{"id":"https://openalex.org/W1993102688","doi":"https://doi.org/10.1109/tip.2012.2195015","title":"Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods","display_name":"Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods","publication_year":2012,"publication_date":"2012-04-18","ids":{"openalex":"https://openalex.org/W1993102688","doi":"https://doi.org/10.1109/tip.2012.2195015","mag":"1993102688","pmid":"https://pubmed.ncbi.nlm.nih.gov/22531764"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2012.2195015","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2012.2195015","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108524187","display_name":"S. Ramani","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Ramani","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100421209","display_name":"Zhihao Liu","orcid":"https://orcid.org/0000-0002-0222-912X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhihao Liu","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086412465","display_name":"Jeffrey M. Rosen","orcid":"https://orcid.org/0000-0002-6637-844X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Rosen","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008080580","display_name":"Jon\u2010Fredrik Nielsen","orcid":"https://orcid.org/0000-0002-2058-3579"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Nielsen","raw_affiliation_strings":["FMRI Laboratory, University of Michigan, Ann Arbor, MI, USA","fMRI Lab., Univ. of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"FMRI Laboratory, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"fMRI Lab., Univ. of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027207271","display_name":"Jeffrey A. Fessler","orcid":"https://orcid.org/0000-0001-9998-3315"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. A. Fessler","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5108524187"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":21.3773,"has_fulltext":false,"cited_by_count":231,"citation_normalized_percentile":{"value":0.99905287,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"21","issue":"8","first_page":"3659","last_page":"3672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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":0.9995999932289124,"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/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9983999729156494,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.8171702027320862},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6855530142784119},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.6553052067756653},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6005674600601196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5824089050292969},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5801634192466736},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.5382241010665894},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5046371221542358},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4713525176048279},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4694744348526001},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3329302668571472},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28311681747436523},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.23372957110404968},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20433646440505981},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1911713182926178}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8171702027320862},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6855530142784119},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.6553052067756653},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6005674600601196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5824089050292969},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5801634192466736},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.5382241010665894},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5046371221542358},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4713525176048279},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4694744348526001},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3329302668571472},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28311681747436523},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.23372957110404968},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20433646440505981},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1911713182926178},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000033","qualifier_name":"anatomy & histology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000033","qualifier_name":"anatomy & histology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000033","qualifier_name":"anatomy & histology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000033","qualifier_name":"anatomy & histology","is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2012.2195015","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2012.2195015","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:22531764","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22531764","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:europepmc.org:2757490","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3411925","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"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":[{"id":"https://metadata.un.org/sdg/11","score":0.6299999952316284,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W18126775","https://openalex.org/W118540534","https://openalex.org/W1968735445","https://openalex.org/W1978333359","https://openalex.org/W1983579205","https://openalex.org/W1983837017","https://openalex.org/W1990381576","https://openalex.org/W1990457366","https://openalex.org/W1992317813","https://openalex.org/W1996543875","https://openalex.org/W2007203285","https://openalex.org/W2007852770","https://openalex.org/W2030313069","https://openalex.org/W2031604650","https://openalex.org/W2047163846","https://openalex.org/W2054640142","https://openalex.org/W2055834582","https://openalex.org/W2066793492","https://openalex.org/W2067145564","https://openalex.org/W2073879852","https://openalex.org/W2083236768","https://openalex.org/W2085765819","https://openalex.org/W2086278062","https://openalex.org/W2086546551","https://openalex.org/W2095106682","https://openalex.org/W2098843744","https://openalex.org/W2099798039","https://openalex.org/W2100053953","https://openalex.org/W2100705753","https://openalex.org/W2104371093","https://openalex.org/W2107844156","https://openalex.org/W2110505738","https://openalex.org/W2113606224","https://openalex.org/W2113920645","https://openalex.org/W2116641053","https://openalex.org/W2119695388","https://openalex.org/W2125542221","https://openalex.org/W2126036157","https://openalex.org/W2126485509","https://openalex.org/W2126759246","https://openalex.org/W2126922884","https://openalex.org/W2130152237","https://openalex.org/W2135209903","https://openalex.org/W2140170995","https://openalex.org/W2140742952","https://openalex.org/W2142005762","https://openalex.org/W2142058898","https://openalex.org/W2142808775","https://openalex.org/W2145568341","https://openalex.org/W2150867817","https://openalex.org/W2160459408","https://openalex.org/W2162053094","https://openalex.org/W2163887005","https://openalex.org/W2163940565","https://openalex.org/W2168543121","https://openalex.org/W2171125155","https://openalex.org/W2489822048","https://openalex.org/W2963726588","https://openalex.org/W3000332379","https://openalex.org/W3095095911","https://openalex.org/W3140025309","https://openalex.org/W4243350223","https://openalex.org/W4298876635","https://openalex.org/W6662286832"],"related_works":["https://openalex.org/W2375378023","https://openalex.org/W2107386309","https://openalex.org/W1928301487","https://openalex.org/W2151220638","https://openalex.org/W2725829804","https://openalex.org/W2545869789","https://openalex.org/W2105149350","https://openalex.org/W2058165188","https://openalex.org/W1964555484","https://openalex.org/W2141090006"],"abstract_inverted_index":{"Regularized":[0],"iterative":[1,65,83,91],"reconstruction":[2,60,155,190,224],"algorithms":[3,27],"for":[4,25,28,78,139,195,201],"imaging":[5],"inverse":[6],"problems":[7],"require":[8,126],"selection":[9],"of":[10,21,31,57,63,81,88,101,108,128,221],"appropriate":[11],"regularization":[12,23],"parameter":[13],"values.":[14],"We":[15,72,142,164,183],"focus":[16],"on":[17,47],"the":[18,29,54,58,64,70,74,89,96,144],"challenging":[19],"problem":[20],"tuning":[22],"parameters":[24],"nonlinear":[26,59,82],"case":[30],"additive":[32],"(possibly":[33],"complex)":[34],"Gaussian":[35],"noise.":[36],"Generalized":[37],"cross-validation":[38],"(GCV)":[39],"and":[40,95,110,123,132,149,160,168,176,198,223],"(weighted)":[41],"mean-squared":[42],"error":[43],"(MSE)":[44],"approaches":[45],"(based":[46],"Steinfs":[48],"Unbiased":[49],"Risk":[50],"Estimate.":[51],"SURE)":[52],"need":[53,137],"Jacobian":[55,76,210],"matrix":[56,77,211],"operator":[61],"(representative":[62],"algorithm)":[66],"with":[67,170],"respect":[68],"to":[69,146,150,180,209,218],"data.":[71],"derive":[73],"desired":[75],"two":[79,118],"types":[80,220],"algorithms:":[84],"a":[85,105],"fast":[86],"variant":[87],"standard":[90],"reweighted":[92],"least-squares":[93],"method":[94],"contemporary":[97],"split-Bregman":[98],"algorithm,":[99],"both":[100],"which":[102],"can":[103,213],"accommodate":[104],"wide":[106],"variety":[107],"analysis-":[109],"synthesis-type":[111],"regularizers.":[112],"The":[113],"proposed":[114],"approach":[115],"iteratively":[116],"computes":[117],"weighted":[119],"SURE-type":[120],"measures:":[121],"Predicted-SURE":[122,175],"Projected-SURE":[124,177],"(that":[125,134],"knowledge":[127],"noise":[129],"variance":[130],"\u00d02),":[131],"GCV":[133,188],"does":[135],"not":[136],"\u00d02)":[138],"these":[140],"algorithms.":[141,225],"apply":[143],"methods":[145],"image":[147,153,196],"restoration":[148,197],"magnetic":[151],"resonance":[152],"(MRI)":[154],"using":[156],"total":[157],"variation":[158],"(TV)":[159],"an":[161],"analysis-type":[162],".1-regularization.":[163],"demonstrate":[165],"through":[166],"simulations":[167],"experiments":[169],"real":[171],"data":[172],"that":[173,186,192],"minimizing":[174,187],"consistently":[178],"lead":[179],"near-MSE-optimal":[181,194],"reconstructions.":[182],"also":[184],"observed":[185],"yields":[189],"results":[191],"are":[193],"slightly":[199],"suboptimal":[200],"MRI.":[202],"Theoretical":[203],"derivations":[204],"in":[205,216],"this":[206],"work":[207],"related":[208],"evaluations":[212],"be":[214],"extended,":[215],"principle,":[217],"other":[219],"regularizers":[222]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":55},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}