{"id":"https://openalex.org/W4407168895","doi":"https://doi.org/10.1109/tnnls.2025.3534784","title":"Interpretable Optimization-Inspired Deep Network for Off-Grid Frequency Estimation","display_name":"Interpretable Optimization-Inspired Deep Network for Off-Grid Frequency Estimation","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4407168895","doi":"https://doi.org/10.1109/tnnls.2025.3534784","pmid":"https://pubmed.ncbi.nlm.nih.gov/40031778"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2025.3534784","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2025.3534784","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","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/A5047825689","display_name":"Pingping Pan","orcid":"https://orcid.org/0000-0003-1970-1280"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pingping Pan","raw_affiliation_strings":["Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0003-1970-1280","affiliations":[{"raw_affiliation_string":"Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101898321","display_name":"Yunjian Zhang","orcid":"https://orcid.org/0000-0002-0303-3671"},"institutions":[{"id":"https://openalex.org/I4210089559","display_name":"Shenzhen Metro (China)","ror":"https://ror.org/008hpge95","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210089559"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunjian Zhang","raw_affiliation_strings":["Shenzhen Kaihong Digital Industry Development Company Ltd., Shenzhen, China","Shenzhen Kaihong Digital Industry Development Company Ltd, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-0303-3671","affiliations":[{"raw_affiliation_string":"Shenzhen Kaihong Digital Industry Development Company Ltd., Shenzhen, China","institution_ids":["https://openalex.org/I4210089559"]},{"raw_affiliation_string":"Shenzhen Kaihong Digital Industry Development Company Ltd, Shenzhen, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101882153","display_name":"You Li","orcid":"https://orcid.org/0000-0002-2246-9366"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"You Li","raw_affiliation_strings":["Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004300680","display_name":"Yishan Ye","orcid":"https://orcid.org/0000-0003-3706-4959"},"institutions":[{"id":"https://openalex.org/I75867142","display_name":"Xiamen University of Technology","ror":"https://ror.org/01285e189","country_code":"CN","type":"education","lineage":["https://openalex.org/I75867142"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yishan Ye","raw_affiliation_strings":["School of Opto-Electronic and Communication Engineering, Xiamen University of Technology, Xiamen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Opto-Electronic and Communication Engineering, Xiamen University of Technology, Xiamen, China","institution_ids":["https://openalex.org/I75867142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101771291","display_name":"Wei He","orcid":"https://orcid.org/0000-0002-9553-2055"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei He","raw_affiliation_strings":["School of Electronics and Communication Engineering, Sun Yat-sen University, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronics and Communication Engineering, Sun Yat-sen University, Shenzhen, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056459699","display_name":"Yutao Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yutao Zhu","raw_affiliation_strings":["China Branch of BRICS Institute of Future Networks, Shenzhen, China"],"raw_orcid":"https://orcid.org/0009-0009-4361-8517","affiliations":[{"raw_affiliation_string":"China Branch of BRICS Institute of Future Networks, Shenzhen, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101532183","display_name":"Renzhong Guo","orcid":"https://orcid.org/0000-0001-9376-2618"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Renzhong Guo","raw_affiliation_strings":["Research Institute for Smart Cities and the School of Architecture and Urban Planning, Shenzhen University, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Smart Cities and the School of Architecture and Urban Planning, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5211,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.93939838,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"36","issue":"8","first_page":"14816","last_page":"14828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.8920000195503235,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.8920000195503235,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10860","display_name":"Speech and Audio Processing","score":0.885200023651123,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T13717","display_name":"Advanced Algorithms and Applications","score":0.861299991607666,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/computer-science","display_name":"Computer science","score":0.5886709094047546},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.5314582586288452},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5277740955352783},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3908177316188812},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.13970711827278137},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1252320110797882},{"id":"https://openalex.org/keywords/geodesy","display_name":"Geodesy","score":0.08495235443115234}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5886709094047546},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.5314582586288452},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5277740955352783},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3908177316188812},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.13970711827278137},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1252320110797882},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.08495235443115234},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2025.3534784","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2025.3534784","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:40031778","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40031778","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3897941615","display_name":null,"funder_award_id":"2023A1515010717","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1983600173","https://openalex.org/W2028823365","https://openalex.org/W2109163609","https://openalex.org/W2611686980","https://openalex.org/W2752693045","https://openalex.org/W2793623685","https://openalex.org/W2798559986","https://openalex.org/W2887288499","https://openalex.org/W2891589246","https://openalex.org/W2902719825","https://openalex.org/W2962683884","https://openalex.org/W2990598036","https://openalex.org/W3017303452","https://openalex.org/W3047238636","https://openalex.org/W3085691116","https://openalex.org/W3120344529","https://openalex.org/W3121104302","https://openalex.org/W3133902371","https://openalex.org/W3152666233","https://openalex.org/W3158906999","https://openalex.org/W3183777577","https://openalex.org/W3185758670","https://openalex.org/W3194646605","https://openalex.org/W3197273387","https://openalex.org/W3206953857","https://openalex.org/W3211682134","https://openalex.org/W4200635639","https://openalex.org/W4205972622","https://openalex.org/W4210422447","https://openalex.org/W4213084171","https://openalex.org/W4226231528","https://openalex.org/W4285182527","https://openalex.org/W4285293024","https://openalex.org/W4295308136","https://openalex.org/W4313525974","https://openalex.org/W4315473431","https://openalex.org/W4316660723","https://openalex.org/W4320005477","https://openalex.org/W4321843473","https://openalex.org/W4367146972","https://openalex.org/W4367663332","https://openalex.org/W4386523922","https://openalex.org/W4387010757","https://openalex.org/W4387042422","https://openalex.org/W4387146007","https://openalex.org/W4387986635","https://openalex.org/W4388953053","https://openalex.org/W4392251600","https://openalex.org/W4392397506"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"The":[0],"accuracy":[1],"of":[2,12,37,170,183],"on-grid":[3,54,92,132],"frequency":[4,24,55,177],"estimation":[5,25,178],"methods":[6],"suffers":[7],"from":[8],"the":[9,31,41,48,52,60,83,101,108,124,130,148,158,164,174,181,184,191],"quantization":[10],"error":[11],"discrete":[13],"grids.":[14],"In":[15,30,106,127],"this":[16,128],"article,":[17],"a":[18,87,140],"deep":[19],"unfolded":[20],"network":[21,72,77],"for":[22,44,111],"off-grid":[23,57,95,135,176],"is":[26,40,51,62,160,167,186],"proposed,":[27],"dubbed":[28],"OGFreq.":[29],"OGFreq,":[32],"there":[33],"exist":[34],"two":[35],"kinds":[36],"variables.":[38],"One":[39],"batch-oriented":[42],"dictionary":[43,61],"frequency-domain":[45],"transform,":[46],"and":[47,56,76,94,134,194],"other":[49],"one":[50,168],"instance-specific":[53,91,109],"bias.":[58],"As":[59],"required":[63],"to":[64,81,190],"be":[65],"universally":[66],"applicable":[67],"among":[68],"all":[69],"observed":[70],"signals,":[71],"layers":[73],"are":[74,79,97,115,137],"designed":[75],"weights":[78],"updated":[80],"approximate":[82],"transform":[84],"bases":[85],"in":[86,113,139],"data-driven":[88,142],"way.":[89],"Besides,":[90],"frequencies":[93],"biases":[96],"solved":[98],"by":[99,117],"unfolding":[100],"iterative":[102],"soft-threshold":[103,120],"algorithm":[104],"(ISTA).":[105],"addition,":[107],"hyperparameters":[110],"sparsity":[112],"ISTA":[114],"obtained":[116],"an":[118],"encoder-decoder":[119],"(EDS)":[121],"module":[122],"with":[123],"attention":[125],"mechanism.":[126],"way,":[129],"dictionary,":[131],"frequency,":[133],"bias":[136],"learned":[138],"unified":[141],"framework.":[143],"Numerical":[144],"experiments":[145],"show":[146],"that":[147],"OGFreq":[149,185],"obtains":[150],"4%":[151],"lower":[152,172],"false":[153],"negative":[154],"rate":[155],"(FNR)":[156],"when":[157,188],"SNR":[159],"20":[161],"dB.":[162],"Moreover,":[163],"computational":[165],"complexity":[166],"order":[169],"magnitude":[171],"than":[173],"iteration-based":[175],"methods.":[179],"Finally,":[180],"robustness":[182],"discussed":[187],"extended":[189],"impulse":[192],"noise":[193],"damped":[195],"signals.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}