{"id":"https://openalex.org/W4327662055","doi":"https://doi.org/10.1109/tsp.2023.3257989","title":"On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers","display_name":"On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4327662055","doi":"https://doi.org/10.1109/tsp.2023.3257989","pmid":"https://pubmed.ncbi.nlm.nih.gov/37383695"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2023.3257989","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tsp.2023.3257989","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10299746/pdf/nihms-1891056.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031370363","display_name":"Justin P. Haldar","orcid":"https://orcid.org/0000-0002-1838-0211"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Justin P. Haldar","raw_affiliation_strings":["Signal and Image Processing Institute, Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1838-0211","affiliations":[{"raw_affiliation_string":"Signal and Image Processing Institute, Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031370363"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.327,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.44968001,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"71","issue":null,"first_page":"1083","last_page":"1092"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9955000281333923,"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-problem","display_name":"Inverse problem","score":0.6586827635765076},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6134161353111267},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.5904414057731628},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5692814588546753},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.51270592212677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5112721920013428},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47372713685035706},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4153901934623718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37733227014541626},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3474028408527374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3329387605190277},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18016809225082397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11199989914894104}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6586827635765076},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6134161353111267},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.5904414057731628},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5692814588546753},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.51270592212677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5112721920013428},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47372713685035706},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4153901934623718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37733227014541626},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3474028408527374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3329387605190277},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18016809225082397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11199989914894104},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2023.3257989","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tsp.2023.3257989","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmid:37383695","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37383695","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society","raw_type":"Journal Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:10299746","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10299746","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10299746/pdf/nihms-1891056.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Signal Process","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:10299746","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10299746","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10299746/pdf/nihms-1891056.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Signal Process","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1066422085","display_name":null,"funder_award_id":"R01NS074980","funder_id":"https://openalex.org/F4320337359","funder_display_name":"National Institute of Neurological Disorders and Stroke"},{"id":"https://openalex.org/G462788903","display_name":"BrainSuite: Software for Analysis and Visualization of Multimodal Brain Imaging Data","funder_award_id":"3r01ns074980-10s1","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G5409794809","display_name":"Next generation in-vivo diffusion imaging at submillimeter resolution","funder_award_id":"2r01mh116173-06","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G82664503","display_name":null,"funder_award_id":"R01\u2010MH116173","funder_id":"https://openalex.org/F4320337346","funder_display_name":"National Institute of Mental Health"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337346","display_name":"National Institute of Mental Health","ror":"https://ror.org/04xeg9z08"},{"id":"https://openalex.org/F4320337359","display_name":"National Institute of Neurological Disorders and Stroke","ror":"https://ror.org/01s5ya894"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4327662055.pdf","grobid_xml":"https://content.openalex.org/works/W4327662055.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W104974959","https://openalex.org/W1497904071","https://openalex.org/W1513339763","https://openalex.org/W1514248469","https://openalex.org/W1534416612","https://openalex.org/W1594234351","https://openalex.org/W1602659231","https://openalex.org/W1843849834","https://openalex.org/W1941583664","https://openalex.org/W1964293263","https://openalex.org/W1964724571","https://openalex.org/W1970948570","https://openalex.org/W1978790599","https://openalex.org/W2000789223","https://openalex.org/W2005836623","https://openalex.org/W2006330194","https://openalex.org/W2008257035","https://openalex.org/W2027446127","https://openalex.org/W2034543179","https://openalex.org/W2045753892","https://openalex.org/W2090624404","https://openalex.org/W2096385086","https://openalex.org/W2096581338","https://openalex.org/W2097897435","https://openalex.org/W2101675075","https://openalex.org/W2102295630","https://openalex.org/W2107906890","https://openalex.org/W2111422394","https://openalex.org/W2113891902","https://openalex.org/W2114147096","https://openalex.org/W2114424556","https://openalex.org/W2116485776","https://openalex.org/W2117406892","https://openalex.org/W2117649283","https://openalex.org/W2119667497","https://openalex.org/W2124079290","https://openalex.org/W2127635814","https://openalex.org/W2132122471","https://openalex.org/W2145020729","https://openalex.org/W2147773647","https://openalex.org/W2151354228","https://openalex.org/W2156739854","https://openalex.org/W2162308311","https://openalex.org/W2165142794","https://openalex.org/W2167577940","https://openalex.org/W2168903001","https://openalex.org/W2169628183","https://openalex.org/W2169670552","https://openalex.org/W2196426102","https://openalex.org/W2268674159","https://openalex.org/W2619979791","https://openalex.org/W2766748446","https://openalex.org/W2798774029","https://openalex.org/W2911290743","https://openalex.org/W2962903101","https://openalex.org/W2999220188","https://openalex.org/W3000314771","https://openalex.org/W3001319253","https://openalex.org/W3001554227","https://openalex.org/W3100220310","https://openalex.org/W3100758187","https://openalex.org/W3104628308","https://openalex.org/W3104934659","https://openalex.org/W3137458037","https://openalex.org/W3165032792","https://openalex.org/W4214718273","https://openalex.org/W4235625704","https://openalex.org/W4249760698","https://openalex.org/W4250589301","https://openalex.org/W4292666002","https://openalex.org/W4312258136","https://openalex.org/W4312428138","https://openalex.org/W6686055759"],"related_works":["https://openalex.org/W2353179089","https://openalex.org/W2923538289","https://openalex.org/W2353125546","https://openalex.org/W2470643824","https://openalex.org/W2349635380","https://openalex.org/W4353089801","https://openalex.org/W2353819554","https://openalex.org/W2359488321","https://openalex.org/W2331917905","https://openalex.org/W3155039083"],"abstract_inverted_index":{"Ill-posed":[0],"linear":[1],"inverse":[2,29,138,209],"problems":[3],"appear":[4],"frequently":[5],"in":[6,59,191],"various":[7],"signal":[8],"processing":[9],"applications.":[10],"It":[11],"can":[12,64,68],"be":[13,65,145],"very":[14],"useful":[15],"to":[16,71,103,126,135,144,154,183,194,228],"have":[17],"theoretical":[18,97],"characterizations":[19,55,63],"that":[20,36,56,101,118],"quantify":[21],"the":[22,32,48,81,107,127,131,137,160,177,217],"level":[23],"of":[24,34,44,51,80,106,159,171,176,203],"ill-posedness":[25],"for":[26,113,207],"a":[27,52,166],"given":[28],"problem":[30],"and":[31,99,110,130,140,199,216,225],"degree":[33],"ambiguity":[35],"may":[37],"exist":[38],"about":[39],"its":[40],"solution.":[41],"Traditional":[42],"measures":[43],"ill-posedness,":[45],"such":[46,62],"as":[47],"condition":[49,162],"number":[50],"matrix,":[53],"provide":[54,72],"are":[57,84,111,119,124,141,180,189],"global":[58],"nature.":[60],"While":[61],"powerful,":[66],"they":[67],"also":[69,142,151],"fail":[70],"full":[73],"insight":[74],"into":[75],"situations":[76],"where":[77,173],"certain":[78,174],"entries":[79,105],"solution":[82,108,116,178],"vector":[83,179],"more":[85,168],"or":[86],"less":[87,181],"ambiguous":[88],"than":[89,185],"others.":[90,186],"In":[91,147],"this":[92],"work,":[93],"we":[94,200],"derive":[95],"novel":[96],"lower-":[98],"upper-bounds":[100],"apply":[102],"individual":[104],"vector,":[109],"valid":[112],"all":[114],"potential":[115,226],"vectors":[117],"nearly":[120],"data-consistent.":[121],"These":[122],"bounds":[123],"agnostic":[125],"noise":[128],"statistics":[129],"specific":[132],"method":[133],"used":[134],"solve":[136],"problem,":[139],"shown":[143],"tight.":[146],"addition,":[148],"our":[149,213],"results":[150,188],"lead":[152],"us":[153],"introduce":[155],"an":[156,192],"entrywise":[157],"version":[158],"traditional":[161,218],"number,":[163],"which":[164],"provides":[165],"substantially":[167],"nuanced":[169],"characterization":[170],"scenarios":[172],"elements":[175],"sensitive":[182],"perturbations":[184],"Our":[187],"illustrated":[190],"application":[193],"magnetic":[195],"resonance":[196],"imaging":[197],"reconstruction,":[198],"include":[201],"discussions":[202],"practical":[204],"computation":[205],"methods":[206],"large-scale":[208],"problems,":[210],"connections":[211],"between":[212],"new":[214],"theory":[215],"Cram\u00e9r-Rao":[219],"bound":[220],"under":[221],"statistical":[222],"modeling":[223],"assumptions,":[224],"extensions":[227],"cases":[229],"involving":[230],"constraints":[231],"beyond":[232],"just":[233],"data-consistency.":[234]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}