STATE UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COLORADO STATE UNIVERSITY","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024895932","display_name":"Samuli Siltanen","orcid":"https://orcid.org/0000-0002-5988-5232"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samuli Siltanen","raw_affiliation_strings":["Department of Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014028993"],"corresponding_institution_ids":["https://openalex.org/I92446798"],"apc_list":null,"apc_paid":null,"fwci":19.3441,"has_fulltext":false,"cited_by_count":531,"citation_normalized_percentile":{"value":0.99300412,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.7408000230789185,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.7408000230789185,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10572","display_name":"Geophysical and Geoelectrical Methods","score":0.7113999724388123,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.6657999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.598049521446228},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5775949358940125},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4782516062259674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44283226132392883},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36461251974105835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36200612783432007},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17815786600112915},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08501064777374268},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0514584481716156}],"concepts":[{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.598049521446228},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5775949358940125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4782516062259674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44283226132392883},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36461251974105835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36200612783432007},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17815786600112915},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08501064777374268},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0514584481716156},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/1.9781611972344","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611972344","pdf_url":null,"source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"monograph"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-025860849","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Inverse":[0,157,245,255,261,302],"problems":[1,23],"arise":[2],"in":[3,25,39,108,149,166,221,230,260],"practical":[4,58],"applications":[5],"whenever":[6],"there":[7],"is":[8,84,126,162],"a":[9,40,48,53,109,132,193,238],"need":[10],"to":[11,19,29,57,115,175],"interpret":[12],"indirect":[13],"measurements.":[14],"This":[15],"book":[16,93],"explains":[17,36],"how":[18,28],"identify":[20],"ill-posed":[21],"inverse":[22,122,203,214],"arising":[24],"practice":[26],"and":[27,50,73,80,102,118,139,146,151,155,187,199,223,229,254,350,356,363],"design":[30],"computational":[31,37,177],"solution":[32],"methods":[33,209],"for":[34,120,144,164,196,210,332,341],"them;":[35],"approaches":[38],"hands-on":[41],"fashion,":[42],"with":[43,131,159,293],"related":[44],"codes":[45],"available":[46],"on":[47,202],"website;":[49],"serves":[51],"as":[52,86,216,218],"convenient":[54],"entry":[55],"point":[56],"inversion.":[59],"The":[60,92],"guiding":[61,88],"linear":[62,211],"inversion":[63,90,178,208],"examples":[64],"are":[65,142],"the":[66,87,98,103,113,127,185],"problem":[67],"of":[68,106,135,316,370],"image":[69],"deblurring,":[70],"x-ray":[71],"tomography,":[72,138,233],"backward":[74],"parabolic":[75],"problems,":[76,215],"including":[77],"heat":[78],"transfer,":[79],"electrical":[81,136,231],"impedance":[82,137,232],"tomography":[83],"used":[85],"nonlinear":[89,95,121,213],"example.":[91],"s":[94],"material":[96],"combines":[97],"analytic-geometric":[99],"research":[100,222],"tradition":[101],"regularization-based":[104],"school":[105],"thought":[107],"fruitful":[110],"manner,":[111],"paving":[112],"way":[114],"new":[116],"theorems":[117],"algorithms":[119],"problems.":[123,204],"Furthermore,":[124],"it":[125],"only":[128],"mathematical":[129],"textbook":[130,195],"thorough":[133],"treatment":[134],"these":[140],"sections":[141],"suitable":[143,194],"beginning":[145],"experienced":[147],"researchers":[148],"mathematics":[150],"engineering.":[152],"Audience:":[153],"Linear":[154,244,371],"Nonlinear":[156,301,306],"Problems":[158],"Practical":[160,290],"Applications":[161],"well-suited":[163],"students":[165],"mathematics,":[167],"engineering,":[168],"physics,":[169],"or":[170,212],"computer":[171],"science":[172],"who":[173],"wish":[174],"learn":[176],"(inverse":[179],"problems).":[180],"Professors":[181],"will":[182,234],"find":[183,236],"that":[184],"exercises":[186],"project":[188],"work":[189],"topics":[190],"make":[191],"this":[192,237],"advanced":[197],"undergraduate":[198],"graduate":[200],"courses":[201],"Researchers":[205],"developing":[206],"large-scale":[207],"well":[217],"engineers":[219],"working":[220],"development":[224],"departments":[225],"at":[226],"high-tech":[227],"companies":[228],"also":[235],"valuable":[239],"guide.":[240],"Contents":[241],"Part":[242,299],"I:":[243],"Problems;":[246,262,303],"Chapter":[247,250,257,263,269,273,278,285,288,296,304,308,313,320,326,335,343],"1:":[248],"Introduction;":[249],"2:":[251],"Nave":[252],"Reconstructions":[253],"Crimes;":[256],"3:":[258],"Ill-Posedness":[259],"4:":[264],"Truncated":[265],"Singular":[266],"Value":[267],"Decomposition;":[268],"5:":[270],"Tikhonov":[271],"Regularization;":[272,277],"6:":[274],"Total":[275],"Variation":[276],"7:":[279],"Besov":[280],"Space":[281],"Regularization":[282],"Using":[283],"Wavelets;":[284],"8:":[286],"Discretization-Invariance;":[287],"9:":[289],"X-ray":[291],"Tomography":[292],"limited":[294],"data;":[295],"10:":[297],"Projects;":[298,345],"II:":[300],"11:":[305],"Inversion;":[307],"12:":[309],"Electrical":[310],"Impedance":[311],"Tomography;":[312],"13:":[314],"Simulation":[315],"Noisy":[317],"EIT":[318],"Data;":[319],"14:":[321],"Complex":[322],"Geometrical":[323],"Optics":[324],"Solutions;":[325],"15:":[327],"A":[328],"Regularized":[329],"D-bar":[330],"Method":[331],"Direct":[333,338],"EIT;":[334,342],"16:":[336],"Other":[337],"Solution":[339,369],"Methods":[340],"17:":[344],"Appendix":[346,353,359,366],"A:":[347],"Banach":[348],"Spaces":[349],"Hilbert":[351],"Spaces;":[352,365],"B:":[354],"Mappings":[355],"Compact":[357],"Operators;":[358],"C:":[360],"Fourier":[361],"Transforms":[362],"Sobolev":[364],"D:":[367],"Iterative":[368],"Equations":[372]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":43},{"year":2024,"cited_by_count":40},{"year":2023,"cited_by_count":50},{"year":2022,"cited_by_count":42},{"year":2021,"cited_by_count":89},{"year":2020,"cited_by_count":50},{"year":2019,"cited_by_count":47},{"year":2018,"cited_by_count":40},{"year":2017,"cited_by_count":28},{"year":2016,"cited_by_count":32},{"year":2015,"cited_by_count":27},{"year":2014,"cited_by_count":24},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
