{"id":"https://openalex.org/W4393379784","doi":"https://doi.org/10.1109/tpami.2024.3383532","title":"Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration","display_name":"Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration","publication_year":2024,"publication_date":"2024-04-01","ids":{"openalex":"https://openalex.org/W4393379784","doi":"https://doi.org/10.1109/tpami.2024.3383532","pmid":"https://pubmed.ncbi.nlm.nih.gov/38557620"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2024.3383532","doi":"https://doi.org/10.1109/tpami.2024.3383532","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2024.3383532","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["ccf-a","cwts-core","dongbi-a","doyens","jufo-3","medline","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2312.15701","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107808531","display_name":"Jiahong Fu","orcid":"https://orcid.org/0009-0008-8514-5298","observed_orcids":["https://orcid.org/0009-0008-8514-5298"]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiahong Fu","raw_affiliation_strings":["School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China"],"raw_orcid":"https://orcid.org/0009-0008-8514-5298","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101698775","display_name":"Qi Xie","orcid":"https://orcid.org/0000-0003-0864-5623","observed_orcids":["https://orcid.org/0000-0003-0864-5623"]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Xie","raw_affiliation_strings":["School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China"],"raw_orcid":"https://orcid.org/0000-0003-0864-5623","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091017287","display_name":"Deyu Meng","orcid":"https://orcid.org/0000-0002-1294-8283","observed_orcids":["https://orcid.org/0000-0002-1294-8283","https://orcid.org/0009-0002-0659-827X"]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Deyu Meng","raw_affiliation_strings":["School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China"],"raw_orcid":"https://orcid.org/0000-0002-1294-8283","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":null,"display_name":"Zongben Xu","orcid":"https://orcid.org/0000-0003-1719-3358","observed_orcids":["https://orcid.org/0000-0003-1719-3358"]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zongben Xu","raw_affiliation_strings":["School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China"],"raw_orcid":"https://orcid.org/0000-0003-1719-3358","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":{"value":2495,"currency":"USD","value_usd":2495},"apc_paid":null,"fwci":2.9854,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.92852239,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"46","issue":"10","first_page":"6577","last_page":"6593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.8687000274658203,"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"}},"topics":[{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.8687000274658203,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.08110000193119049,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.02280000038444996,"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/deep-unfolding","display_name":"deep unfolding","score":0.9729999899864197},{"id":"https://openalex.org/keywords/proximal-operator","display_name":"proximal operator","score":0.8220000267028809},{"id":"https://openalex.org/keywords/rotation-equivariance","display_name":"rotation equivariance","score":0.9789999723434448},{"id":"https://openalex.org/keywords/image-restoration","display_name":"image restoration","score":0.7799999713897705},{"id":"https://openalex.org/keywords/blind-super-resolution","display_name":"blind super-resolution","score":0.7820000052452087},{"id":"https://openalex.org/keywords/medical-image-reconstruction","display_name":"medical image reconstruction","score":0.996999979019165},{"id":"https://openalex.org/keywords/interpretability","display_name":"interpretability","score":0.6539999842643738},{"id":"https://openalex.org/keywords/image-priors","display_name":"image priors","score":0.6449999809265137}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.8976022005081177},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7177808284759521},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6974990367889404},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6771819591522217},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.6308181881904602},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5604405999183655},{"id":"https://openalex.org/C193415008","wikidata":"https://www.wikidata.org/wiki/Q639681","display_name":"Network architecture","level":2,"score":0.499981164932251},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4236142635345459},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.42080923914909363},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.41409990191459656},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3825029134750366},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3800693154335022},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32768261432647705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2395819127559662},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tpami.2024.3383532","doi":"https://doi.org/10.1109/tpami.2024.3383532","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2024.3383532","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["ccf-a","cwts-core","dongbi-a","doyens","jufo-3","medline","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:38557620","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38557620","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,"listed_in":[],"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 pattern analysis and machine intelligence","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2312.15701","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.15701","pdf_url":"https://arxiv.org/pdf/2312.15701","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"doi:10.48550/arxiv.2312.15701","doi":"https://doi.org/10.48550/arxiv.2312.15701","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.15701","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2312.15701","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.15701","pdf_url":"https://arxiv.org/pdf/2312.15701","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3834103512","display_name":null,"funder_award_id":"62331028","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4178513135","display_name":null,"funder_award_id":"62206214","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5817505303","display_name":null,"funder_award_id":"62272375","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8021425888","display_name":null,"funder_award_id":"12226004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8698885527","display_name":null,"funder_award_id":"U21A6005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393379784.pdf","grobid_xml":"https://content.openalex.org/works/W4393379784.grobid-xml"},"referenced_works_count":97,"referenced_works":["https://openalex.org/W1533861849","https://openalex.org/W1570089119","https://openalex.org/W1677182931","https://openalex.org/W1791560514","https://openalex.org/W1901129140","https://openalex.org/W1906770428","https://openalex.org/W1919542679","https://openalex.org/W1930824406","https://openalex.org/W1980454827","https://openalex.org/W2021347102","https://openalex.org/W2044810215","https://openalex.org/W2047920195","https://openalex.org/W2056370875","https://openalex.org/W2077646121","https://openalex.org/W2079127706","https://openalex.org/W2087416986","https://openalex.org/W2100556411","https://openalex.org/W2100705753","https://openalex.org/W2103559027","https://openalex.org/W2119290843","https://openalex.org/W2121927366","https://openalex.org/W2130248603","https://openalex.org/W2146842127","https://openalex.org/W2152023291","https://openalex.org/W2154129661","https://openalex.org/W2157285372","https://openalex.org/W2162221686","https://openalex.org/W2172275395","https://openalex.org/W2194775991","https://openalex.org/W2209874411","https://openalex.org/W2257718385","https://openalex.org/W2279221249","https://openalex.org/W2466666260","https://openalex.org/W2508457857","https://openalex.org/W2509784253","https://openalex.org/W2552808051","https://openalex.org/W2569680626","https://openalex.org/W2573726823","https://openalex.org/W2576915720","https://openalex.org/W2604885021","https://openalex.org/W2607406448","https://openalex.org/W2613155248","https://openalex.org/W2624120837","https://openalex.org/W2626454479","https://openalex.org/W2738743584","https://openalex.org/W2739757502","https://openalex.org/W2740982616","https://openalex.org/W2741137940","https://openalex.org/W2753044865","https://openalex.org/W2765202580","https://openalex.org/W2765713907","https://openalex.org/W2769152880","https://openalex.org/W2775397671","https://openalex.org/W2780930362","https://openalex.org/W2784344583","https://openalex.org/W2785397276","https://openalex.org/W2884068670","https://openalex.org/W2895176907","https://openalex.org/W2907946893","https://openalex.org/W2911459672","https://openalex.org/W2912435603","https://openalex.org/W2913360047","https://openalex.org/W2921200302","https://openalex.org/W2930755307","https://openalex.org/W2948149465","https://openalex.org/W2949128855","https://openalex.org/W2962814024","https://openalex.org/W2963299736","https://openalex.org/W2963878020","https://openalex.org/W2963891322","https://openalex.org/W3002619967","https://openalex.org/W3012811655","https://openalex.org/W3034917448","https://openalex.org/W3035250394","https://openalex.org/W3046386147","https://openalex.org/W3048794210","https://openalex.org/W3081639259","https://openalex.org/W3087119976","https://openalex.org/W3092290620","https://openalex.org/W3130644973","https://openalex.org/W3155710154","https://openalex.org/W3157246243","https://openalex.org/W3168684807","https://openalex.org/W3174251322","https://openalex.org/W3187297415","https://openalex.org/W3203107667","https://openalex.org/W3212589799","https://openalex.org/W4225538054","https://openalex.org/W4235713725","https://openalex.org/W4283023197","https://openalex.org/W4285600427","https://openalex.org/W4296057686","https://openalex.org/W4298392935","https://openalex.org/W4313136310","https://openalex.org/W4386083034","https://openalex.org/W6767104088","https://openalex.org/W6842324833"],"related_works":["https://openalex.org/W4308194202","https://openalex.org/W4312908055","https://openalex.org/W2974611604","https://openalex.org/W7220980527","https://openalex.org/W4413144413","https://openalex.org/W4312097312","https://openalex.org/W3180322328","https://openalex.org/W7131319057","https://openalex.org/W3197977908","https://openalex.org/W4221164616"],"abstract_inverted_index":{"The":[0],"deep":[1,23,92,170,197,287],"unfolding":[2,93,171,198,288],"approach":[3],"has":[4,108],"attracted":[5],"significant":[6],"attention":[7],"in":[8,86,147,169,285,301],"computer":[9],"vision":[10,259,303],"tasks,":[11,260],"which":[12,126],"well":[13],"connects":[14],"conventional":[15],"image":[16,84,124,263,266,269],"processing":[17],"modeling":[18],"manners":[19],"with":[20,55,217,250],"more":[21],"recent":[22,113],"learning":[24],"techniques.":[25],"Specifically,":[26],"by":[27,111],"establishing":[28],"a":[29,71,87,96,103,112,162,183,213],"direct":[30],"correspondence":[31],"between":[32],"algorithm":[33],"operators":[34],"at":[35],"each":[36,43],"implementation":[37],"step":[38],"and":[39,239,268,290],"network":[40,53,79,98,188,216,284],"modules":[41],"within":[42],"layer,":[44],"one":[45],"can":[46],"rationally":[47],"construct":[48],"an":[49],"almost":[50],"\"white":[51],"box\"":[52],"architecture":[54,289],"high":[56],"interpretability.":[57],"In":[58,90],"this":[59,175,177],"architecture,":[60,105],"only":[61],"the":[62,66,78,121,128,149,196,204,207,228,245,271,282],"predefined":[63],"component":[64],"of":[65,137,279],"proximal":[67,72,97,142,187,215,283],"operator,":[68],"known":[69],"as":[70,102],"network,":[73],"needs":[74],"manual":[75],"configuration,":[76],"enabling":[77],"to":[80,181,237,276],"automatically":[81],"extract":[82],"intrinsic":[83,251],"priors":[85,194],"data-driven":[88],"manner.":[89],"current":[91,286],"methods,":[94],"such":[95,212,234,248],"is":[99,127,240,274],"generally":[100],"designed":[101,214],"CNN":[104,117],"whose":[106],"necessity":[107],"been":[109],"proven":[110],"theory.":[114],"That":[115],"is,":[116],"structure":[118],"substantially":[119],"delivers":[120],"translational":[122],"symmetry":[123,151,193],"prior,":[125,152],"most":[129,229],"universally":[130],"possessed":[131],"structural":[132,155],"prior":[133,156],"across":[134],"various":[135],"types":[136],"images.":[138,159],"However,":[139],"standard":[140],"CNN-based":[141],"networks":[143,249],"have":[144],"essential":[145],"limitations":[146],"capturing":[148],"rotation":[150,185,192,222],"another":[153],"universal":[154],"underlying":[157],"general":[158,302],"This":[160,224,296],"leaves":[161],"large":[163],"room":[164],"for":[165,203,211,233,243],"further":[166],"performance":[167],"improvement":[168],"approaches.":[172],"To":[173],"address":[174],"issue,":[176],"study":[178],"makes":[179],"efforts":[180],"suggest":[182],"high-accuracy":[184],"equivariant":[186,209],"that":[189],"effectively":[190],"embeds":[191],"into":[195],"framework.":[199],"Especially,":[200],"we":[201],"deduce,":[202],"first":[205],"time,":[206],"theoretical":[208,231],"error":[210,235],"arbitrary":[218,221],"layers":[219],"under":[220],"degrees.":[223],"analysis":[225],"should":[226],"be":[227,277],"refined":[230],"conclusion":[232],"evaluation":[236],"date":[238],"also":[241],"indispensable":[242],"supporting":[244],"rationale":[246],"behind":[247],"interpretability":[252],"requirements.":[253],"Through":[254],"experimental":[255],"validation":[256],"on":[257],"different":[258],"including":[261],"blind":[262],"super-resolution,":[264],"medical":[265],"reconstruction,":[267],"de-raining,":[270],"proposed":[272],"method":[273],"validated":[275],"capable":[278],"directly":[280],"replacing":[281],"readily":[291],"enhancing":[292],"their":[293],"state-of-the-art":[294],"performance.":[295],"indicates":[297],"its":[298],"potential":[299],"usability":[300],"tasks.":[304]},"counts_by_year":[{"year":2026,"cited_by_count":14},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":3}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2024-04-02T00:00:00"}