{"id":"https://openalex.org/W2659961129","doi":"https://doi.org/10.1109/tip.2017.2717182","title":"Nested Conjugate Gradient Algorithm With Nested Preconditioning for Non-Linear Image Restoration","display_name":"Nested Conjugate Gradient Algorithm With Nested Preconditioning for Non-Linear Image Restoration","publication_year":2017,"publication_date":"2017-06-19","ids":{"openalex":"https://openalex.org/W2659961129","doi":"https://doi.org/10.1109/tip.2017.2717182","mag":"2659961129","pmid":"https://pubmed.ncbi.nlm.nih.gov/28641260"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2017.2717182","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2017.2717182","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/A5049659006","display_name":"Deepak G. Skariah","orcid":"https://orcid.org/0000-0002-6687-5446"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Deepak G. Skariah","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024531181","display_name":"Muthuvel Arigovindan","orcid":"https://orcid.org/0000-0003-1967-792X"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Muthuvel Arigovindan","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049659006"],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.9866,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73579975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"9","first_page":"4471","last_page":"4482"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9980999827384949,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9965000152587891,"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.830061674118042},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7931976318359375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6983358860015869},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.605170726776123},{"id":"https://openalex.org/keywords/proximal-gradient-methods-for-learning","display_name":"Proximal gradient methods for learning","score":0.5833792686462402},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5615341663360596},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5582138895988464},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4758074879646301},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4672759771347046},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4623163342475891},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.45604565739631653},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.44650155305862427},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.41747093200683594},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3865499496459961},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3593391180038452},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35557276010513306},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.34664109349250793},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.2545344829559326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1891428828239441},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09566542506217957},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.0870542824268341},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06987747550010681}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.830061674118042},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7931976318359375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6983358860015869},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.605170726776123},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.5833792686462402},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5615341663360596},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5582138895988464},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4758074879646301},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4672759771347046},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4623163342475891},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.45604565739631653},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.44650155305862427},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.41747093200683594},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3865499496459961},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3593391180038452},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35557276010513306},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.34664109349250793},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.2545344829559326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1891428828239441},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09566542506217957},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0870542824268341},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06987747550010681}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2017.2717182","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2017.2717182","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:28641260","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28641260","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::73411","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401429","display_name":"ePrints@IISc (Indian Institute of Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.4300000071525574,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G8469436589","display_name":null,"funder_award_id":"SB/FTP/ETA-240/2013","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W89654658","https://openalex.org/W1972406935","https://openalex.org/W1974751761","https://openalex.org/W1978333359","https://openalex.org/W1981220107","https://openalex.org/W2000462146","https://openalex.org/W2007454648","https://openalex.org/W2016999436","https://openalex.org/W2055834582","https://openalex.org/W2071609006","https://openalex.org/W2076094332","https://openalex.org/W2098841537","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2105910985","https://openalex.org/W2126926806","https://openalex.org/W2137620427","https://openalex.org/W2149414429","https://openalex.org/W2157011125","https://openalex.org/W2162361955","https://openalex.org/W2167849846","https://openalex.org/W2523352299","https://openalex.org/W3003915866","https://openalex.org/W4247591450","https://openalex.org/W4250589301","https://openalex.org/W4293775970","https://openalex.org/W4301014524","https://openalex.org/W6603640814","https://openalex.org/W6674632333","https://openalex.org/W6683700251","https://openalex.org/W6727201239"],"related_works":["https://openalex.org/W2348618647","https://openalex.org/W4319027779","https://openalex.org/W1993524345","https://openalex.org/W2390078254","https://openalex.org/W2364728921","https://openalex.org/W2364021889","https://openalex.org/W2604655597","https://openalex.org/W2947596922","https://openalex.org/W4379882024","https://openalex.org/W4283316574"],"abstract_inverted_index":{"We":[0,83,100],"develop":[1],"a":[2,33,46,90,116],"novel":[3],"optimization":[4],"algorithm,":[5],"which":[6,67],"we":[7],"call":[8],"nested":[9],"non-linear":[10,48],"conjugate":[11,37],"gradient":[12,38],"(CG)":[13],"algorithm":[14,29],"(NNCG),":[15],"for":[16,70,93,112,120],"image":[17],"restoration":[18],"based":[19],"on":[20],"quadratic":[21],"data":[22],"fitting":[23],"and":[24,96,115],"smooth":[25],"non-quadratic":[26],"regularization.":[27],"The":[28,40,63],"is":[30,43,53,61,75],"constructed":[31,44],"as":[32,45],"nesting":[34],"of":[35],"two":[36],"iterations.":[39],"outer":[41,71],"iteration":[42,59],"preconditioned":[47],"CG":[49,58,65,72],"algorithm;":[50],"the":[51,56,86,107],"preconditioning":[52,69],"performed":[54],"by":[55,77],"inner":[57,64],"that":[60,85,103],"linear.":[62],"iteration,":[66,73],"performs":[68],"itself":[74],"accelerated":[76],"an":[78],"another":[79],"FFT-based":[80],"non-iterative":[81],"preconditioner.":[82],"prove":[84],"method":[87,105,110,119],"converges":[88],"to":[89],"stationary":[91],"point":[92],"both":[94],"convex":[95,113],"non-convex":[97,117,121],"regularization":[98,122],"functionals.":[99],"demonstrate":[101],"experimentally":[102],"proposed":[104],"outperforms":[106],"well-known":[108],"majorization-minimization":[109],"used":[111],"regularization,":[114],"inertial-proximal":[118],"functional.":[123]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}