{"id":"https://openalex.org/W2026114584","doi":"https://doi.org/10.1109/tip.2013.2270109","title":"An Iterative Linear Expansion of Thresholds for $\\ell_{1}$-Based Image Restoration","display_name":"An Iterative Linear Expansion of Thresholds for $\\ell_{1}$-Based Image Restoration","publication_year":2013,"publication_date":"2013-06-19","ids":{"openalex":"https://openalex.org/W2026114584","doi":"https://doi.org/10.1109/tip.2013.2270109","mag":"2026114584","pmid":"https://pubmed.ncbi.nlm.nih.gov/23797257"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2013.2270109","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2013.2270109","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/190632","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071082236","display_name":"Hanjie Pan","orcid":"https://orcid.org/0000-0003-0805-7696"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hanjie Pan","raw_affiliation_strings":["Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong","Dept of Electron. Eng., Chinese Univ. of Hong Kong, Shatin, China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Dept of Electron. Eng., Chinese Univ. of Hong Kong, Shatin, China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017511611","display_name":"Thierry Blu","orcid":"https://orcid.org/0000-0001-5759-0011"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Thierry Blu","raw_affiliation_strings":["Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong","Dept of Electron. Eng., Chinese Univ. of Hong Kong, Shatin, China"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Dept of Electron. Eng., Chinese Univ. of Hong Kong, Shatin, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071082236"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":3.4552,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.9185202,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"9","first_page":"3715","last_page":"3728"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994000196456909,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9988999962806702,"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/image-restoration","display_name":"Image restoration","score":0.6502846479415894},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5325530767440796},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.5110310316085815},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.47376707196235657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45469748973846436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44029369950294495},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4264051020145416},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.40740248560905457},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3937152922153473},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3806660771369934}],"concepts":[{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.6502846479415894},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5325530767440796},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.5110310316085815},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.47376707196235657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45469748973846436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44029369950294495},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4264051020145416},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.40740248560905457},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3937152922153473},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3806660771369934}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2013.2270109","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2013.2270109","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:23797257","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23797257","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 image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:190632","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/190632","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:190632","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/190632","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6200000047683716}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W1560910787","https://openalex.org/W1570089119","https://openalex.org/W1574645113","https://openalex.org/W1578281517","https://openalex.org/W1591116419","https://openalex.org/W1975377467","https://openalex.org/W1977905043","https://openalex.org/W1978333359","https://openalex.org/W1984568490","https://openalex.org/W1986737463","https://openalex.org/W1986931325","https://openalex.org/W1988601656","https://openalex.org/W1992719146","https://openalex.org/W1997958347","https://openalex.org/W2006262045","https://openalex.org/W2007203285","https://openalex.org/W2009702064","https://openalex.org/W2013030361","https://openalex.org/W2013850411","https://openalex.org/W2016278923","https://openalex.org/W2016859302","https://openalex.org/W2028349405","https://openalex.org/W2060331468","https://openalex.org/W2063331068","https://openalex.org/W2065030431","https://openalex.org/W2077237786","https://openalex.org/W2079724595","https://openalex.org/W2092663520","https://openalex.org/W2095106682","https://openalex.org/W2100556411","https://openalex.org/W2100705753","https://openalex.org/W2103559027","https://openalex.org/W2103913786","https://openalex.org/W2105536051","https://openalex.org/W2107844156","https://openalex.org/W2109449402","https://openalex.org/W2110505738","https://openalex.org/W2115447612","https://openalex.org/W2115706991","https://openalex.org/W2118064110","https://openalex.org/W2119862467","https://openalex.org/W2119883478","https://openalex.org/W2122315118","https://openalex.org/W2123031198","https://openalex.org/W2126607811","https://openalex.org/W2135046866","https://openalex.org/W2140598595","https://openalex.org/W2140742952","https://openalex.org/W2142058898","https://openalex.org/W2146482778","https://openalex.org/W2147068866","https://openalex.org/W2148556090","https://openalex.org/W2149206122","https://openalex.org/W2149414429","https://openalex.org/W2158252006","https://openalex.org/W2161761402","https://openalex.org/W2161765392","https://openalex.org/W2163989778","https://openalex.org/W2167732364","https://openalex.org/W2334911726","https://openalex.org/W2949483514","https://openalex.org/W3022380717","https://openalex.org/W3101710822","https://openalex.org/W3101762025","https://openalex.org/W3106359998","https://openalex.org/W4235713725","https://openalex.org/W4254546220","https://openalex.org/W4255521522","https://openalex.org/W6669934412","https://openalex.org/W6680934908","https://openalex.org/W6681413097"],"related_works":["https://openalex.org/W2357322570","https://openalex.org/W90581812","https://openalex.org/W2365681766","https://openalex.org/W2107386309","https://openalex.org/W2545869789","https://openalex.org/W2393963626","https://openalex.org/W2141090006","https://openalex.org/W2058165188","https://openalex.org/W1964555484","https://openalex.org/W2105149350"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,30,73,115,159,175],"novel":[4],"algorithmic":[5],"framework":[6,192],"to":[7,62,68,83,98,104,129],"solve":[8,84,130],"image":[9,19,44,149],"restoration":[10,55],"problems":[11],"under":[12],"sparsity":[13],"assumptions.":[14],"As":[15],"usual,":[16],"the":[17,21,42,47,54,59,63,70,85,91,100,120,135,138,147,152,163,190,201,205],"reconstructed":[18,43],"is":[20,95,118,167],"minimum":[22],"of":[23,29,40,76,113,137,146,162,178,184,199,207],"an":[24,35,131],"objective":[25,48,92],"functional":[26,49],"that":[27,45,57,119,189],"consists":[28],"data":[31],"fidelity":[32],"term":[33],"and":[34,82,103,181,204],"\u2113\u2081":[36],"regularization.":[37],"However,":[38],"instead":[39,145],"estimating":[41],"minimizes":[46],"directly,":[50],"we":[51,126],"focus":[52],"on":[53,170],"process":[56,71,107],"maps":[58],"degraded":[60],"measurements":[61],"reconstruction.":[64],"Our":[65],"idea":[66],"amounts":[67],"parameterize":[69],"as":[72],"linear":[74,86,116,139],"combination":[75],"few":[77],"elementary":[78,153],"thresholding":[79,101,154],"functions":[80,102,155],"(LET)":[81],"weighting":[87],"coefficients":[88,140],"by":[89],"minimizing":[90],"functional.":[93],"It":[94],"then":[96],"possible":[97],"update":[99],"iterate":[105],"this":[106],"(":[108],"i-LET).":[109],"The":[110],"key":[111],"advantage":[112],"such":[114],"parametrization":[117],"problem":[121,133],"size":[122],"reduces":[123],"dramatically--each":[124],"time":[125,203],"only":[127],"need":[128],"optimization":[132],"over":[134,174],"dimension":[136],"(typically":[141],"less":[142],"than":[143],"10)":[144],"whole":[148],"dimension.":[150],"With":[151],"satisfying":[156],"certain":[157],"constraints,":[158],"global":[160],"convergence":[161],"iterated":[164],"LET":[165],"algorithm":[166],"guaranteed.":[168],"Experiments":[169],"several":[171],"test":[172],"images":[173],"wide":[176],"range":[177],"noise":[179],"levels":[180],"different":[182],"types":[183],"convolution":[185],"kernels":[186],"clearly":[187],"indicate":[188],"proposed":[191],"usually":[193],"outperforms":[194],"state-of-the-art":[195],"algorithms":[196],"in":[197],"terms":[198],"both":[200],"CPU":[202],"number":[206],"iterations.":[208]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}